TEST BANK for Business Statistics A First Course 8th Edition by David Levine, Kathryn Szabat, David

TEST BANK for Business Statistics A First Course 8th Edition by David Levine, Kathryn Szabat, David Stephan

TEST BANK GAIL ILLICH

JAMES BALDONE

McLennan Community College

Birmingham Southern College

B USINESS S TATISTICS : A F IRST C OURSE EIGHTH EDITION

David M. Levine Baruch College, City University of New York

Kathryn A. Szabat La Salle University

David F. Stephan Two Bridges Instructional Technology

The author and publisher of this book have used their best efforts in preparing this book. These efforts include the development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs.

Reproduced by Pearson from electronic files supplied by the author.

Copyright © 2020, 2016, 2013 by Pearson Education, Inc. 221 River Street, Hoboken, NJ 07030. All rights reserved.

No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.

ISBN-13: 978-0-13-518241-3 ISBN-10: 0-13-518241-7

Table of Contents First Things First ..............................................................................................................................1 Chapter 1

Defining and Collecting Data ................................................................................. 1-1

Chapter 2

Organizing and Visualizing Variables .................................................................... 2-1

Chapter 3

Numerical Descriptive Measures ............................................................................ 3-1

Chapter 4

Basic Probability ..................................................................................................... 4-1

Chapter 5

Discrete Probability Distributions........................................................................... 5-1

Chapter 6

The Normal Distribution ......................................................................................... 6-1

Chapter 7

Sampling Distributions ........................................................................................... 7-1

Chapter 8

Confidence Interval Estimation .............................................................................. 8-1

Chapter 9

Fundamentals of Hypothesis Testing: One-Sample Tests ...................................... 9-1

Chapter 10

Two-Sample Tests and One-Way ANOVA ......................................................... 10-1

Chapter 11 Chi-Square Tests ................................................................................................... 11-1 Chapter 12 Simple Linear Regression ..................................................................................... 12-1 Chapter 13 Multiple Regression .............................................................................................. 13-1 Chapter 14 Business Analytics ................................................................................................ 14-1 Chapter 15 Statistical Applications in Quality Management (Online) .................................... 15-1

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First Thing First 1

First Things First 1. The process of using data collected from a small group to reach conclusions about a large group is called a) statistical inference. b) DCOVA framework. c) operational definition. d) descriptive statistics.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: inferential statistics 2. Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called a) statistical inference. b) DCOVA framework. c) operational definition. d) descriptive statistics.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: descriptive statistics 3. The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of a) inferential statistics. b) descriptive statistics. c) operational definition. d) DCOVA framework.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: descriptive statistics 4. The estimation of the population average family expenditure on food based on the sample average expenditure of 1,000 families is an example of a) inferential statistics. b) descriptive statistics. c) DCOVA framework. d) operational definition.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: inferential statistics 5. Which of the following is not an element of descriptive statistical problems? a) An inference made about the population based on the sample.

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First Thing First 2 b) The population or sample of interest. c) Tables, graphs, or numerical summary tools. d) Identification of patterns in the data.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: descriptive statistics 6. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the variable of interest in the study. a) The age of an American pine tree in Yosemite National Forest. b) The height of an adult American pine tree in Yosemite National Forest. c) The number of American pine trees in Yosemite National Forest. d) The species of trees in Yosemite National Forest.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: variable 7. Most analysts focus on the cost of tuition as the way to measure the cost of a college education.

But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand University wishes to estimate the textbook costs of first-year students at Drummand. To do so, she monitored the textbook cost of 250 first-year students and found that their average textbook cost was $600 per semester. Identify the variable of interest to the researcher. a) The textbook cost of first-year Drummand University students. b) The year in school of Drummand University students. c) The age of Drummand University students. d) The cost of incidental expenses of Drummand University students.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: variable 8. True or False: Problems may arise when statistically unsophisticated users who do not understand the assumptions behind the statistical procedures or their limitations are misled by results obtained from computer software.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: statistical package 9. True or False: Managers need an understanding of statistics to be able to present and describe information accurately, draw conclusions about large populations based on small samples, improve processes, and make reliable forecasts.

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First Thing First 3 ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: reasons for learning statistics 10. True or False: A professor computed the sample average exam score of 20 students and used it to estimate the average exam score of the 1,500 students taking the exam. This is an example of inferential statistics.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: descriptive statistics, inferential statistics 11. True or False: Using the number of registered voters who turned out to vote for the primary in Iowa to predict the number of registered voters who will turn out to vote in Vermont’s primary is an example of descriptive statistics.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: descriptive statistics, inferential statistics 12. True or False: Compiling the number of registered voters who turned out to vote for the primary in Iowa is an example of descriptive statistics.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: descriptive statistics, inferential statistics 13. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. In this study, methods involving the collection, presentation, and characterization of the data are called _______.

ANSWER: descriptive statistics/methods TYPE: FI DIFFICULTY: Easy KEYWORDS: descriptive statistics

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First Thing First 4 14. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. In this study, methods that result in decisions concerning population characteristics based only on the sample results are called _______.

ANSWER: inferential statistics/methods TYPE: FI DIFFICULTY: Easy KEYWORDS: inferential statistics 15. The oranges grown in corporate farms in an agricultural state were damaged by some unknown fungi a few years ago. Suppose the manager of a large farm wanted to study the impact of the fungi on the orange crops on a daily basis over a 6-week period. On each day a random sample of orange trees was selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated. In this study, drawing conclusions on any one day about the true population characteristics based on information obtained from the sample is called _______.

ANSWER: inferential statistics/methods TYPE: FI DIFFICULTY: Moderate KEYWORDS: inferential statistics 16. The oranges grown in corporate farms in an agricultural state were damaged by some unknown fungi a few years ago. Suppose the manager of a large farm wanted to study the impact of the fungi on the orange crops on a daily basis over a 6-week period. On each day a random sample of orange trees was selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated. In this study, the presentation and characterization of the two main measures calculated each day (i.e., average number of damaged oranges per tree and proportion of trees having damaged oranges) is called _______ .

ANSWER: descriptive statistics/methods TYPE: FI DIFFICULTY: Moderate KEYWORDS: descriptive statistics 17. The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were discharged during 2010. Using the information obtained from the sample to predict population characteristics with respect to malpractice litigation is an example of _______.

ANSWER: inferential statistics TYPE: FI DIFFICULTY: Moderate KEYWORDS: inferential statistics

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First Thing First 5 18. The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were discharged during 2010. The collection, presentation, and characterization of the data from patient medical records are examples of _______.

ANSWER: descriptive statistics/methods TYPE: FI DIFFICULTY: Easy KEYWORDS: descriptive statistics 19. True or False: Business analytics combine “traditional” statistical methods with methods and techniques from management science and information systems to form an interdisciplinary tool that supports fact-based management decision making.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: business analytics 20. Which of the following is not true about business analytics? a) It enables you to use statistical methods to analyze and explore data to uncover unforeseen relationships. b) It enables you to use management science methods to develop optimization models that impact an organization’s strategy, planning, and operations. c) It enables you to use complex mathematics to replace the need for organizational decision making and problem solving. d) It enables you to use information systems methods to collect and process data sets of all sizes.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: business analytics 21. True or False: “Big data” is a concrete concept with a precise operational definition.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: big data 22. True or False: “Big data” are data being collected in huge volumes and at very fast rates, and they typically arrive in a variety of forms, organized and unorganized.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: big data

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First Thing First 6 23. True or False: In the current data-driven environment of business, the decisions you make will be increasingly based on gut or intuition supported by personal experience.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: business analytics 24. True or False: The D in the DCOVA framework stands for “data”.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 25. True or False: The D in the DCOVA framework stands for “define”.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 26. True or False: The C in the DCOVA framework stands for “categorize”.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 27. True or False: The C in the DCOVA framework stands for “collect”.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 28. True or False: The O in the DCOVA framework stands for “operationalize”.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 29. True or False: The O in the DCOVA framework stands for “organize”.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework

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First Thing First 7 30. True or False: The V in the DCOVA framework stands for “verify”.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 31. True or False: The V in the DCOVA framework stands for “visualize”.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 32. True or False: The A in the DCOVA framework stands for “apply”.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 33. True or False: The V in the DCOVA framework stands for “value”.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: DCOVA framework 34. Which of the following is not an attribute of big data? a. Variegated b. Velocity c. Volume d. Variety ANSWER: a TYPE: TF DIFFICULTY: Easy KEYWORDS: business analytics 35. True or False: If rising temperatures are followed immediately by an increase in crime in urban areas, we would attribute the two events to be an instance of logical causality.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Starting points for learning statistics, page 6 text.

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First Thing First 8 36. True or False: Because of its irregular pattern and the fact it must be collected by irregular means, unstructured data is not a type of big data.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: FTF2 Business Analytics: The Changing Face of Statistics, page 4 text.

37. Which of the following types of software can store dashboards? a. Minitab b. Both Minitab and Tableau c. Tableau d. Excel and Minitab ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: business analytics, software 38. Which of the following is not a good practice for using software properly? a. Using preexisting solutions to solve new problems b. Using generic names to identify applications such as Assignment01, Assignment02, etc. c. Always build solutions from scratch. d. b and c ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: business analytics, software

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Defining and Collecting Data

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CHAPTER 1: DEFINING AND COLLECTING DATA 1. Which of the following is a discrete quantitative (numerical) variable? a) The Dow Jones Industrial average b) The volume of water released from a dam c) The distance you drove yesterday. d) The number of employees of an insurance company ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: discrete variable, types of data 2. Which of the following is a continuous quantitative (numerical) variable? a) The color of a student’s eyes b) The number of employees of an insurance company c) The amount of milk in a 2-liter carton. d) The number of gallons of milk sold at the local grocery store yesterday ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: continuous variable, types of data 3. To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot each 30 minutes of a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot each period, then X is an example of a) a categorical variable. b) a discrete variable. c) a continuous variable. d) a statistic.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: discrete variable, types of data

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Defining and Collecting Data 4. Researchers are concerned that the weight of the average American school child is increasing implying, among other things, that children’s clothing should be manufactured and marketed in larger sizes. If X is the weight of school children sampled in a nationwide study without rounding, then X is an example of a) a categorical variable. b) a discrete variable. c) a continuous variable. d) a table of random numbers.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: continuous variable, types of data 5. The classification of student class designation (freshman, sophomore, junior, senior) is an example of a) a categorical variable. b) a discrete variable. c) a continuous variable. d) a table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 6. The classification of student major (accounting, economics, management, marketing, other) is an example of a) a categorical variable. b) a discrete variable. c) a continuous variable. d) a table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data

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Defining and Collecting Data

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7. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The answer on “whether you visited campus bars on the weekend before the final exam week” from students in the sample is an example of __________. a) a categorical variable. b) a discrete variable. c) a continuous variable. d) a table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data SCENARIO 1-1 The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products.

8. Referring to Scenario 1-1, the possible responses to the question "How many Blu-ray players made by other manufacturers have you used?" are values from a a) discrete variable. b) continuous variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: discrete variable, types of data 9. Referring to Scenario 1-1, the possible responses to the question "Are you happy, indifferent, or unhappy with the performance per dollar spent on the Blu-ray player?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data

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Defining and Collecting Data 10. Referring to Scenario 1-1, the possible responses to the question "What is your annual income rounded to the nearest thousands?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: discrete variable, types of data EXPLANATION: Even though money is usually considered as a continuous variable, it should be considered as a discrete variable when rounded to the nearest thousands.

11. Referring to Scenario 1-1, the possible responses to the question "How much time do you use the Blu-ray player every week on the average?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: continuous variable, types of data 12. Referring to Scenario 1-1, the possible responses to the question "How many people are there in your household?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: discrete variable, types of data 13. Referring to Scenario 1-1, the possible responses to the question "How would you rate the quality of your purchase experience with 1 = excellent, 2 = good, 3 = decent, 4 = poor, 5 = terrible?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data

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Defining and Collecting Data

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14. Referring to Scenario 1-1, the possible responses to the question "What brand of Blu-ray player did you purchase?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 15. Referring to Scenario 1-1, the possible responses to the question "Out of a 100-point score with 100 being the highest and 0 being the lowest, what is your satisfaction level on the videocassette recorder that you purchased?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: discrete variable, types of data 16. Referring to Scenario 1-1, the possible responses to the question "In which year were you born?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: discrete variable, types of data 17. Referring to Scenario 1-1, the possible responses to the question "How many Blu-ray players made by other manufacturers have you used? “results in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: ratio scale, types of data

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Defining and Collecting Data 18. Referring to Scenario 1-1, the possible responses to the question "Are you happy, indifferent, or unhappy with the performance per dollar spent on the Blu-ray player?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: ordinal scale, types of data 19. Referring to Scenario 1-1, the possible responses to the question "What is your annual income rounded to the nearest thousands?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: ratio scale, types of data 20. Referring to Scenario 1-1, the possible responses to the question "How much time do you use the Blu-ray player every week on the average?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: ratio scale, types of data 21. Referring to Scenario 1-1, the possible responses to the question "How many people are there in your household?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: ratio scale, types of data

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Defining and Collecting Data

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22. Referring to Scenario 1-1, the possible responses to the question "How would you rate the quality of your purchase experience with 1 = excellent, 2 = good, 3 = decent, 4 = poor, 5 = terrible?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: b TYPE: MC DIFFICULTY: Moderate EXPLANATION: The rating is ordinal scale not an interval scale because the difference in rating between “excellent” and “good” does not have to be the same as the difference between “poor” and “terrible”.

KEYWORDS: ordinal scale, types of data 23. Referring to Scenario 1-1, the possible responses to the question "What brand of Blu-ray player did you purchase?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: nominal scale, types of data 24. Referring to Scenario 1-1, the possible responses to the question "Out of a 100-point score with 100 being the highest and 0 being the lowest, what is your satisfaction level with the Blu-ray player that you purchased results in: a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: c TYPE: MC DIFFICULTY: Difficult EXPLANATION: The rating is interval scale not ordinal scale because the difference in rating between “80” and “90” can be treated as the same as the difference between “30” and “40” but a rating of “80” does not imply twice the level of satisfaction level as a rating of “40”.

KEYWORDS: interval scale, types of data

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Defining and Collecting Data 25. Referring to Scenario 1-1, the possible responses to the question "What is your age at last birthday ?” results in: a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: d- A 40-year-old is twice as old as a 20-year-old TYPE: MC DIFFICULTY: Difficult KEYWORDS: interval scale, types of data 26. True or False: The possible responses to the question “How long have you been living at your current residence?” are values from a continuous variable.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: continuous variable, types of data 27. True or False: The possible responses to the question “How many times in the past three months have you visited a city park?” are values from a discrete variable.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: discrete variable, types of data 28. True or False: A continuous variable may take on any value within its relevant range even though the measurement device may not be precise enough to record it.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: continuous variable, types of data 29. True or False: Faculty rank (professor to lecturer) is an example of discrete numerical data.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 30. True or False: Student grades (A to F) are an example of continuous numerical data.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: categorical variables, types of data

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Defining and Collecting Data

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31. True or False: The amount of coffee consumed by an individual in a day is an example of a discrete numerical variable.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: continuous variables, types of data 32. True or False: The answer to the question “What is your favorite color?” is an example of an ordinal scaled variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale 33. True or False: The answer to the question “How do you rate the quality of your business statistics course” is an example of an ordinal scaled variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ordinal scale 34. True or False: The answer to the question “How many hours on average do you spend watching TV every week?” is an example of a ratio scaled variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ratio scale 35. True or False: The answer to the question “What is your sleeping bag temperature rating?” is an example of a ratio scaled variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interval scale 36. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. The number of claims a person has made in the last 3 years is an example of a _______ numerical variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete variable, types of data

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1-10 Defining and Collecting Data 37. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. The distance a person drives in a year is an example of a _______ variable.

ANSWER: continuous TYPE: FI DIFFICULTY: Easy KEYWORDS: continuous variable, types of data 38. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A person's age is an example of a _______ numerical variable.

ANSWER: continuous TYPE: FI DIFFICULTY: Easy KEYWORDS: continuous variable, types of data 39. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. How long a person has been a licensed driver is an example of a _______ numerical variable.

ANSWER: continuous TYPE: FI DIFFICULTY: Moderate KEYWORDS: continuous variable, types of data 40. An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. The number of tickets a person has received in the last 3 years is an example of a _______ numerical variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete variable, types of data 41. In purchasing an automobile, there are several variables to consider. The body style of the car (sedan, coupe, wagon, etc.) is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data

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Defining and Collecting Data

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42. In purchasing an automobile, there are several variables to consider. The classification of the car as a subcompact, compact, standard, or luxury size is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 43. In purchasing an automobile, there are several variables to consider. The color of the car is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 44. Most colleges admit students based on their achievements in several different areas. Whether a student has taken any advanced placement courses is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 45. Most colleges admit students based on their achievements in several different areas. The grade obtained in senior level English. (A, B, C, D, or F) is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Moderate KEYWORDS: categorical variable, types of data 46. Most colleges admit students based on their achievements in several different areas. The total SAT score achieved by a student is an example of a _______ numerical variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Moderate KEYWORDS: discrete variable, types of data 47. The Dean of Students conducted a survey on campus. The gender of the student is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data

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1-12 Defining and Collecting Data 48. The Dean of Students conducted a survey on campus. Class designation (Freshman, Sophomore, Junior, Senior) is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 49. The Dean of Students conducted a survey on campus. Major area of study is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 50. The Dean of Students conducted a survey on campus. SAT score in mathematics is an example of a _______ numerical variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: continuous variable, types of data 51. The Dean of Students conducted a survey on campus. Grade point average (GPA) is an example of a _______ numerical variable.

ANSWER: continuous TYPE: FI DIFFICULTY: Easy KEYWORDS: continuous variable, types of data 52. The Dean of Students conducted a survey on campus. Number of credits currently enrolled for is an example of a _______ numerical variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete variable, types of data 53. The Dean of Students conducted a survey on campus. Number of clubs, groups, teams, and organizations affiliated with on campus is an example of a _______ numerical variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete variable, types of data

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54. A personal computer user survey was conducted. Computer brand primarily used is an example of a _______ variable.

ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 55. A personal computer user survey was conducted. Number of personal computers owned is an example of a _______ numerical variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Easy KEYWORDS: discrete variable, types of data 56. A personal computer user survey was conducted. The number of years using a personal computer is an example of a _______ numerical variable.

ANSWER: continuous TYPE: FI DIFFICULTY: Moderate KEYWORDS: continuous variable, types of data 57. A personal computer user survey was conducted. Hours of personal computer use per week is an example of a _______ numerical variable ANSWER: continuous TYPE: FI DIFFICULTY: Moderate KEYWORDS: continuous variable, types of data 58. A personal computer user survey was conducted. Primary word processing package used is an example of a _______ variable ANSWER: categorical TYPE: FI DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 59. A personal computer user survey was conducted. The number of computer magazine subscriptions is an example of a _______ numerical variable.

ANSWER: discrete TYPE: FI DIFFICULTY: Moderate KEYWORDS: discrete variable, types of data

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1-14 Defining and Collecting Data 60. The brand of TV one owns is an example of an ordinal scaled variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale, ordinal scale 61. The brand of TV one owns is an example of a numerical variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical variable 62. Whether the university is private, or public is an example of a nominal scaled variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale 63. Whether the university is private, or public is an example of a categorical variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical variable 64. Marital status is an example of an ordinal scaled variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale, ordinal scale 65. Marital status is an example of a numerical variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical variable 66. The grade level (K-12) of a student is an example of a nominal scaled variable.

ANSWER: True- Nominal scale is used just to identify the grade level as would be as a vehicle identification number. No subjective value is imputed.

TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale, ordinal scale

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67. The grade level (K-12) of a student is an example of a numerical variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical variable 68. The level of satisfaction (“Very unsatisfied”, “Fairly unsatisfied”, “Fairly satisfied”, and “Very satisfied”) in a class is an example of an ordinal scaled variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ordinal scale 69. The level of satisfaction (“Very unsatisfied”, “Fairly unsatisfied”, “Fairly satisfied”, and “Very satisfied”) in a class is an example of a categorical variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical variable 70. The quality (“terrible”, “poor”, “fair”, “acceptable”, “very good” and “excellent”) of a day care center is an example of a nominal scaled variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nominal scale, ordinal scale 71. The quality (“terrible”, “poor”, “fair”, “acceptable”, “very good” and “excellent”) of a day care center is an example of a numerical variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: categorical variable 72. The amount of alcohol consumed by a person per week will be measured on an interval scale.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interval scale, ratio scale

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1-16 Defining and Collecting Data 73. The amount of alcohol consumed by a person per week is an example of a continuous variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: continuous variable 74. The number of defective apples in a single box will be measured on an interval scale.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interval scale, ratio scale 75. The number of defective apples in a single box is an example of a continuous variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: discrete variable, continuous variable 76. The number of calories contained in a 12-ounce package of cheese will be measured on a ratio scale.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ratio scale 77. The number of calories contained in a 12-ounce package of cheese is an example of a discrete variable.

ANSWER: True- Calories are measured in whole numbers TYPE: TF DIFFICULTY: Easy KEYWORDS: discrete variable, continuous variable 78. The amount of time a student spent studying for an exam will be measured on a ratio scale.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ratio scale 79. The amount of time a student spent studying for an exam is an example of a continuous variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: continuous variable

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SCENARIO 1-2 A Wall Street Journal poll asked 2,150 adults in the U.S. a series of questions to find out their view on the U.S. economy.

80. Referring to Scenario 1-2, the population of interest is a) all the males living in the U.S. when the polled was taken. b) all the females living in the U.S. when the polled was taken. c) all the adults living in the U.S. when the poll was taken. d) all the people living in the U.S. when the poll was taken.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: population 81. Referring to Scenario 1-2, the 2,150 adults make up a) the population b) the sample c) the primary data source d) the secondary data source ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sample 82. Referring to Scenario 1-2, the possible responses to the question "How satisfied are you with the U.S. economy today with 1 = very satisfied, 2 = moderately satisfied, 3 = neutral, 4 = moderately dissatisfied and 5 = very dissatisfied?” are values from a a) discrete variable. b) continuous variable. c) categorical variable. d) table of random numbers.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 83. Referring to Scenario 1-2, the possible responses to the question "How many people in your household are unemployed currently?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: discrete variable, types of data

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1-18 Defining and Collecting Data 84. Referring to Scenario 1-2, the possible responses to the question "What do you think is the current number of people unemployed in the country?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: discrete variable, types of data 85. Referring to Scenario 1-2, the possible responses to the question "How many more months do you think the U.S. economy will require to get out of a recession?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: discrete variable, types of data 86. Referring to Scenario 1-2, the possible responses to the question "How many out of every 10 U.S. voters do you think feel that the U.S. economy is in a good shape?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy EXPLANATION: The percentage of voters is the ratio of two discrete variables and, hence, the ratio is also a discrete variable.

KEYWORDS: discrete variable, types of data 87. Referring to Scenario 1-2, the possible responses to the question "How would you rate the condition of the U.S. economy with 1 = excellent, 2 = good, 3 = decent, 4 = poor, 5 = terrible?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data

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88. Referring to Scenario 1-2, the possible responses to the question "Are you 1. Currently employed, 2. Unemployed but actively looking for job, 3. Unemployed and quit looking for job?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: categorical variable, types of data 89. Referring to Scenario 1-2, the possible responses to the question "In which year do you think the last recession in the U.S. started?" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: discrete variable, types of data 90. Referring to Scenario 1-2, the possible responses to the question "On the scale of 1 to 100 with 1 being extremely anxious and 100 being total not anxious, rate your level of anxiety in this U.S. economy" are values from a a) discrete numerical variable. b) continuous numerical variable. c) categorical variable. d) table of random numbers.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: discrete variable, types of data 91. Referring to Scenario 1-2, the possible responses to the question "How satisfied are you with the U.S. economy today with 1 = very satisfied, 2 = moderately satisfied, 3 = neutral, 4 = moderately dissatisfied and 5 = very dissatisfied?” result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: ratio scale, types of data

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1-20 Defining and Collecting Data 92. Referring to Scenario 1-2, the possible responses to the question "How many people in your household are unemployed currently?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: ordinal scale, types of data 93. Referring to Scenario 1-2, the possible responses to the question "What do you think is the current unemployment rate?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: ratio scale, types of data 94. Referring to Scenario 1-2, the possible responses to the question "How many out of every 10 U.S. voters do you think feel that the U.S. economy is in a good shape?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: ratio scale, types of data 95. Referring to Scenario 1-2, the possible responses to the question "How would you rate the condition of the U.S. economy with 1 = excellent, 2 = good, 3 = decent, 4 = poor, 5 = terrible?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: ordinal scale, types of data

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96. Referring to Scenario 1-2, the possible responses to the question "Are you 1. Currently employed, 2. Unemployed but actively looking for job, 3. Unemployed and quit looking for job?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: nominal scale, types of data 97. Referring to Scenario 1-2, the possible responses to the question "In which year do you think the last recession in the U.S. started?" result in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: interval scale, types of data EXPLANATION: The calendar year does not have a true zero and, hence, is an interval scale variable.

98. Referring to Scenario 1-2, the possible responses to the question "On the scale of 1 to 100 with 1 being extremely anxious and 100 being totally not anxious, rate your level of anxiety in this U.S. economy?" results in a) a nominal scale variable. b) an ordinal scale variable. c) an interval scale variable. d) a ratio scale variable.

ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: ordinal scale, types of data 99. The universe or "totality of items or things" under consideration is called a) a sample. b) a population. c) a primary data source. d) a secondary data source.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: population

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1-22 Defining and Collecting Data 100. The portion of the universe that has been selected for analysis is called a) a sample. b) a frame. c) a primary data source. d) a secondary data source.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sample 101. Which of the following is most likely a population as opposed to a sample? a) respondents to a newspaper survey. b) the first 5 students completing an assignment. c) every third person to arrive at the bank. d) registered voters in a county.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: population, sample 102. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled. a) The 250 randomly selected adult American pine trees. b) The 25,000 adult American pine trees in the forest. c) All the adult American pine trees taller than 60 feet. d) All American pine trees, of any age, in the forest.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: population, sample 103. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the sample in the study. a) The 250 randomly selected adult American pine trees. b) The 25,000 adult American pine trees in the forest. c) All the adult American pine trees taller than 60 feet. d) All American pine trees, of any age, in the forest.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: population, sample

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104. Most analysts focus on the cost of tuition as the way to measure the cost of a college education.

But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand University wishes to estimate the textbook costs of first-year students at Drummand. To do so, she monitored the textbook cost of 250 first-year students and found that their average textbook cost was $600 per semester. Identify the population of interest to the researcher. a) All Drummand University students. b) All college students. c) All first-year Drummand University students. d) The 250 students that were monitored.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: population, sample 105. Most analysts focus on the cost of tuition as the way to measure the cost of a college education.

But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand University wishes to estimate the textbook costs of first-year students at Drummand. To do so, she monitored the textbook cost of 250 first-year students and found that their average textbook cost was $600 per semester. Identify the sample in the study. a) All Drummand University students. b) All college students. c) All first-year Drummand University students. d) The 250 students that were monitored.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: population, sample 106. Researchers suspect that the average number of units earned per semester by college students is rising. A researcher at Calendula College wishes to estimate the number of units earned by students during the spring semester at Calendula. To do so, he randomly selects 100 student transcripts and records the number of units each student earned in the spring term. He found that the average number of semester units completed was 12.96 units per student. Identify the population of interest to the researcher. a) All Calendula College students. b) All college students. c) All Calendula College students enrolled in the spring. d) All college students enrolled in the spring.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: population, sample

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1-24 Defining and Collecting Data 107. The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. The population of interest is a) all the customers who have bought a Blu-ray player made by the company over the past 12 months. b) all the customers who have bought a Blu-ray player made by the company and brought it in for repair over the past 12 months. c) all the customers who have used a Blu-ray player over the past 12 months. d) all the customers who have ever bought a Blu-ray player made by the company.

ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: population 108. True or False: A population is the totality of items or things under consideration.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: population 109. True or False: A sample is the portion of the universe that is selected for analysis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sample 110. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers to study their preferences for the various components of a potential package. All the employees in the corporation constitute the _______.

ANSWER: population TYPE: FI DIFFICULTY: Easy KEYWORDS: population 111. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers to study their preferences for the various components of a potential package. The 500 employees who will participate in this study constitute the _______.

ANSWER: sample TYPE: FI DIFFICULTY: Easy KEYWORDS: sample

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112. A summary measure that is computed to describe a characteristic from only a sample of the population is called a) an ordered array. b) a summary table. c) a statistic. d) a parameter.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: statistic 113. A summary measure that is computed to describe a characteristic of an entire population is called a) a parameter. b) an ordered array. c) a statistic. d) a summary table.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: parameter 114. Which of the following is most likely a parameter as opposed to a statistic? a) The average score of the first five students completing an assignment. b) The proportion of females registered to vote in a county. c) The average height of people randomly selected from a database. d) The proportion of trucks stopped yesterday that were cited for bad brakes.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: parameter, statistic 115. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students and computed the portion of students in the sample who visited campus bars on the weekend before the final exam. The portion of all students at her university who visited campus bars on the weekend before the final exam week is an example of a) a categorical variable. b) a discrete variable. c) a parameter. d) a statistic.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: parameter

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1-26 Defining and Collecting Data 116. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The portion of students in the sample who visited campus bars on the weekend before the final exam week is an example of __________. a) a summary table. b) a categorical variable. c) a parameter. d) a statistic ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: statistic 117. True or False: A statistic is usually used to provide an estimate for a usually unobserved parameter.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: statistic, parameter, inferential statistics 118. True or False: A statistic is usually unobservable while a parameter is usually observable.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: statistic, parameter, inferential statistic 119. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. The Director will use the data from the sample to compute _______.

ANSWER: statistics TYPE: FI DIFFICULTY: Easy KEYWORDS: statistic 120. The Human Resources Director of a large corporation wishes to develop an employee benefits package and decides to select 500 employees from a list of all (N = 40,000) workers in order to study their preferences for the various components of a potential package. Information obtained from the sample will be used to draw conclusions about the true population _______.

ANSWER: parameters TYPE: FI DIFFICULTY: Easy KEYWORDS: parameter

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121. The oranges grown in corporate farms in an agricultural state were damaged by some unknown fungi a few years ago. Suppose the manager of a large farm wanted to study the impact of the fungi on the orange crops daily over a 6-week period. On each day a random sample of orange trees was selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated. The two main measures calculated each day (i.e., average number of damaged oranges per tree and proportion of trees having damaged oranges) are called _______.

ANSWER: statistics TYPE: FI DIFFICULTY: Moderate KEYWORDS: statistic 122. The oranges grown in corporate farms in an agricultural state were damaged by some unknown fungi a few years ago. Suppose the manager of a large farm wanted to study the impact of the fungi on the orange crops daily over a 6-week period. On each day a random sample of orange trees was selected from within a random sample of acres. The daily average number of damaged oranges per tree and the proportion of trees having damaged oranges were calculated. The two main measures calculated each day (i.e., average number of damaged oranges per tree and proportion of trees having damaged oranges) may be used daily to estimate the respective true population _______.

ANSWER: parameters TYPE: FI DIFFICULTY: Easy KEYWORDS: parameters 123. The Quality Assurance Department of a large urban hospital is attempting to monitor and evaluate patient satisfaction with hospital services. Prior to discharge, a random sample of patients is asked to fill out a questionnaire to rate such services as medical care, nursing, therapy, laboratory, food, and cleaning. The Quality Assurance Department prepares weekly reports that are presented at the Board of Directors meetings and extraordinary/atypical ratings are easy to flag. Values computed from the sample results each week are called _______.

ANSWER: statistics TYPE: FI DIFFICULTY: Easy KEYWORDS: statistic 124. The Quality Assurance Department of a large urban hospital is attempting to monitor and evaluate patient satisfaction with hospital services. Prior to discharge, a random sample of patients is asked to fill out a questionnaire to rate such services as medical care, nursing, therapy, laboratory, food, and cleaning. The Quality Assurance Department prepares weekly reports that are presented at the Board of Directors meetings and extraordinary/atypical ratings are easy to flag. True population characteristics estimated from the sample results each week are called _______.

ANSWER: parameters TYPE: FI DIFFICULTY: Easy KEYWORDS: parameter

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1-28 Defining and Collecting Data 125. The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were discharged during 2010. The proportion of malpractice claims filed from the sample of 31 thousand patients is a _______.

ANSWER: statistic TYPE: FI DIFFICULTY: Moderate KEYWORDS: statistic 126. The Commissioner of Health in New York State wanted to study malpractice litigation in New York. A sample of 31 thousand medical records was drawn from a population of 2.7 million patients who were discharged during 2010. The true proportion of malpractice claims filed from the population of 2.7 million patients is a _______.

ANSWER: parameter TYPE: FI DIFFICULTY: Easy KEYWORDS: parameter 127. Jared was working on a project to look at global warming and accessed an Internet site where he captured average global surface temperatures from 1866. Which of the four methods of data collection was he using? a) Published sources b) Experimentation c) Surveying d) Observation ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 128. The British Airways Internet site provides a questionnaire instrument that can be answered electronically. Which of the 4 methods of data collection is involved when people complete the questionnaire? a) Published sources b) Experimentation c) Surveying d) Observation ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data

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129. A marketing research firm, in conducting a comparative taste test, provided three types of peanut butter to a sample of households randomly selected within the state. Which of the 4 methods of data collection is involved when people are asked to compare the three types of peanut butter? a) Published sources b) Experimentation c) Surveying d) Observation ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 130. Tim was planning for a meeting with his boss to discuss a raise in his annual salary. In preparation, he wanted to use the Consumer Price Index to determine the percentage increase in his real (inflation-adjusted) salary over the last three years. Which of the 4 methods of data collection was involved when he used the Consumer Price Index? a) Published sources b) Experimentation c) Surveying d) Observation ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 131. Which of the 4 methods of data collection is involved when a person counts the number of cars passing designated locations on the Los Angeles freeway system? a) Published sources b) Experimentation c) Surveying d) Observation ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: sources of data 132. A statistics student found a reference in the campus library that contained the median family incomes for all 50 states. She would report her data as being collected using a) a designed experiment. b) observational data. c) a random sample. d) a published source.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data

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1-30 Defining and Collecting Data 133. The personnel director at a large company studied the eating habits of the company’s employees. The director noted whether employees brought their own lunches to work, ate at the company cafeteria, or went out to lunch. The goal of the study was to improve the food service at the company cafeteria. This type of data collection would best be considered as a) an observational study. b) a designed experiment. c) a random sample. d) a quota sample.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 134. A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the beaches from environmental disasters. Twenty-five hundred Florida residents were surveyed. What type of data collection procedure was most likely used to collect the data for this study? a) A designed experiment b) A published source c) A random sample d) Observational data ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: sources of data 135. Which of the following is NOT a reason for the need for sampling? a) It is usually too costly to study the whole population. b) It is usually too time consuming to look at the whole population. c) It is sometimes destructive to observe the entire population. d) It is always more informative by investigating a sample than the entire population.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: reasons for sampling 136. Which of the following is NOT a reason for selecting a sample? a) A sample is less time consuming than a census. b) A sample is less costly to administer than a census. c) A sample is usually not a good representation of the target population. d) A sample is less cumbersome and more practical to administer.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: reasons for sampling

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137. Which of the following sampling methods is a probability sample? a) Convenience sample b) Quota sample c) Stratified sample d) Judgment sample ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: probability sample 138. At US Data Corporation’s web site, they advertised that “Because of our commitment to quality and our vast amount of industry knowledge and experience, we have grown to be one of America’s leading providers of mailing lists, marketing data, sales leads and research data. We maintain databases of information on consumers and businesses nationwide that set industry standards for mission critical currency, reliability and accuracy.” Trying to reach 500 potential donors for their annual phone donation campaign, a local fire department purchased a list of donors from the company. This list is an example of a a) stratified sample b) systematic sample c) judgment sample d) frame ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: frame 139. The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. Which of the following will be a good frame for drawing a sample? a) Telephone directory. b) Voting registry. c) The list of customers who returned the registration card. d) A list of potential customers purchased from a database marketing company.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: frame

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1-32 Defining and Collecting Data 140. A sample of 300 subscribers to a magazine is selected from a population frame of 9,000 subscribers. If, upon examining the data, it is determined that no subscriber had been selected in the sample more than once, a) the sample could not have been random. b) the sample may have been selected without replacement or with replacement. c) the sample had to have been selected with replacement. d) the sample had to have been selected without replacement.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling method, sampling with replacement, sampling without replacement 141. Which of the following scenarios will yield a nonprobability sample? a) The subjects of the sample are chosen based on known probability. b) Items or individuals are chosen without regard to their probability of occurrence. c) Every individual or item from the frame has an equal chance of being selected. Selection may be with replacement or without replacement. d) Decide on a sample size, n; divide the frame of N individuals into groups of k individuals where k = N/n; randomly select one individual from the first group; select every kth individual thereafter.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, nonprobability sample, sampling with replacement, sampling without replacement 142. To obtain a sample of 10 books in the store, the manager walked to the first shelf next to the cash register to pick the first 10 books on that shelf. This is an example of a a) systematic sample b) simple random sample c) stratified sample d) convenience sample ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, nonprobability sample, convenience sample

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143. To demonstrate a sampling method, the instructor in a class picked the first 5 students sitting in the last row of the class. This is an example of a a) systematic sample b) simple random sample c) stratified sample d) convenience sample ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, nonprobability sample, convenience sample 144. A company selling apparel online sends out emails every Monday to all its customers who made a purchase. This is an example of a a) systematic sample b) convenience sample c) simple random sample d) stratified sample ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, nonprobability sample, convenience sample 145. To gather information on the preferences of instructors at universities on topics for a business statistics textbook that it will publish, a publishing company invited 10 faculty members who have adopted one of the textbooks that it has published. This is an example of a a) systematic sample b) judgment sample c) simple random sample d) stratified sample ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, nonprobability sample, judgment sample 146. To find out the potential impact of a new zoning law on a neighborhood, the legislators conduct a focus group interview by inviting the members of the housing owner’s association of that neighborhood. This is an example of a a) systematic sample b) simple random sample c) judgment sample d) cluster sample ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, nonprobability sample, judgment sample

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1-34 Defining and Collecting Data 147. Which of the following yields a systematic sample? a) All students in a class are divided into groups of 15. One student is randomly chosen from the 1st group, the remaining observations are every 15th student thereafter. b) The best 15 students, according to the opinion of the instructor, in a class are selected. c) All students in a class are grouped according to their gender. A random sample of 8 is selected from the males and a separate random sample of 7 is drawn from the females. d) A random sample of 15 students is selected from a class without replacement.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, probability sample, systematic sample 148. Which of the following yields a stratified sample? a) All students in a class are divided into groups of 15. One student is randomly chosen from the 1st group, the remaining observations are every 15th student thereafter. b) The best 15 students, according to the opinion of the instructor, in a class are selected. c) All students in a class are grouped according to their gender. A random sample of 8 is selected from the males and a separate random sample of 7 is drawn from the females. d) The first 15 students in a class are selected without replacement.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, probability sample, stratified sample 149. Which of the following yields a cluster sample? a) All students in a class are divided into groups of 15. One student is randomly chosen from the 1st group, the remaining observations are every 15th student thereafter. b) The best 15 students, according to the opinion of the instructor, in a class are selected. c) All students in a class are grouped according to their gender. A random sample of 8 is selected from the males and a separate random sample of 7 is selected from the females. d) All students in a class are divided into groups according to the rows that they are seated.

One of the groups is randomly selected.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, probability sample, cluster sample

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150. Which of the following yields a simple random sample? a) All students in a class are divided into groups of 15. One student is randomly chosen from the 1st group, the remaining observations are every 15th student thereafter. b) The best 15 students, according to the opinion of the instructor, in a class are selected. c) The names of 50 students in a class are written on 50 different pieces of paper and put in a hat. The first 15 pieces of paper are selected blindly one at a time without replacing them back in the hat after shuffling the papers thoroughly. d) All students in a class are divided into groups according to the rows that they are seated.

One of the groups is randomly selected.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, probability sample, simple random sample 151. Which of the following yields a simple random sample? a) All students in a class are grouped according to their gender. A random sample of 8 is selected from the males and a separate random sample of 7 is drawn from the females. b) The best 15 students, according to the opinion of the instructor, in a class are selected. c) The names of 50 students in a class are written on 50 different pieces of paper and put in a hat. The first 15 pieces of paper are selected blindly one at a time after shuffling the papers thoroughly and each of the selected pieces is placed back into the hat before the next piece is selected. d) All students in a class are divided into groups according to the rows that they are seated.

One of the groups is randomly selected.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling method, probability sample, simple random sample 152. For a population frame containing N = 1,007 individuals, what code number should you assign to the first person on the list to use a table of random numbers? a) 0 b) 1 c) 01 d) 0001 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: random number

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1-36 Defining and Collecting Data 153. Which of the following types of samples can you use if you want to make valid statistical inferences from a sample to a population? a) A judgment sample b) A quota sample c) A convenience sample d) A probability sample ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: probability sample, sampling method 154. The evening host of a dinner dance reached into a bowl, mixed all the tickets around, and selected the ticket to award the grand door prize. What sampling method was used? a) Simple random sample b) Systematic sample c) Stratified sample d) Cluster sample ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: simple random sample, probability sample, sampling method 155. The Dean of Students mailed a survey to a total of 400 students. The sample included 100 students randomly selected from each of the freshman, sophomore, junior, and senior classes on campus last term. What sampling method was used? a) Simple random sample b) Systematic sample c) Stratified sample d) Cluster sample ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: stratified sample, probability sample, sampling method 156. A telemarketer set the company’s computerized dialing system to contact every 25th person listed in the local telephone directory. What sampling method was used? a) Simple random sample b) Systematic sample c) Stratified sample d) Cluster sample ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: systematic sample, probability sample, sampling method

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157. Since a _______ is not a randomly selected probability sample, there is no way to know how well it represents the overall population. a) Simple random sample b) Convenience sample c) Stratified sample d) Cluster sample ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: convenience sample, nonprobability sample, sampling method 158. A population frame for a survey contains a listing of 72,345 names. Using a table of random numbers, how many digits will the code numbers for each member of your population contain? a) 3 b) 4 c) 5 d) 6 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: random number 159. A population frame for a survey contains a listing of 6,179 names. Using a table of random numbers, which of the following code numbers will appear on your list? a) 06 b) 0694 c) 6946 d) 61790 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: random number 160. Which of the following can be reduced by proper interviewer training? a) Sampling error b) Measurement error c) Both above d) None of the above ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: measurement error, survey worthiness

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1-38 Defining and Collecting Data 161. Which of the following sampling methods will more likely be susceptible to ethical violation? a) Simple random sample b) Cluster sample c) Convenience sample d) Stratified sample ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: ethical issues, sampling method 162. Which of the following sampling methods will more likely be susceptible to ethical violation when used to form conclusions about the entire population? a) Simple random sample b) Cluster sample c) Judgment sample d) Stratified sample ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: judgment sample, ethical issues, sampling method 163. Which of the following sampling methods will more likely be susceptible to ethical violation when used to form conclusions about the entire population? a) Simple random sample b) Cluster sample c) Systematic sample d) Convenience sample ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: convenience sample, ethical issues, sampling method 164. True or False: As a population becomes large, it is usually better to obtain statistical information from the entire population.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: population, sample, reasons for samplings 165. True or False: If a simple random sample is chosen with replacement, everyone has the same chance of selection on every selection.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: simple random sample, probability sample, sampling method, sampling with replacement, sampling without replacement

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166. True or False: When dealing with human surveys, we are usually interested in sampling with replacement.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling with replacement, sampling method, survey worthiness 167. True or False: The only reliable way a researcher can make statistical inferences from a sample to a population is to use nonprobability sampling methods.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: nonprobability, probability sample, sampling method 168. True or False: A sample is always a good representation of the target population.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sample, population, sampling method 169. True or False: There can be only one sample selected from a population.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sample, sampling method 170. True or False: Using different frames to generate data can lead to totally different conclusions.

ANSWER: True TYPE:TF DIFFICULTY: Easy KEYWORDS: frame, sampling method 171. True or False: Sampling error can be eliminated by taking larger sample sizes.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: sampling error 172. True or False: Sampling error can be reduced by taking larger sample sizes.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling error

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1-40 Defining and Collecting Data 173. True or False: A convenience sample is a type of probability sample.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: chunk sample 174. True or False: Items or individuals in a judgment sample are chosen according to their probability of occurrence.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: judgment sample, nonprobability sample 175. True or False: When participants can self-select into the sample, you have a nonprobability sample.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: nonprobability sample 176. True or False: Systematic samples are less efficient than a stratified sample.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: systematic sample, stratified sample 177. True or False: The professor of a business statistics class wanted to find out the mean amount of time per week her students spent studying for the class. Among the 50 students in her class, 20% were freshmen, 50% were sophomores and 30% were juniors. She decided to select 2 students randomly from the freshmen, 5 randomly from the sophomores and 3 randomly from the juniors. This is an example of a systematic sample.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: stratified sample 178. To estimate the mean number of hours a student at a major university spent in the library, a researcher obtained the list of students from the registrar’s office, from which she can select a random sample of 200 students. This list is a _______.

ANSWER: frame TYPE: FI DIFFICULTY: Easy KEYWORDS: frame

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179. ________results from the exclusion of certain groups of subjects from a population frame.

ANSWER: Coverage error TYPE: FI DIFFICULTY: Difficult KEYWORDS: coverage error, survey worthiness, frame 180. Coverage error results in a ________.

ANSWER: selection bias TYPE: FI DIFFICULTY: Difficult KEYWORDS: selection bias, survey worthiness 181. ________results from the failure to collect data on all subjects in the sample.

ANSWER: Nonresponse error or bias TYPE: FI DIFFICULTY: Moderate KEYWORDS: nonresponse error, survey worthiness 182. The sampling process begins by locating appropriate data sources called ___________.

ANSWER: frames TYPE: FI DIFFICULTY: Easy KEYWORDS: frames, sampling method 183. True or False: If you randomly select a student from the first row of a business statistics class and then every other fifth student thereafter until you get a sample of 20 students, this is an example of a convenience sample.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: chunk sample 184. True or False: You stand at the main entrance to a departmental store and pick the first 20 customers that enter the store after it has opened its door for business on a single day. This is an example of a systematic sample.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: systematic sample

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1-42 Defining and Collecting Data 185. True or False: An electronic appliance chain gathered customer opinions on their services using the customer feedback forms that are attached to the product registration forms. This is an example of a convenience sample.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: convenience sample 186. True or False: To gather opinions on the efficacy of U.S. foreign policies, a sample of 50 faculty members is selected from the pool of university professors who have taught political science at the graduate level. This is an example of a judgment sample.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: judgment sample 187. True or False: In business statistics class students sit randomly without preferences. A sample is selected by including everybody who sits in the first row. This is an example of a cluster sample.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster sample 188. True or False: The question “How many times have you abused illicit drugs in the last 6 months?” will most likely result in nonresponse error.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: nonresponse error, survey worthiness 189. True or False: The question “Is your household income last year somewhere between $50,000 and $100,000?” will most likely result in coverage error.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: coverage error, survey worthiness 190. True or False: The only way one can eliminate sampling error is to take the whole population as the sample.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error, survey worthiness

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191. True or False: Coverage error can become an ethical issue if a group is intentionally excluded from the frame.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issue, coverage error, survey worthiness, frame 192. True or False: Measurement error will become an ethical issue when the findings are presented without reference to sample size and margin of error.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issue, measurement error, sampling error, survey worthiness 193. True or False: Measurement error can become an ethical issue when a survey sponsor chooses leading questions that guide the responses in a direction.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issue, measurement error, survey worthiness 194. True or False: Measurement error can become an ethical issue when an interviewer purposely guides the responses in a direction.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issue, measurement error, survey worthiness 195. True or False: Sampling error becomes an ethical issue if the findings are purposely presented without reference to sample size and margin of error so that the sponsor can promote a viewpoint that might otherwise be truly insignificant.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issue, sampling error, survey worthiness 196. True or False: The professor of a business statistics class wanted to find out the mean amount of time per week her students spent studying for the class. She divided the students into the left, right and center groups according to the location they sat in the class that day. One of these 3 groups was randomly selected and everyone in the group was asked the mean amount of time per week he/she spent studying for the class. This is an example of a cluster sample.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: cluster sample

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1-44 Defining and Collecting Data 197. True or False: The professor of a business statistics class wanted to find out the mean amount of time per week her students spent studying for the class. She divided the fifty students on her roster into ten groups starting from the first student on the roster. The first student was randomly selected from the first group. Then every tenth student was selected from the remaining students.

This is an example of a cluster sample.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: systematic sample 198. True or False: Selection bias occurs more frequently in systematic samples than in simple random samples.

ANSWER: True TYPE: TF DIFFICULTY: easy KEYWORDS: simple random sample, systematic sample 199. True or False: The question: “Have you used any form of illicit drugs over the past 2 months?” will most likely result in measurement error if the question is answered.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: measurement error, survey worthiness 200. True or False: The question: “How much did you earn last year rounded to the nearest hundreds of dollars?” will most likely result in measurement error.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: measurement error, survey worthiness

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SCENARIO 1-3 The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products.

201. Referring to Scenario 1-3, the manager decides to ask a sample of customers, who have bought a Blu-ray player made by the company and filed a complaint over the past year, to fill in a survey about whether they are satisfied with the product. This method will most likely suffer from a) nonresponse error. b) measurement error. c) coverage error. d) non-probability sampling.

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: coverage error, survey worthiness 202. Referring to Scenario 1-3, if there are 4 different brands of Blu-ray players made by the company, the best sampling strategy would be to use a a) a simple random sample. b) a stratified sample. c) a cluster sample. d) a systematic sample.

ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: stratified sample, probability sample, sampling method 203. Referring to Scenario 1-3, which of the following questions in the survey will NOT likely induce a measurement error? a) How many times have you illegally copied copyrighted sporting events? b) What is your exact annual income? c) How many times have you brought the Blu-ray player back for service? d) How many times have you failed to set the time on the Blu-ray player?

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: measurement error, survey worthiness

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1-46 Defining and Collecting Data 204. Referring to Scenario 1-3, if a customer survey questionnaire is included in all the Blu-ray players made and sold by the company over the past 12 months, this method of collecting data will most like suffer from a) nonresponse error. b) measurement error. c) coverage error. d) nonprobability sampling.

ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: nonresponse error, survey worthiness 205. True or False: In observational studies, investigators impute treatments on the sample participants.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: data sources, observational studies, treatments 206. When recoding variables, a successful recoding of each variable requires the properties of being ___________ and ___________.

ANSWER: Mutually exclusive , collectively exhaustive.

TYPE: FI DIFFICULTY: Moderate KEYWORDS: recoding variables

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CHAPTER 2: ORGANIZING AND VISUALIZING VARIABLES SCENARIO 2-1 An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of insured drivers and recorded, X, the number of claims each made in the last 3 years, with the following results.

X f 1 14 2 18 3 12 4 5 5 1 1. Referring to Scenario 2-1, how many drivers are represented in the sample? a) 5 b) 15 c) 18 d) 50 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: frequency distribution 2. Referring to Scenario 2-1, how many total claims are represented in the sample? a) 15 b) 50 c) 111 d) 250 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, frequency distribution 3. A type of vertical bar chart in which the categories are plotted in the descending rank order of the magnitude of their frequencies is called a a) contingency table. b) Pareto chart. c) stem-and-leaf display. d) pie chart.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Pareto chart SCENARIO 2-2 Copyright ©2020 Pearson Education, Inc.

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Organizing and Visualizing Variables At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer.

X f_ 1 7 2 5 3 11 4 8 5 9 4. Referring to Scenario 2-2, how many regional offices are represented in the survey results? a) 5 b) 11 c) 15 d) 40 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: interpretation, frequency distribution 5. Referring to Scenario 2-2, across all the regional offices, how many total employees were supervised by those surveyed? a) 15 b) 40 c) 127 d) 200 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, frequency distribution 6. The width of each bar in a histogram corresponds to the a) differences between the boundaries of the class. b) number of observations in each class. c) midpoint of each class. d) percentage of observations in each class.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: histogram

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SCENARIO 2-3 Every spring semester, the School of Business coordinates a luncheon with local business leaders for graduating seniors, their families, and friends. Corporate sponsorship pays for the lunches of each of the seniors, but students must purchase tickets to cover the cost of lunches served to guests they bring with them. The following histogram represents the attendance at the senior luncheon, where X is the number of guests each graduating senior invited to the luncheon and f is the number of graduating seniors in each category.

160

152

140 120 100

85

80 60 40 20

18

17

3

0

4

5

0 0

1

2 Guests per Student

3

7. Referring to the histogram from Scenario 2-3, how many graduating seniors attended the luncheon? a) 4 b) 152 c) 275 d) 388 ANSWER: c TYPE: MC DIFFICULTY: Difficult EXPLANATION: The number of graduating seniors is the sum of all the frequencies, f.

KEYWORDS: interpretation, histogram 8. Referring to the histogram from Scenario 2-3, if all the tickets purchased were used, how many guests attended the luncheon? a) 4 b) 152 c) 275 d) 388 ANSWER: d TYPE: MC DIFFICULTY: Difficult EXPLANATION: The total number of guests is

 Xf 6

i 1

i i

KEYWORDS: interpretation, histogram

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Organizing and Visualizing Variables 9. A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course. Shown below is a pie chart of the results. What percentage of the class took the course prior to reaching their senior year?

Freshmen 10%

Seniors 14%

Juniors 30% Sophomores 46%

a) b) c) d)

14% 44% 54% 86%

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: interpretation, pie chart 10. When polygons or histograms are constructed, which axis must show the true zero or "origin"? a) The horizontal axis. b) The vertical axis. c) Both the horizontal and vertical axes. d) Neither the horizontal nor the vertical axis.

ANSWER: b- Origin is at intersection of the Y axes.

TYPE: MC DIFFICULTY: Easy KEYWORDS: polygon, histogram 11. When constructing charts, the following is plotted at the class midpoints: a) frequency histograms. b) percentage polygons. c) cumulative percentage polygon (ogives). d) All of the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: percentage polygon

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SCENARIO 2-4 A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below.

Stem Leaves 3 24 4 03478999 5 0112345 6 12566 7 01 8 9 2 12. Referring to Scenario 2-4, what percentage of the respondents rated overall television quality with a rating of 80 or above? a) 0 b) 4 c) 96 d) 100 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 13. Referring to Scenario 2-4, what percentage of the respondents rated overall television quality with a rating of 50 or below? a) 11 b) 40 c) 44 d) 56 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 14. Referring to Scenario 2-4, what percentage of the respondents rated overall television quality with a rating from 50 through 75? a) 11 b) 40 c) 44 d) 56 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation

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Organizing and Visualizing Variables SCENARIO 2-5 The following are the duration in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.

Time (in Minutes) 0 but less than 5 5 but less than 10 10 but less than 15 15 but less than 20 20 but less than 25 25 but less than 30 30 or more

Relative Frequency 0.37 0.22 0.15 0.10 0.07 0.07 0.02

15. Referring to Scenario 2-5, what is the width of each class? a) 1 minute b) 5 minutes c) 2% d) 100% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: class interval, relative frequency distribution 16. Referring to Scenario 2-5, if 1,000 calls were randomly sampled, how many calls lasted under 10 minutes? a. 220 b. 370 c. 410 d. 590 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation 17. Referring to Scenario 2-5, if 100 calls were randomly sampled, how many calls lasted 15 minutes or longer? a. 10 b. 14 c. 26 d. 74 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation

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18. Referring to Scenario 2-5, if 10 calls lasted 30 minutes or more, how many calls lasted less than 5 minutes? a) 10 b) 185 c) 295 d) 500 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation 19. Referring to Scenario 2-5, what is the cumulative relative frequency for the percentage of calls that lasted under 20 minutes? a) 0.10 b) 0.59 c) 0.76 d) 0.84 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: cumulative relative frequency 20. Referring to Scenario 2-5, what is the cumulative relative frequency for the percentage of calls that lasted 10 minutes or more? a) 0.16 b) 0.24 c) 0.41 d) 0.90 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: cumulative relative frequency 21. Referring to Scenario 2-5, if 100 calls were randomly sampled, _______ of them would have lasted at least 15 minutes but less than 20 minutes a) 6 b) 8 c) 10 d) 16 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: relative frequency distribution, interpretation

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Organizing and Visualizing Variables 22. Referring to Scenario 2-5, if 100 calls were sampled, _______ of them would have lasted less than 15 minutes. a) 26 b) 74 c) 10 d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation 23. Referring to Scenario 2-5, if 100 calls were sampled, _______of them would have lasted 20 minutes or more. a) 26 b) 16 c) 74 d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, interpretation 24. Referring to Scenario 2-5, if 100 calls were sampled, _______ of them would have lasted less than 5 minutes or at least 30 minutes or more. a) 35 b) 37 c) 39 d) None of the above.

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: relative frequency distribution, interpretation 25. Which of the following is appropriate for displaying data collected on the different brands of cars students at a major university drive? a) b) c) d)

A Pareto chart A two-way classification table A histogram A scatter plot

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Pareto diagram

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26. One of the developing countries is experiencing a baby boom, with the number of births rising for the fifth year in a row, according to a BBC News report. Which of the following is best for displaying this data? a) A Pareto chart b) A two-way classification table c) A histogram d) A time-series plot ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: time-series plot 27. When studying the simultaneous responses to two categorical questions, you should set up a a) contingency table. b) frequency distribution table. c) cumulative percentage distribution table. d) histogram.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table 28. Data on 1,500 students’ height were collected at a larger university in the East Coast. Which of the following is the best chart for presenting the information? a) A pie chart. b) A Pareto chart. c) A side-by-side bar chart. d) A histogram.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: choice of chart, histogram 29. Data on the number of part-time hours students at a public university worked in a week were collected. Which of the following is the best chart for presenting the information? a) A pie chart. b) A Pareto chart. c) A percentage table. d) A percentage polygon.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: choice of chart, percentage polygon

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Organizing and Visualizing Variables

30. Data on the number of credit hours of 20,000 students at a public university enrolled in a Spring semester were collected. Which of the following is the best for presenting the information? a) A pie chart. b) A Pareto chart. c) A stem-and-leaf display. d) A contingency table.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: choice of chart, stem-and-leaf 31. A survey of 150 executives were asked what they think is the most common mistake candidates make during job interviews. Six different mistakes were given. Which of the following is the best for presenting the information? a) A bar chart. b) A histogram c) A stem-and-leaf display. d) A contingency table.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: choice of chart, bar chart 32. You have collected information on the market share of 5 different search engines used by U.S. Internet users in a quarter. Which of the following is the best for presenting the information? a) A pie chart. b) A histogram c) A stem-and-leaf display. d) A contingency table.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: choice of chart, pie chart

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Organizing and Visualizing Variables

2-11

33. You have collected information on the consumption by the 15 largest coffee-consuming nations.

Which of the following is the best for presenting the shares of the consumption? a) A pie chart. b) A Pareto chart c) A side-by-side bar chart. d) A contingency table.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: choice of chart, Pareto chart NOTE: Even though a pie chart can also be used, the Pareto chart is preferable for separating the “vital few” from the “trivial many”.

34. You have collected data on the approximate retail price (in $) and the energy cost per year (in $) of 15 refrigerators. Which of the following is the best for presenting the data? a) A pie chart. b) A scatter plot c) A side-by-side bar chart. d) A contingency table.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: choice of chart, scatter plot 35. You have collected data on the number of U.S. households actively using online banking and/or online bill payment over a 10-year period. Which of the following is the best for presenting the data? a) A pie chart. b) A stem-and-leaf display c) A side-by-side bar chart. d) A time-series plot.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: choice of chart, time-series plot 36. You have collected data on the monthly seasonally adjusted civilian unemployment rate for the United States over a 10-year period. Which of the following is the best for presenting the data? a) A contingency table. b) A stem-and-leaf display c) A time-series plot. d) A side-by-side bar chart.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: choice of chart, time-series plot

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Organizing and Visualizing Variables

37. You have collected data on the number of complaints for 6 different brands of automobiles sold in the US over a 10-year period. Which of the following is the best for presenting the data? a) A contingency table. b) A stem-and-leaf display c) A time-series plot. d) A side-by-side bar chart.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: choice of chart, side-by-side bar chart 38. You have collected data on the responses to two questions asked in a survey of 40 college students majoring in business—What is your gender (Male = M; Female = F) and What is your major (Accountancy = A; Computer Information Systems = C; Marketing = M). Which of the following is the best for presenting the data? a) A contingency table. b) A stem-and-leaf display c) A time-series plot. d) A Pareto chart.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: choice of chart, contingency table SCENARIO 2-6 A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.

Studying for Exam Went Bar Hopping

Did Well in Midterm 80 30

Did Poorly in Midterm 20 70

39. Referring to Scenario 2-6, of those who went bar hopping the weekend before the midterm in the sample, _______ percent of them did well on the midterm. a) 15 b) 27.27 c) 30 d) 55 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation

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Organizing and Visualizing Variables

2-13

40. Referring to Scenario 2-6, of those who did well on the midterm in the sample, _______ percent of them went bar hopping the weekend before the midterm. a) 15 b) 27.27 c) 30 d) 50 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation 41. Referring to Scenario 2-6, _______ percent of the students in the sample went bar hopping the weekend before the midterm and did well on the midterm. a) 15 b) 27.27 c) 30 d) 50 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation 42. Referring to Scenario 2-6, _______ percent of the students in the sample spent the weekend studying and did well on the midterm. a) 40 b) 50 c) 72.72 d) 80 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation 43. Referring to Scenario 2-6, if the sample is a good representation of the population, we can expect _______ percent of the students in the population to spend the weekend studying and do poorly on the midterm. a) 10 b) 20 c) 45 d) 50 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, interpretation

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Organizing and Visualizing Variables

44. Referring to Scenario 2-6, if the sample is a good representation of the population, we can expect _______ percent of those who spent the weekend studying to do poorly on the midterm. a) 10 b) 20 c) 45 d) 50 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: contingency table, interpretation 45. Referring to Scenario 2-6, if the sample is a good representation of the population, we can expect _______ percent of those who did poorly on the midterm to have spent the weekend studying. a) 10 b) 22.22 c) 45 d) 50 ANSWER: b TYPE: MC DIFFICULTY: Moderate.

KEYWORDS: contingency table, interpretation 46. In a contingency table, the number of rows and columns a) must always be the same. b) must always be 2. c) must add to 100%. d) None of the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: contingency table

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Organizing and Visualizing Variables

2-15

47. Retailers are always interested in determining why a customer selected their store to make a purchase. A sporting goods retailer conducted a customer survey to determine why its customers shopped at the store. The results are shown in the bar chart below. What proportion of the customers responded that they shopped at the store because of the merchandise or the convenience?

Prices

20%

Merchandise

50%

Convenience

15%

Other

15%

0%

a) b) c) d)

10%

20%

30% Responses

40%

50%

60%

35% 50% 65% 85%

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: bar chart, interpretation SCENARIO 2-7 The Stem-and-Leaf display below contains data on the number of months between the date a civil suit is filed and when the case is actually adjudicated for 50 cases heard in superior court.

Stem Leaves 1 234447899 2 22223455678889 3 0011135778 4 02345579 5 112466 6 158 48. Referring to Scenario 2-7, locate the first leaf, i.e., the lowest valued leaf with the lowest valued stem. This represents a wait of ________ months.

ANSWER: 12 TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation

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Organizing and Visualizing Variables

49. Referring to Scenario 2-7, the civil suit with the longest wait between when the suit was filed and when it was adjudicated had a wait of ________ months.

ANSWER: 68 TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 50. Referring to Scenario 2-7, the civil suit with the fourth shortest waiting time between when the suit was filed and when it was adjudicated had a wait of ________ months.

ANSWER: 14 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 51. Referring to Scenario 2-7, ________ percent of the cases were adjudicated within the first 2 years.

ANSWER: 30 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 52. Referring to Scenario 2-7, ________ percent of the cases were not adjudicated within the first 4 years.

ANSWER: 20 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 53. Referring to Scenario 2-7, if a frequency distribution with equal sized classes was made from this data, and the first class was "10 but less than 20," the frequency of that class would be ________.

ANSWER: 9 TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 54. Referring to Scenario 2-7, if a frequency distribution with equal sized classes was made from this data, and the first class was "10 but less than 20," the relative frequency of the third class would be ________.

ANSWER: 0.20 or 20% or 10/50 TYPE: FI DIFFICULTY: Moderate KEYWORDS: relative frequency distribution

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Organizing and Visualizing Variables

2-17

55. Referring to Scenario 2-7, if a frequency distribution with equal sized classes was made from this data, and the first class was "10 but less than 20," the cumulative percentage of the second class would be ________.

ANSWER: 46% or 0.46 or 23/50 TYPE: FI DIFFICULTY: Moderate KEYWORDS: cumulative percentage distribution SCENARIO 2-8 The Stem-and-Leaf display represents the number of times in a year that a random sample of 100 "lifetime" members of a health club actually visited the facility.

Stem Leaves 0 012222233333344566666667789999 1 1111222234444455669999 2 00011223455556889 3 0000446799 4 011345567 5 0077 6 8 7 67 8 3 9 0247 56. Referring to Scenario 2-8, the person who has the largest leaf associated with the smallest stem visited the facility ________ times.

ANSWER: 9 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 57. Referring to Scenario 2-8, the person who visited the health club less than anyone else in the sample visited the facility ________ times.

ANSWER: 0 or no TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation 58. Referring to Scenario 2-8, the person who visited the health club more than anyone else in the sample visited the facility ________ times.

ANSWER: 97 TYPE: FI DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, interpretation

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Organizing and Visualizing Variables

59. Referring to Scenario 2-8, ________ of the 100 members visited the health club at least 52 times in a year.

ANSWER: 10 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 60. Referring to Scenario 2-8, ________ of the 100 members visited the health club no more than 12 times in a year.

ANSWER: 38 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, interpretation 61. Referring to Scenario 2-8, if a frequency distribution with equal sized classes was made from this data, and the first class was "0 but less than 10," the frequency of the fifth class would be ________.

ANSWER: 9 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, frequency distribution 62. Referring to Scenario 2-8, if a frequency distribution with equal sized classes was made from this data, and the first class was "0 but less than 10," the relative frequency of the last class would be ________.

ANSWER: 4% or 0.04 or 4/100 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, relative frequency distribution 63. Referring to Scenario 2-8, if a frequency distribution with equal sized classes was made from this data, and the first class was "0 but less than 10," the cumulative percentage of the next-to-last class would be ________.

ANSWER: 96% or 0.96 or 96/100 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, cumulative percentage distribution

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Organizing and Visualizing Variables

2-19

64. Referring to Scenario 2-8, if a frequency distribution with equal sized classes was made from this data, and the first class was "0 but less than 10," the class midpoint of the third class would be ________.

ANSWER: 25 or (20+30)/2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: stem-and-leaf display, class midpoint SCENARIO 2-9 The frequency distribution below represents the rents of 250 randomly selected federally subsidized apartments in a small town.

Rent in $ Frequency 1,100 but less than 1,200 113 1,200 but less than 1,300 85 1,300 but less than 1,400 32 1,400 but less than 1,500 16 1,500 but less than 1,600 4 65. Referring to Scenario 2-9, ________ apartments rented for at least $1,200 but less than $1,400.

ANSWER: 117 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution 66. Referring to Scenario 2-9, ________ percent of the apartments rented for $1,400 or more.

ANSWER: 8% or 20/250 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, cumulative percentage distribution 67. Referring to Scenario 2-9, ________ percent of the apartments rented for at least $1,300.

ANSWER: 20.8% or 52/250 TYPE: FI DIFFICULTY: Moderate KEYWORDS: frequency distribution, cumulative percentage distribution 68. Referring to Scenario 2-9, the class midpoint of the second class is ________.

ANSWER: 1,250 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, class midpoint

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Organizing and Visualizing Variables

69. Referring to Scenario 2-9, the relative frequency of the second class is ________.

ANSWER: 85/250 or 17/50 or 34% or 0.34 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, relative frequency distribution 70. Referring to Scenario 2-9, the percentage of apartments renting for less than $1,400 is ________.

ANSWER: 230/250 or 23/25 or 92% or 0.92 TYPE: FI DIFFICULTY: Moderate KEYWORDS: frequency distribution, cumulative percentage distribution SCENARIO 2-10 The relative frequency histogram below represents scores achieved by 200 job applicants on a personality profile.

0.30 Rel.Freq.

0.20

0.20

0.20

0.20

0.10

0.10

0.10

0.00 0

10

20

30

0.10

40

50

0.10

60

70

71. Referring to the histogram from Scenario 2-10, ________ percent of the job applicants scored between 10 and 20.

ANSWER: 20% TYPE: FI DIFFICULTY: Easy KEYWORDS: histogram, percentage distribution 72. Referring to the histogram from Scenario 2-10, ________ percent of the job applicants scored below 50.

ANSWER: 80% TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, percentage distribution Copyright ©2020 Pearson Education, Inc.

Organizing and Visualizing Variables

2-21

73. Referring to the histogram from Scenario 2-10, the number of job applicants who scored between 30 and below 60 is _______.

ANSWER: 80 TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram 74. Referring to the histogram from Scenario 2-10, the number of job applicants who scored 50 or above is _______.

ANSWER: 40 TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram 75. Referring to the histogram from Scenario 2-10, 90% of the job applicants scored above or equal to ________.

ANSWER: 10 TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, cumulative percentage distribution 76. Referring to the histogram from Scenario 2-10, half of the job applicants scored below ________.

ANSWER: 30 TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, cumulative percentage distribution 77. Referring to the histogram from Scenario 2-10, _______ percent of the applicants scored below 20 or at least 50.

ANSWER: 50% TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, cumulative percentage distribution 78. Referring to the histogram from Scenario 2-10, _______ percent of the applicants scored between 20 and below 50.

ANSWER: 50% TYPE: FI DIFFICULTY: Moderate KEYWORDS: histogram, cumulative percentage distribution

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Organizing and Visualizing Variables

SCENARIO 2-11 The ordered array below resulted from selecting a sample of 25 batches of 500 computer chips and determining how many in each batch were defective.

Defects 1 2 4 17 20 21

4 23

5 23

5 25

6 26

7 27

9 27

9 28

12 29

12 29

15

79. Referring to Scenario 2-11, if a frequency distribution for the defects data is constructed, using "0 but less than 5" as the first class, the frequency of the “20 but less than 25” class would be ________.

ANSWER: 4 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution 80. Referring to Scenario 2-11, if a frequency distribution for the defects data is constructed, using "0 but less than 5" as the first class, the relative frequency of the “15 but less than 20” class would be ________.

ANSWER: 0.08 or 8% or 2/25 TYPE: FI DIFFICULTY: Moderate KEYWORDS: relative frequency distribution 81. Referring to Scenario 2-11, construct a frequency distribution for the defects data, using "0 but less than 5" as the first class.

ANSWER: Defects Frequency 0 but less than 5 4 5 but less than 10 6 10 but less than 15 2 15 but less than 20 2 20 but less than 25 4 25 but less than 30 7 TYPE: PR DIFFICULTY: Easy KEYWORDS: frequency distribution

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Organizing and Visualizing Variables

2-23

82. Referring to Scenario 2-11, construct a relative frequency or percentage distribution for the defects data, using "0 but less than 5" as the first class.

ANSWER: Defects Percentage 0 but less than 5 16 5 but less than 10 24 10 but less than 15 8 15 but less than 20 8 20 but less than 25 16 25 but less than 30 28 TYPE: PR DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, percentage distribution 83. Referring to Scenario 2-11, construct a cumulative percentage distribution for the defects data if the corresponding frequency distribution uses "0 but less than 5" as the first class.

ANSWER: Defects CumPct 0 0 5 16 10 40 15 48 20 56 25 72 30 100 TYPE: PR DIFFICULTY: Moderate KEYWORDS: cumulative percentage distribution 84. Referring to Scenario 2-11, construct a histogram for the defects data, using "0 but less than 5" as the first class.

ANSWER: 7

7

Frequency 6

6 5 4

4

4

3 2

2

2

1 0

0

5

10

15 20 Number of Defects

25

30

TYPE: PR DIFFICULTY: Easy KEYWORDS: histogram, frequency distribution Copyright ©2020 Pearson Education, Inc.

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Organizing and Visualizing Variables

85. Referring to Scenario 2-11, construct a cumulative percentage polygon for the defects data if the corresponding frequency distribution uses "0 but less than 5" as the first class.

ANSWER: Cumulative Percentage Polygon 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0

5

10

15

20

25

30

Number of Defects

TYPE: PR DIFFICULTY: Moderate KEYWORDS: cumulative percentage polygon 86. The point halfway between the boundaries of each class interval in a grouped frequency distribution is called the _______.

ANSWER: class midpoint TYPE: FI DIFFICULTY: Easy KEYWORDS: cumulative percentage polygon, frequency distribution 87. A _______ is a vertical bar chart in which the rectangular bars are constructed at the boundaries of each class interval.

ANSWER: histogram TYPE: FI DIFFICULTY: Easy KEYWORDS: histogram 88. It is essential that each class grouping or interval in a frequency distribution be ________ and ________.

ANSWER: non-overlapping and of equal width TYPE: FI DIFFICULTY: Moderate KEYWORDS: frequency distribution, class interval

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Organizing and Visualizing Variables

2-25

89. To compare one large set of numerical data to another, a ________ distribution must be developed from the frequency distribution.

ANSWER: relative frequency or percentage TYPE: FI DIFFICULTY: Easy KEYWORDS: relative frequency distribution, percentage distribution 90. When comparing two or more large sets of numerical data, the distributions being developed should use the same ________.

ANSWER: class boundaries.

TYPE: FI DIFFICULTY: Easy KEYWORDS: class boundaries 91. The width of each class grouping or interval in a frequency distribution should be ________.

ANSWER: the same or equal TYPE: FI DIFFICULTY: Easy KEYWORDS: class interval, frequency distribution 92. In constructing a polygon, each class grouping is represented by its _______ and then these are consecutively connected to one another.

ANSWER: midpoint TYPE: FI DIFFICULTY: Easy KEYWORDS: polygon, class interval, midpoint 93. A _______ is a summary table in which numerical data are tallied into class intervals or categories.

ANSWER: frequency distribution TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution, class interval 94. True or False: In general, grouped frequency distributions should have between 5 and 15 class intervals.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: frequency distribution, number of classes

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Organizing and Visualizing Variables

95. True or False: The sum of relative frequencies in a distribution always equals 1.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: relative frequency 96. True or False: The sum of cumulative frequencies in a distribution always equals 1.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: cumulative distribution 97. True or False: In graphing two categorical data, the side-by-side bar chart is best suited when comparing joint responses.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: side-by-side bar chart 98. True or False: When constructing a frequency distribution, classes should be selected so that they are of equal width.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: frequency distribution 99. True or False: A research analyst was directed to arrange raw data collected on the yield of wheat, ranging from 40 to 93 bushels per acre, in a frequency distribution. He should choose 30 as the class interval width.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: frequency distribution, class interval 100. True or False: If the values of the seventh and eighth class in a cumulative percentage distribution are the same, we know that there are no observations in the eighth class.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: cumulative percentage distribution

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Organizing and Visualizing Variables

2-27

101. True or False: One of the advantages of a pie chart is that it clearly shows that the total of all the categories of the pie adds to 100%.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pie chart 102. True or False: The larger the number of observations in a numerical data set, the larger the number of class intervals needed for a grouped frequency distribution.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: class interval, frequency distribution 103. True or False: Determining the class boundaries of a frequency distribution is highly subjective.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: class boundaries, frequency distribution 104. True or False: The original data values cannot be determined once they are grouped into a frequency distribution table.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: frequency distribution 105. True or False: The percentage distribution cannot be constructed from the frequency distribution directly.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: percentage distribution, frequency distribution 106. True or False: The stem-and-leaf display is often superior to the frequency distribution in that it maintains the original values for further analysis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: stem-and-leaf display, frequency distribution

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Organizing and Visualizing Variables

107. True or False: The relative frequency is the frequency in each class divided by the total number of observations.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: relative frequency distribution 108. True or False: Ogives are plotted at the midpoints of the class groupings.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: ogives, midpoint 109. True or False: Percentage polygons are plotted at the boundaries of the class groupings.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: percentage polygons 110. True or False: The main principle behind the Pareto chart is the ability to separate the "vital few" from the "trivial many."

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Pareto chart 111. True or False: A histogram can have gaps between the bars, whereas bar charts cannot have gaps.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: histogram, bar chart 112. True or False: Histograms are used for numerical data while bar charts are suitable for categorical data.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: histogram, bar chart

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Organizing and Visualizing Variables

2-29

113. True or False: A Walmart store in a small town monitors customer complaints and organizes these complaints into six distinct categories. Over the past year, suppose the company has received 534 complaints. One possible graphical method for representing these data would be a Pareto chart.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Pareto chart 114. True or False: Apple Computer, Inc. collected information on the age of their customers.

Suppose the youngest customer was 12 and the oldest was 72. To study the distribution of the age among its customers, it can use a Pareto chart.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Pareto chart 115. True or False: Apple Computer, Inc. collected information on the age of their customers.

Suppose the youngest customer was 12 and the oldest was 72. To study the distribution of the age among its customers, it is best to use a pie chart.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: pie chart 116. True or False: Apple Computer, Inc. collected information on the age of their customers.

Suppose the youngest customer was 12 and the oldest was 72. To study the distribution of the age among its customers, it can use a percentage polygon.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: percentage polygon 117. True or False: Apple Computer, Inc. collected information on the age of their customers.

Suppose the youngest customer was 12 and the oldest was 72. To study the percentage of their customers who are below a certain age, it can use an ogive.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: ogive

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Organizing and Visualizing Variables

118. True or False: If you wish to construct a graph of a relative frequency distribution, you would most likely construct an ogive first.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Ogive 119. True or False: An ogive is a cumulative percentage polygon.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Ogive, cumulative percentage polygon 120. True or False: A side-by-side bar chart is two histograms plotted side-by-side.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: side-by-side bar chart 121. True or False: A good choice for the number of class groups to use in constructing frequency distribution is to have at least 5 but no more than 15 class groups.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: number of classes 122. True or False: In general, a frequency distribution should have at least 8 class groups but no more than 20.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: number of classes 123. True of False: To determine the width of class interval, divide the number of class groups by the range of the data.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: class interval

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Organizing and Visualizing Variables

2-31

124. True or False: The percentage polygon is formed by having the lower boundary of each class represent the data in that class and then connecting the sequence of lower boundaries at their respective class percentages.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: percentage polygon 125. True or False: A polygon can be constructed from a bar chart.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: polygon 126. To evaluate two categorical variables at the same time, a _______ could be developed.

ANSWER: contingency or cross-classification table or side-by-side bar chart TYPE: FI DIFFICULTY: Easy KEYWORDS: contingency table, cross-classification table 127. Relationships in a contingency table can be examined more fully if the frequencies are converted into _______ .

ANSWER: percentages or proportions TYPE: FI DIFFICULTY: Easy KEYWORDS: contingency table SCENARIO 2-12 The table below contains the opinions of a sample of 200 people broken down by gender about the latest congressional plan to eliminate anti-trust exemptions for professional baseball.

Female Male Totals

For 38 12 50

Neutral 54 36 90

Against Totals 12 104 48 96 60 200

128. Referring to Scenario 2-12, construct a table of row percentages.

ANSWER: For Neutral Against Female 36.54 51.92 11.54 Male 12.50 37.50 50.00 Totals 25.00 45.00 30.00 TYPE: PR DIFFICULTY: Easy KEYWORDS: row percentages

Totals 100.00 100.00 100.00

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129. Referring to Scenario 2-12, construct a table of column percentages.

ANSWER: For Neutral Against Totals Female 76.00 60.00 20.00 52.00 Male 24.00 40.00 80.00 48.00 Totals 100.00 100.00 100.00 100.00 TYPE: PR DIFFICULTY: Easy KEYWORDS: column percentages 130. Referring to Scenario 2-12, construct a table of total percentages.

ANSWER: For Neutral Against Totals Female 19.00 27.00 6.00 52.00 Male 6.00 18.00 24.00 48.00 Totals 25.00 45.00 30.00 100.00 TYPE: PR DIFFICULTY: Easy KEYWORDS: total percentages 131. Referring to Scenario 2-12, of those for the plan in the sample, ________ percent were females.

ANSWER: 76% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 132. Referring to Scenario 2-12, of those neutral in the sample, ________ percent were males.

ANSWER: 40% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 133. Referring to Scenario 2-12, of the males in the sample, ________ percent were for the plan.

ANSWER: 12.50% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 134. Referring to Scenario 2-12, of the females in the sample, ________ percent were against the plan.

ANSWER: 11.54% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table

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135. Referring to Scenario 2-12, of the females in the sample, ________ percent were either neutral or against the plan.

ANSWER: 63.46% or (51.92+11.54)% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 136. Referring to Scenario 2-12, ________ percent of the 200 were females who were against the plan.

ANSWER: 6% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 137. Referring to Scenario 2-12, ________ percent of the 200 were males who were neutral.

ANSWER: 18% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 138. Referring to Scenario 2-12, ________ percent of the 200 were females who were either neutral or against the plan.

ANSWER: 33% TYPE: FI DIFFICULTY: Difficult KEYWORDS: contingency table 139. Referring to Scenario 2-12, _______ percent of the 200 were males who were not against the plan.

ANSWER: 24% TYPE: FI DIFFICULTY: Difficult KEYWORDS: contingency table 140. Referring to Scenario 2-12, _______ percent of the 200 were not neutral.

ANSWER: 55% TYPE: FI DIFFICULTY: Difficult KEYWORDS: contingency table, row percentages 141. Referring to Scenario 2-12, _______ percent of the 200 were against the plan.

ANSWER: 30% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages Copyright ©2020 Pearson Education, Inc.

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142. Referring to Scenario 2-12, ________ percent of the 200 were males.

ANSWER: 48% TYPE: FI DIFFICULTY: Easy KEYWORDS: contingency table, column percentages 143. Referring to Scenario 2-12, if the sample is a good representation of the population, we can expect _______ percent of the population will be for the plan.

ANSWER: 25% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages 144. Referring to Scenario 2-12, if the sample is a good representation of the population, we can expect _______ percent of the population will be males.

ANSWER: 48% TYPE: FI DIFFICULTY: Moderate KEYWORDS: column percentages, contingency table 145. Referring to Scenario 2-12, if the sample is a good representation of the population, we can expect _______ percent of those for the plan in the population will be males.

ANSWER: 24% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 146. Referring to Scenario 2-12, if the sample is a good representation of the population, we can expect _______ percent of the males in the population will be against the plan.

ANSWER: 50% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table 147. Referring to Scenario 2-12, if the sample is a good representation of the population, we can expect _______ percent of the females in the population will not be against the plan.

ANSWER: 88.46% or (36.54+51.92) TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table

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Organizing and Visualizing Variables

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SCENARIO 2-13 Given below is the stem-and-leaf display representing the amount of detergent used in gallons (with leaves in 10ths of gallons) in a day by 25 drive-through car wash operations in Phoenix.

9 | 147 10 | 02238 11 | 135566777 12 | 223489 13 | 02 148. Referring to Scenario 2-13, if a frequency distribution for the amount of detergent used is constructed, using "9.0 but less than 10.0 gallons" as the first class, the frequency of the “11.0 but less than 12.0 gallons” class would be ________.

ANSWER: 9 TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution 149. Referring to Scenario 2-13, if a percentage histogram for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, the percentage of drive-through car wash operations that use “12.0 but less than 13.0 gallons” of detergent would be ________.

ANSWER: 24% TYPE: FI DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, percentage distribution 150. Referring to Scenario 2-13, if a percentage histogram for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drive-through car wash operations use less than 12 gallons of detergent in a day?

ANSWER: 68% TYPE: FI DIFFICULTY: Easy KEYWORDS: percentage distribution, cumulative relative frequency 151. Referring to Scenario 2-13, if a relative frequency or percentage distribution for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drive-through car wash operations use at least 10 gallons of detergent in a day?

ANSWER: 88% TYPE: FI DIFFICULTY: Easy KEYWORDS: relative frequency distribution, percentage distribution

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Organizing and Visualizing Variables

152. Referring to Scenario 2-13, if a relative frequency or percentage distribution for the detergent data is constructed, using "9.0 but less than 10.0 gallons" as the first class, what percentage of drivethrough car wash operations use at least 10 gallons but less than 13 gallons of detergent in a day?

ANSWER: 80% TYPE: FI DIFFICULTY: Easy KEYWORDS: relative frequency distribution, percentage distribution 153. Referring to Scenario 2-13, construct a frequency distribution for the detergent data, using "9.0 but less than 10.0 gallons" as the first class.

ANSWER: Purchases (gals) Frequency 9.0 but less than 10.0 3 10.0 but less than 11.0 5 11.0 but less than 12.0 9 12.0 but less than 13.0 6 13.0 but less than 14.0 2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: frequency distribution 154. Referring to Scenario 2-13, construct a relative frequency or percentage distribution for the detergent data, using "9.0 but less than 10.0" as the first class.

ANSWER: Gasoline Purchases (gals) Percentage 9.0 but less than 10.0 12% 10.0 but less than 11.0 20 11.0 but less than 12.0 36 12.0 but less than 13.0 24 13.0 but less than 14.0 8 TYPE: PR DIFFICULTY: Moderate KEYWORDS: relative frequency distribution, percentage distribution 155. Referring to Scenario 2-13, construct a cumulative percentage distribution for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class.

ANSWER: Gasoline Frequency Percentage Purchases (gals) Less Than Less Than 9.0 but less than 10.0 3 12 10.0 but less than 11.0 8 32 11.0 but less than 12.0 17 68 12.0 but less than 13.0 23 92 13.0 but less than 14.0 25 100 TYPE: PR DIFFICULTY: Moderate KEYWORDS: cumulative percentage distribution

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156. Referring to Scenario 2-13, construct a percentage histogram for the detergent data, using "9.0 but less than 10.0" as the first class.

ANSWER: % Histogram 40 35 30 %

25 20 15 10 5 0 9.0 -- 9.9

10.0 -- 10.9 11.0 -- 11.9 12.0 -- 12.9 13.0 -- 13.9 Purchased

TYPE: PR DIFFICULTY: Moderate KEYWORDS: histogram, frequency distribution 157. Referring to Scenario 2-13, construct a cumulative percentage polygon for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class.

ANSWER: Ogive 100 80 %

60 40 20 0 9

10

11

12

13

14

Purchase

TYPE: PR DIFFICULTY: Moderate KEYWORDS: cumulative percentage polygon

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Organizing and Visualizing Variables

158. Referring to Scenario 2-13, construct a percentage polygon for the detergent data if the corresponding frequency distribution uses "9.0 but less than 10.0" as the first class.

ANSWER:

%

% Polygon 40 35 30 25 20 15 10 5 0

%

8.5

9.5

10.5

11.5

12.5

13.5

14.5

Purchase

TYPE: PR DIFFICULTY: Moderate KEYWORDS: percentage distribution, percentage polygon SCENARIO 2-14 The table below contains the number of people who own a portable Blu-ray player in a sample of 600 broken down by gender.

Own a Portable Blu-ray player Yes No

Male 96 224

Female 40 240

159. Referring to Scenario 2-14, construct a table of row percentages.

ANSWER: Own Yes No Total

Male 70.59% 48.28% 53.33%

Female 29.41% 51.72% 46.67%

Total 100.00% 100.00% 100.00%

TYPE: PR DIFFICULTY: Easy KEYWORDS: row percentages 160. Referring to Scenario 2-14, construct a table of column percentages.

ANSWER: Own Yes No Total

Male 30.00% 70.00% 100.00%

Female 14.29% 85.71% 100.00%

Total 22.67% 77.33% 100.00%

TYPE: PR DIFFICULTY: Easy KEYWORDS: column percentages Copyright ©2020 Pearson Education, Inc.

Organizing and Visualizing Variables

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161. Referring to Scenario 2-14, construct a table of total percentages.

ANSWER: Own Yes No Total

Male 16.00% 37.33% 53.33%

Female 6.67% 40.00% 46.67%

Total 22.67% 77.33% 100.00%

TYPE: PR DIFFICULTY: Easy KEYWORDS: total percentages 162. Referring to Scenario 2-14, of those who owned a portable Blu-ray player in the sample, ________ percent were females.

ANSWER: 29.41% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages 163. Referring to Scenario 2-14, of those who did not own a portable Blu-ray player in the sample, ________ percent were males.

ANSWER: 48.28% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages 164. Referring to Scenario 2-14, of the males in the sample, ________ percent owned a portable Blu-ray player.

ANSWER: 30% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 165. Referring to Scenario 2-14, of the females in the sample, ________ percent did not own a portable Blu-ray player.

ANSWER: 85.71% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 166. Referring to Scenario 2-14 of the females in the sample, ________ percent owned a portable Blu-ray player.

ANSWER: 14.29% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

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Organizing and Visualizing Variables

167. Referring to Scenario 2-14, ________ percent of the 600 were females who owned a portable Blu-ray player.

ANSWER: 6.67% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, total percentage 168. Referring to Scenario 2-14, ________ percent of the 600 were males who owned a portable Blu-ray player.

ANSWER: 16% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, total percentage 169. Referring to Scenario 2-14, ________ percent of the 600 were females who either owned or did not own a portable Blu-ray player.

ANSWER: 46.67% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, total percentage 170. Referring to Scenario 2-14, _______ percent of the 600 were males who did not own a portable Blu-ray player.

ANSWER: 37.33% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, total percentage 171. Referring to Scenario 2-14, _______ percent of the 600 owned a portable Blu-ray player.

ANSWER: 22.67% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 172. Referring to Scenario 2-14, _______ percent of the 600 did not own a portable Blu-ray player.

ANSWER: 77.33% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

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Organizing and Visualizing Variables

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173. Referring to Scenario 2-14, ________ percent of the 600 were females.

ANSWER: 46.67% TYPE: FI DIFFICULTY: Easy KEYWORDS: contingency table, row percentages 174. Referring to Scenario 2-14, if the sample is a good representation of the population, we can expect _______ percent of the population will own a portable Blu-ray player.

ANSWER: 22.67% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 175. Referring to Scenario 2-14, if the sample is a good representation of the population, we can expect _______ percent of the population will be males.

ANSWER: 53.33% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 176. Referring to Scenario 2-14, if the sample is a good representation of the population, we can expect _______ percent of those who own a portable Blu-ray player in the population will be males.

ANSWER: 70.59% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, row percentages 177. Referring to Scenario 2-14, if the sample is a good representation of the population, we can expect _______ percent of the males in the population will own a portable Blu-ray player.

ANSWER: 30% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages 178. Referring to Scenario 2-14, if the sample is a good representation of the population, we can expect _______ percent of the females in the population will not own a portable Blu-ray player.

ANSWER: 85.71% TYPE: FI DIFFICULTY: Moderate KEYWORDS: contingency table, column percentages

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Organizing and Visualizing Variables

SCENARIO 2-15 The figure below is the ogive for fat (in grams) for a sample of 36 pizza products where the upper boundaries of the intervals are: 5, 10, 15, 20, 25, and 30.

Cumulative Percentage Polygon for Fat 100% 80% 60% 40% 20% 0% -0.01

4.99

9.99

14.99 19.99 24.99 29.99 34.99

Fat (grams) 179. Referring to Scenario 2-15, roughly what percentage of pizza products contains less than 10 grams of fat? a) 3% b) 14% c) 50% d) 75% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: cumulative percentage polygon, ogive, interpretation 180. Referring to Scenario 2-15, what percentage of pizza products contains at least 20 grams of fat? a) 5% b) 25% c) 75% d) 96% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: cumulative percentage polygon, ogive, interpretation

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Organizing and Visualizing Variables

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181. Referring to Scenario 2-15, what percentage of pizza products contains between 10 and 25 grams of fat? a) 14% b) 44% c) 62% d) 81% ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: cumulative percentage polygon, ogive, interpretation SCENARIO 2-16 The figure below is the percentage polygon for the number of calories for a sample of 36 pizzas products where the upper limits of the intervals are: 310, 340, 370, 400 and 430.

Percentage Polygon for Calories 30% 25% 20% 15% 10% 5% 0% 264.99

294.99

324.99

354.99

384.99

414.99

444.99

Calories

182. Referring to Scenario 2-16, roughly what percentage of pizza products contains between 400 and 430 calories? a) 0% b) 11% c) 89% d) 100% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: percentage polygon, interpretation

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Organizing and Visualizing Variables

183. Referring to Scenario 2-16, roughly what percentage of pizza products contains between 340 and 400 calories? a) 22% b) 25% c) 28% d) 50% ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: percentage polygon, interpretation 184. Referring to Scenario 2-16, roughly what percentage of pizza products contains at least 340 calories? a) 25% b) 28% c) 39% d) 61% ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: percentage polygon, interpretation SCENARIO 2-17 The following table presents total retail sales in millions of dollars for the leading apparel companies over a two-year period in the past.

APPAREL COMPANY Gap TJX Limited Kohl’s Nordstrom Talbots Ann Taylor

Year 1 Year 2 1,159.0 781.7 596.5 544.9 402.6 139.9 114.2

962.0 899.0 620.4 678.9 418.3 130.1 124.8

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185. Referring to Scenario 2-17, construct a table of column percentages.

ANSWER: Apparel Company Year 1 Gap 31.00% TJX 20.91% Limited 15.95% Kohl's 14.57% Nordstrom 10.77% Talbots 3.74% Ann Taylor 3.05% Total 100.00% TYPE: PR DIFFICULTY: Moderate KEYWORDS: column percentages

Year 2 25.09% 23.45% 16.18% 17.71% 10.91% 3.39% 3.26% 100.00%

186. Referring to Scenario 2-17, construct a side-by-side bar chart.

ANSWER:

Side-by-side Bar Chart AnnTaylor Talbots Nordstrom Kohl’s Limited

Year 2

TJX

Year 1

1,400.00

1,200.00

1,000.00

800.00

600.00

400.00

200.00

0.00

Gap

Total Sales (millions $) TYPE: PR DIFFICULTY: Moderate KEYWORDS: column percentages, side-by-side bar chart 187. True or False: Referring to Scenario 2-17, in general, retail sales for the apparel industry have seen a modest growth between Year 1 and Year 2.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: column percentages, side-by-side bar chart, interpretation

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Organizing and Visualizing Variables

188. Referring to Scenario 2-17, among the 8 stores, _______ saw a sales decline.

ANSWER: Gap and Talbots TYPE: FI DIFFICULTY: Easy KEYWORDS: column percentages, side-by-side bar chart, interpretation SCENARIO 2-18 The stem-and-leaf display below shows the result of a survey on 50 students on their satisfaction with their school with the higher scores represent higher level of satisfaction.

Stem-and-Leaf Display Stem unit 10 Statistics Sample Size 50 Mean 71.06 Median 73.5 Std. Deviation 14.13695 Minimum 41 Maximum 97

4 13667 5 00389 6 0114457799 7 000134455666788 8 01134457789 9 0227

189. Referring to Scenario 2-18, what was the highest level of satisfaction?

ANSWER: 97 TYPE: PR DIFFICULTY: Easy KEYWORDS: stem-and-leaf display 190. Referring to Scenario 2-18, what was the lowest level of satisfaction?

ANSWER: 41 TYPE: PR DIFFICULTY: Easy KEYWORDS: stem-and-leaf display 191. Referring to Scenario 2-18, how many students have a satisfaction level in the 50s?

ANSWER: 5 TYPE: PR DIFFICULTY: Easy KEYWORDS: stem-and-leaf display 192. Referring to Scenario 2-18, how many students have a satisfaction level below 60?

ANSWER: 10 TYPE: PR DIFFICULTY: Easy KEYWORDS: stem-and-leaf display Copyright ©2020 Pearson Education, Inc.

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193. Referring to Scenario 2-18, how many students have a satisfaction level of at least 80?

ANSWER: 15 TYPE: PR DIFFICULTY: Easy KEYWORDS: stem-and-leaf display 194. True or False: Referring to Scenario 2-18, the level of satisfaction is concentrated around 75.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: stem-and-leaf display 195. True or False: Referring to Scenario 2-18, if a student is randomly selected, his/her most likely level of satisfaction will be in the 70s among the 40s, 50s, 60s, 70s, 80s and 90s.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: stem-and-leaf display 196. True or False: Referring to Scenario 2-18, if a student is randomly selected, his/her most likely level of satisfaction will be in the 60s among the 40s, 50s, 60s, 70s, 80s and 90s.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: stem-and-leaf display

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Organizing and Visualizing Variables

197. True or False: Given below is the scatter plot of the price/earnings ratio versus earnings per share of 20 U.S. companies. There appears to be a negative relationship between price/earnings ratio and earnings per share.

Scatter Plot 70.00 60.00 P/E Ratio

50.00 40.00 30.00 20.00 10.00 0.00 0.00

0.20

0.40

0.60

0.80

1.00

Earning Per Share

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: scatter plot 198. True or False: Given below is the scatter plot of the price/earnings ratio versus earnings per share of 20 U.S. companies. There appear to be a positive relationship between price/earnings ratio and earnings per share.

Scatter Plot 70.00 60.00 P/E Ratio

50.00 40.00 30.00 20.00 10.00 0.00 0.00

0.20

0.40

0.60

0.80

Earning Per Share

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: scatter plot Copyright ©2020 Pearson Education, Inc.

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Organizing and Visualizing Variables

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199. True or False: Given below is the scatter plot of the market value (thousands$) and profit (thousands$) of 50 U.S. companies. Higher market values appear to be associated with higher profits.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: scatter plot 200. True or False: Given below is the scatter plot of the market value (thousands$) and profit (thousands$) of 50 U.S. companies. There appears to be a negative relationship between market value and profit.

Market Value ($000)

Scatter Plot

Profits ($000)

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: scatter plot

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Organizing and Visualizing Variables

201. True or False: Given below is the scatter plot of the number of employees and the total revenue ($millions) of 20 U.S. companies. There appears to be a positive relationship between total revenue and the number of employees.

Employees

Scatter Plot

Revenue ($millions)

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: scatter plot 202. True or False: Given below is the scatter plot of the number of employees and the total revenue ($millions) of 20 U.S. companies. Companies that have higher numbers of employees appear to also have higher total revenue.

Employees

Scatter Plot

Revenue ($millions)

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: scatter plot Copyright ©2020 Pearson Education, Inc.

Organizing and Visualizing Variables

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203. The addition of visual elements that either fail to convey any useful information or that obscure important points about the data to enhance the visualization of data is called _______.

ANSWER: chart junk TYPE: FI DIFFICULTY: Easy KEYWORDS: challenges in visualizing data 204. True or False: The Best Practices for Creating Visual Summaries recommend avoiding uncommon chart type such as doughnut, radar, cone and pyramid charts.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: challenges in visualizing data 205. True or False: The Best Practices for Creating Visual Summaries recommend using the simplest possible visualization.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: challenges in visualizing data 206. True or False: The Best Practices for Creating Visual Summaries recommend labeling all axes only when it is possible.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: challenges in visualizing data 207. True or False: The Best Practices for Creating Visual Summaries recommend using varying scale to conserve precious space whenever possible.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: challenges in visualizing data 208. True or False: The Best Practices for Creating Visual Summaries recommend always starting the scale for a vertical axis at zero.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: challenges in visualizing data

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Organizing and Visualizing Variables

209. True or False: The Best Practices for Creating Visual Summaries recommend always including a scale for each axis if the chart contains axes.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: challenges in visualizing data 210. True or False: When you work with many variables, you must be mindful of the limits of the information technology as well as the limits of the ability of your readers to perceive and comprehend your results.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: organizing and visualizing many variables 211.

True or False: A multidimensional contingency table allows you to tally the responses of more than two continuous variables.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: multidimensional contingency table, organizing and visualizing many variables 212.

True or False: A multidimensional contingency table allows you to tally the responses of more than two categorical variables.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: multidimensional contingency table, organizing and visualizing many variables 213. In determining the class interval width, _______ is the denominator in the formula.

ANSWER: Number of classes TYPE: FI DIFFICULTY: Easy KEYWORDS: frequency distribution

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Numerical Descriptive Measures

CHAPTER 3: NUMERICAL DESCRIPTIVE MEASURES 1. Which of the following statistics is not a measure of central tendency? a) Arithmetic mean. b) Median. c) Mode. d) Q3.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: measure of central tendency, arithmetic mean, median, mode, quartiles 2. Which measure of central tendency can be used for both numerical and categorical variables? a) Arithmetic mean. b) Median. c) Mode. d) Geometric mean.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: measure of central tendency, mode, arithmetic mean, median, geometric mean 3. Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency? a) The arithmetic mean and median only. b) The median and mode only. c) The mode and geometric mean only. d) The arithmetic mean and mode only.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: measure of central tendency, resistant to outliers, mean, median, mode 4. In a right-skewed distribution a) the median equals the arithmetic mean. b) the median is less than the arithmetic mean. c) the median is greater than the arithmetic mean. d) none of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: shape

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3-2

Numerical Descriptive Measures 5. Which of the following statements about the median is not true? a) It is more affected by extreme values than the arithmetic mean. b) It is a measure of central tendency. c) It is equal to Q2. d) It is equal to the mode in bell-shaped "normal" distributions.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: median, measure of central tendency, resistant to outliers, quartile 6. In a perfectly symmetrical bell-shaped "normal" distribution a) the arithmetic mean equals the median. b) the median equals the mode. c) the arithmetic mean equals the mode. d) All the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: shape, normal distribution 7. In a perfectly symmetrical distribution a) the range equals the interquartile range. b) the interquartile range equals the arithmetic mean. c) the median equals the arithmetic mean. d) the variance equals the standard deviation.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: shape 8. When extreme values are present in a set of data, which of the following descriptive summary measures are most appropriate: a) CV and range. b) arithmetic mean and standard deviation. c) interquartile range and median. d) variance and interquartile range.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: resistant to outliers, coefficient of variation, range, arithmetic mean, standard deviation, interquartile range, median, variance

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Numerical Descriptive Measures

3-3

9. In general, which of the following descriptive summary measures cannot be easily approximated from a boxplot? a) The variance. b) The range. c) The interquartile range. d) The median.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: boxplot, variance, range, interquartile range, median 10. The smaller the spread of scores around the arithmetic mean, a) the smaller the interquartile range. b) the smaller the standard deviation. c) the smaller the coefficient of variation. d) All the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: variation, arithmetic mean, interquartile range, standard deviation, coefficient of variation 11. Which descriptive summary measures are resistant statistics? a) The arithmetic mean and standard deviation. b) The interquartile range and range. c) The mode and variance. d) The median and interquartile range.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: resistant to outliers, arithmetic mean, standard deviation, interquartile range, range, mode, variance, median 12. In right-skewed distributions, which of the following is the correct statement? a) The distance from Q1 to Q2 is greater than the distance from Q2 to Q3. b) The distance from Q1 to Q2 is less than the distance from Q2 to Q3. c) The arithmetic mean is less than the median. d) The mode is greater than the arithmetic mean.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: shape, quartiles, arithmetic mean, mode

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3-4

Numerical Descriptive Measures 13. In perfectly symmetrical distributions, which of the following is NOT a correct statement? a) The distance from Q1 to Q2 equals to the distance from Q2 to Q3. b) The distance from the smallest observation to Q1 is the same as the distance from Q3 to the largest observation. c) The distance from the smallest observation to Q2 is the same as the distance from Q2 to the largest observation. d) The distance from Q1 to Q3 is half of the distance from the smallest to the largest observation.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: five-number summary, shape, quartiles 14. In left-skewed distributions, which of the following is the correct statement? a) The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3. b) The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation. c) The distance from the smallest observation to Q2 is less than the distance from Q2 to the largest observation. d) The distance from Q1 to Q3 is twice the distance from the Q1 to Q2.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: five-number summary, shape, quartiles 15. According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______ percent of the observations will be contained within 2 standard deviations around the arithmetic mean. a) 68.26 b) 88.89 c) 93.75 d) 95.44 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: empirical rule, normal distribution

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Numerical Descriptive Measures

3-5

16. According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______ percent of the observations will be contained within 1 standard deviation around the arithmetic mean. a) 68.26 b) 75.00 c) 88.89 d) 93.75 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: empirical rule, normal distribution 17. According to the empirical rule, if the data form a "bell-shaped" normal distribution, _______ percent of the observations will be contained within 3 standard deviations around the arithmetic mean. a) 68.26 b) 75.00 c) 95.0 d) 99.7 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: empirical rule, normal distribution 18. Which of the following is NOT a measure of central tendency? a) The arithmetic mean. b) The geometric mean. c) The mode. d) The interquartile range.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: measure of central tendency, arithmetic mean, geometric mean, mode, interquartile range 19. Which of the following is NOT sensitive to extreme values? a) The range. b) The standard deviation. c) The interquartile range. d) The coefficient of variation.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: resistant to outliers, range, standard deviation, interquartile range, coefficient of variation

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3-6

Numerical Descriptive Measures 20. Which of the following is sensitive to extreme values? a) The median. b) The interquartile range. c) The arithmetic mean. d) The 1st quartile.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: resistant to outliers, median, interquartile range, arithmetic mean, quartiles 21. Which of the following is the easiest to compute? a) The arithmetic mean. b) The median. c) The mode. d) The geometric mean.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mode, arithmetic mean, median, geometric mean 22. According to the Chebyshev rule, at least 75% of all observations in any data set are contained within how many standard deviations around the mean? a) 1 b) 2 c) 3 d) 4 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule 23. According to the Chebyshev rule, at least 93.75% of all observations in any data set are contained within how many standard deviations around the mean? a) 1 b) 2 c) 3 d) 4 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chebyshev rule

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Numerical Descriptive Measures

3-7

24. According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within 3 standard deviations around the mean? a) 67% b) 75% c) 88.89% d) 99.7% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule 25. According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within 2 standard deviations around the mean? a) 67% b) 75% c) 88.89% d) 95% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Chebyshev rule

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3-8

Numerical Descriptive Measures 26. A manufacturer of flashlight batteries took a sample of 130 batteries from a day’s production and used them continuously until they were drained. The number of hours until failure is recorded.

Given below is the boxplot of the number of hours it took to drain each of the 130 batteries. The distribution of the number of hours is

Boxplot

Hours

260

a) b) c) d)

460

660

860

right-skewed left-skewed symmetrical none of the above

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: boxplot

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1060

Numerical Descriptive Measures

3-9

27. Data on the change in the cost of tuition, a shared dormitory room, and the most popular meal plan from one academic year to the next academic year for a sample of 100 public universities are collected. Below is the boxplot for the change in cost in dollars. The distribution of the change in cost is

Boxplot

Change in Cost ($)

300

800 a) b) c) d)

1300

1800

2300

right-skewed left-skewed symmetrical none of the above

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: boxplot SCENARIO 3-1 Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid. The ages of 25 senior citizens were as follows: 60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 28. Referring to Scenario 3-1, calculate the arithmetic mean age of the senior citizens to the nearest hundredth of a year.

ANSWER: 74.04 years TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean 29. Referring to Scenario 3-1, determine the median age of the senior citizens.

ANSWER: 73 years TYPE: PR DIFFICULTY: Easy KEYWORDS: median Copyright ©2020 Pearson Education, Inc.

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Numerical Descriptive Measures

30. Referring to Scenario 3-1 determine the first quartile of the ages of the senior citizens.

ANSWER: 65.5 years TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartiles 31. Referring to Scenario 3-1 determine the third quartile of the ages of the senior citizens.

ANSWER: 81.5 years TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartiles 32. Referring to Scenario 3-1, determine the interquartile range of the ages of the senior citizens.

ANSWER: 16 years TYPE: PR DIFFICULTY: Moderate KEYWORDS: interquartile range 33. Referring to Scenario 3-1, determine which of the following is the correct statement. a) One fourth of the senior citizens sampled are below 65.5 years of age. b) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age. c) The mean age of senior citizens sampled is 73.5 years of age. d) All the above are correct.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: quartiles, arithmetic mean 34. Referring to Scenario 3-1, identify which of the following is the correct statement. a) One fourth of the senior citizens sampled are below 64 years of age. b) The middle 50% of the senior citizens sampled are between 65.5 and 73.0 years of age. c) 25% of the senior citizens sampled are older than 81.5 years of age. d) All the above are correct.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: quartiles 35. Referring to Scenario 3-1, calculate the skewness statistic for the age of the senior citizens accurate to two decimal places.

ANSWER: 0.36 TYPE: PR DIFFICULTY: Moderate KEYWORDS: skewness, shape

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Numerical Descriptive Measures

3-11

36. Referring to Scenario 3-1, what type of shape does the distribution of the sample appear to have?

ANSWER: Slightly positive or right-skewed.

TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape, skewness 37. Referring to Scenario 3-1, calculate the kurtosis statistic for the age of the senior citizens accurate to two decimal places.

ANSWER: -1.01 TYPE: PR DIFFICULTY: Moderate KEYWORDS: kurtosis, shape 38. Referring to Scenario 3-1, does the distribution of the sample appear to be leptokurtic or platykurtic?

ANSWER: leptokurtic TYPE: PR DIFFICULTY: Easy KEYWORDS: kurtosis, shape 39. Referring to Scenario 3-1, calculate the variance of the ages of the senior citizens correct to the nearest hundredth of a year squared.

ANSWER: 94.96 years2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: variance 40. Referring to Scenario 3-1, calculate the standard deviation of the ages of the senior citizens correct to the nearest hundredth of a year.

ANSWER: 9.74 years TYPE: PR DIFFICULTY: Moderate KEYWORDS: standard deviation 41. Referring to Scenario 3-1, calculate the coefficient of variation of the ages of the senior citizens.

ANSWER: 13.16% TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of variation

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3-12

Numerical Descriptive Measures

42. True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 1.9.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: median 43. True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: median 44. True or False: In a set of numerical data, the value for Q3 can never be smaller than the value for Q1.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: quartiles 45. True or False: In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: quartiles 46. True or False: If the distribution of a data set were perfectly symmetrical, the distance from Q1 to the median would always equal the distance from Q3 to the median in a boxplot.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: boxplot, quartiles, shape 47. True or False: In right-skewed distributions, the distance from Q3 to the largest value is greater than the distance from the smallest observation to Q1.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: quartiles, shape

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Numerical Descriptive Measures

3-13

48. True or False: In left-skewed distributions, the distance from the smallest value to Q1 is greater than the distance from Q3 to the largest value.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: five-number summary, quartiles, shape 49. True or False: A boxplot is a graphical representation of a five-number summary.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: boxplot, five-number summary 50. True or False: The five-number summary consists of the smallest value, the first quartile, the median, the third quartile, and the largest value.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: five-number summary 51. True or False: In a boxplot, the box portion represents the data between the first and third quartile values.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: boxplot 52. True or False: The line drawn within the box of the boxplot always represents the arithmetic mean.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: boxplot, arithmetic mean 53. True or False: The line drawn within the box of the boxplot always represents the median.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: boxplot, median

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3-14

Numerical Descriptive Measures

54. True or False: In a sample of size 40, the sample mean is 15. In this case, the sum of all observations in the sample is  X i = 600.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: arithmetic mean 55. True or False: A population with 200 elements has an arithmetic mean of 10. From this information, it can be shown that the population standard deviation is 15.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: arithmetic mean, standard deviation 56. True or False: In exploratory data analysis, a boxplot can be used to illustrate the median, quartiles, and extreme values.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: boxplot, five-number summary 57. True or False: The median of a data set with 20 items would be the average of the 10th and the 11th items in the ordered array.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: median, arithmetic mean 58. True or False: The coefficient of variation measures variability in a data set relative to the size of the arithmetic mean.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of variation 59. True or False: The coefficient of variation is expressed as a percentage.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of variation

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Numerical Descriptive Measures

3-15

60. True or False: The coefficient of variation is a measure of central tendency in the data.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of variation, measure of variation 61. True or False: The interquartile range is a measure of variation or dispersion in a set of data.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: interquartile range, measure of variation 62. True or False: The interquartile range is a measure of central tendency in a set of data.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interquartile range, measure of variation 63. True or False: The geometric mean is a measure of variation or dispersion in a set of data.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: geometric mean, measure of central tendency 64. True or False: The geometric mean is useful in measuring the rate of change of a variable over time.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: geometric mean 65. True or False: If a set of data is perfectly symmetrical, the arithmetic mean must be identical to the median.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: shape, arithmetic mean, median 66. True or False: The coefficient of variation is a measure of relative variation.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: coefficient of variation

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3-16

Numerical Descriptive Measures

67. True or False: If the data set is approximately bell-shaped, the empirical rule will more accurately reflect the greater concentration of data close to the mean as compared to the Chebyshev rule.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: empirical rule, Chebyshev rule, normal distribution 68. If the arithmetic mean of a numerical data set is greater than the median, the data are _______ skewed.

ANSWER: positive or right TYPE: FI DIFFICULTY: Easy KEYWORDS: shape, arithmetic mean, median SCENARIO 3-2 The data below represent the number of grams of carbohydrates in a serving of breakfast cereal in a sample of 11 different servings.

11 15 23 29 19 22 21 20 15 25 17 69. Referring to Scenario 3-2, the arithmetic mean carbohydrates in this sample is ________ grams.

ANSWER: 217/11 = 19.73 TYPE: FI DIFFICULTY: Moderate KEYWORDS: arithmetic mean 70. Referring to Scenario 3-2, the median carbohydrate amount in the cereal is ________ grams.

ANSWER: 20 TYPE: FI DIFFICULTY: Moderate KEYWORDS: median 71. Referring to Scenario 3-2, the skewness statistic for the carbohydrate amount in the cereal is ________.

ANSWER: 0.09 TYPE: FI DIFFICULTY: Moderate KEYWORDS: skewness, shape 72. Referring to Scenario 3-2, is the carbohydrate amount in the cereal right- or left-skewed?

ANSWER: Right-skewed TYPE: PR DIFFICULTY: Easy KEYWORDS: skewness, shape

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Numerical Descriptive Measures

3-17

73. Referring to Scenario 3-2, the kurtosis statistic for the carbohydrate amount in the cereal is ________.

ANSWER: -0.06 TYPE: FI DIFFICULTY: Moderate KEYWORDS: kurtosis, shape 74. Referring to Scenario 3-2, is the carbohydrate amount in the cereal leptokurtic or platykurtic?

ANSWER: platykurtic TYPE: PR DIFFICULTY: Easy KEYWORDS: kurtosis, shape 75. Referring to Scenario 3-2, the first quartile of the carbohydrate amounts is ________ grams.

ANSWER: 15 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 76. Referring to Scenario 3-2, the third quartile of the carbohydrate amounts is ________ grams.

ANSWER: 23 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 77. Referring to Scenario 3-2, the range in the carbohydrate amounts is ________ grams.

ANSWER: 18 TYPE: FI DIFFICULTY: Easy KEYWORDS: range 78. Referring to Scenario 3-2, the interquartile range in the carbohydrate amounts is ________ grams.

ANSWER: 8 TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range 79. Referring to Scenario 3-2, the variance of the carbohydrate amounts is ________ (grams squared).

ANSWER: 26.02 TYPE: FI DIFFICULTY: Moderate KEYWORDS: variance Copyright ©2020 Pearson Education, Inc.

3-18

Numerical Descriptive Measures

80. Referring to Scenario 3-2, the standard deviation of the carbohydrate amounts is ________ grams.

ANSWER: 5.10 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standard deviation 81. Referring to Scenario 3-2, the coefficient of variation of the carbohydrate amounts is ________ percent.

ANSWER: 25.86% TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of variation 82. Referring to Scenario 3-2, the five-number summary of the carbohydrate amounts consists of ________, ________, ________, ________, ________.

ANSWER: 11, 15, 20, 23, 29 TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary 83. Referring to Scenario 3-2, construct a boxplot for the carbohydrate amounts.

ANSWER: Box-and-whisker Plot

10

15

20

25

30

TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot

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Numerical Descriptive Measures

3-19

SCENARIO 3-3 The ordered array below represents the number of vitamin supplements sold by a health food store in a sample of 16 days.

19, 19, 20, 20, 22, 23, 25, 26, 27, 30, 33, 34, 35, 36, 38, 41 Note: For this sample, the sum of the values is 448, and the sum of the squared differences between each value and the mean is 812.

84. Referring to Scenario 3-3, the arithmetic mean of the number of vitamin supplements sold in this sample is ________.

ANSWER: 28 TYPE: FI DIFFICULTY: Easy KEYWORDS: arithmetic mean 85. Referring to Scenario 3-3, the first quartile of the number of vitamin supplements sold in this sample is ________.

ANSWER: 20 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 86. Referring to Scenario 3-3, the third quartile of the number of vitamin supplements sold in this sample is ________.

ANSWER: 35 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 87. Referring to Scenario 3-3, the median number of vitamin supplements sold in this sample is ________.

ANSWER: 26.5 TYPE: FI DIFFICULTY: Moderate KEYWORDS: median 88. Referring to Scenario 3-3, the skewness statistic of the number of vitamin supplements sold in this sample is ________.

ANSWER: 0.29 TYPE: FI DIFFICULTY: Moderate KEYWORDS: skewness, shape

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3-20

Numerical Descriptive Measures

89. Referring to Scenario 3-3, is the number of vitamin supplements sold in this sample right- or leftskewed?

ANSWER: Right-skewed TYPE: PR DIFFICULTY: Easy KEYWORDS: skewness, shape 90. Referring to Scenario 3-3, the kurtosis statistic of the number of vitamin supplements sold in this sample is ________.

ANSWER: -1.32 TYPE: FI DIFFICULTY: Moderate KEYWORDS: kurtosis, shape 91. Referring to Scenario 3-3, is the number of vitamin supplements sold in this sample leptokurtic or platykurtic?

ANSWER: platykurtic TYPE: PR DIFFICULTY: Easy KEYWORDS: kurtosis, shape 92. Referring to Scenario 3-3, the range of the number of vitamin supplements sold in this sample is ________.

ANSWER: 22 TYPE: FI DIFFICULTY: Easy KEYWORDS: range 93. Referring to Scenario 3-3, the interquartile range of the number of vitamin supplements sold in this sample is ________.

ANSWER: 15 TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range 94. Referring to Scenario 3-3, the variance of the number of vitamin supplements sold in this sample is ________.

ANSWER: 54.13 TYPE: FI DIFFICULTY: Easy KEYWORDS: variance

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Numerical Descriptive Measures

3-21

95. Referring to Scenario 3-3, the standard deviation of the number of vitamin supplements sold in this sample is ________.

ANSWER: 7. 36 TYPE: FI DIFFICULTY: Easy KEYWORDS: standard deviation 96. Referring to Scenario 3-3, the coefficient of variation of the number of vitamin supplements sold in this sample is ________ percent.

ANSWER: 26.3% TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of variation 97. Referring to Scenario 3-3, the five-number summary of the data in this sample consists of ________, ________, ________, ________, ________.

ANSWER: 19, 20, 26.5, 35, 41 TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary 98. Referring to Scenario 3-3, construct a boxplot for the data in this sample.

ANSWER: Box-and-whisker Plot

10

20

30

40

TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot 99. Referring to Scenario 3-3, what type of shape does the distribution of the sample appear to have?

ANSWER: Slightly positive or right-skewed.

TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape SCENARIO 3-4 Copyright ©2020 Pearson Education, Inc.

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Numerical Descriptive Measures

The ordered array below represents the number of cargo manifests approved by customs inspectors of the Port of New York in a sample of 35 days: 16, 17, 18, 18, 19, 20, 20, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 27, 28, 28, 29, 29, 31, 31, 32, 32 Note: For this sample, the sum of the values is 838, and the sum of the squared differences between each value and the mean is 619.89.

100. Referring to Scenario 3-4, the arithmetic mean of the customs data is ________.

ANSWER: 23.9 TYPE: FI DIFFICULTY: Easy KEYWORDS: arithmetic mean 101. Referring to Scenario 3-4, the median of the customs data is ________.

ANSWER: 23 TYPE: FI DIFFICULTY: Moderate KEYWORDS: median 102. Referring to Scenario 3-4, the first quartile of the customs data is ________.

ANSWER: 21 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 103. Referring to Scenario 3-4, the third quartile of the customs data is ________.

ANSWER: 27 TYPE: FI DIFFICULTY: Moderate KEYWORDS: quartiles 104. Referring to Scenario 3-4, the range of the customs data is ________.

ANSWER: 16 TYPE: FI DIFFICULTY: Easy KEYWORDS: range 105. Referring to Scenario 3-4, the interquartile range of the customs data is ________.

ANSWER: 6 TYPE: FI DIFFICULTY: Moderate KEYWORDS: interquartile range

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Numerical Descriptive Measures

3-23

106. Referring to Scenario 3-4, the variance of the customs data is ________.

ANSWER: 18.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: variance 107. Referring to Scenario 3-4, the standard deviation of the customs data is ________.

ANSWER: 4.3 TYPE: FI DIFFICULTY: Easy KEYWORDS: standard deviation 108. Referring to Scenario 3-4, the coefficient of variation of the customs data is ________ percent.

ANSWER: 17.8% or 18% TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of variation 109. Referring to Scenario 3-4, the five-number summary for the data in the customs sample consists of ________, ________, ________, ________, ________.

ANSWER: 16, 21, 23, 27, 32 TYPE: FI DIFFICULTY: Moderate KEYWORDS: five-number summary 110. Referring to Scenario 3-4, construct a boxplot of this sample.

ANSWER: Box-and-whisker Plot

10

15

20

25

30

35

TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot

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3-24

Numerical Descriptive Measures

SCENARIO 3-5 The rate of return of a Fortune 500 company over the past 15 years are: 3.17%, 4.43%, 5.93%, 5.43%, 7.29%, 8.21%, 6.23%, 5.23%, 4.34%, 6.68%, 7.14%, -5.56%, -5.23%, -5.73%, -10.34% 111. Referring to Scenario 3-5, compute the arithmetic mean rate of return per year.

ANSWER: 2.48% TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean 112. Referring to Scenario 3-5, compute the geometric mean rate of return per year for the first four years.

ANSWER: 4.73% Geometric mean for the first four values using Excel’s geomean function.

TYPE: PR DIFFICULTY: moderate KEYWORDS: geometric mean rate of return 113. Referring to Scenario 3-5, what is the range of the rate of return?

ANSWER: 18.55% TYPE: PR DIFFICULTY: Easy KEYWORDS: range 114. Referring to Scenario 3-5, construct a boxplot for the rate of return.

ANSWER: Box-and-whisker Plot

-0.15

-0.1

-0.05

0

0.05

0.1

TYPE: PR DIFFICULTY: Easy KEYWORDS: boxplot 115. Referring to Scenario 3-5, what is the shape of the distribution for the rate of return?

ANSWER: Left-skewed TYPE: PR DIFFICULTY: Easy KEYWORDS: shape

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Numerical Descriptive Measures

3-25

SCENARIO 3-6 The rate of return of an Internet Service Provider over a 10-year period are: 10.25%, 12.64%, 8.37%, 9.29%, 6.23%, 42.53%, 29.23%, 15.25%, 21.52%, -2.35%.

116. Referring to Scenario 3-6, compute the arithmetic mean rate of return per year.

ANSWER: 15.30% TYPE: PR DIFFICULTY: Easy KEYWORDS: arithmetic mean 117. Referring to Scenario 3-6, compute the geometric mean rate of return per year for the first three years.

ANSWER: 10.41% TYPE: PR DIFFICULTY: Moderate KEYWORDS: geometric mean rate of return 118. Referring to Scenario 3-6, construct a boxplot for the rate of return ANSWER:

Boxplot

-0.1 0.1 0.3 TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot

0.5

119. Referring to Scenario 3-6, what is the shape of the distribution for the rate of return?

ANSWER: Right-skewed TYPE: PR DIFFICULTY: Moderate KEYWORDS: boxplot, shape 120. You were told that the 1st, 2nd and 3rd quartiles of female students’ weight at a major university are 95 lbs., 125 lbs., and 138 lbs... What percentage of the students weigh more than 138 lbs...?

ANSWER: 25 percent TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartile Copyright ©2020 Pearson Education, Inc.

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Numerical Descriptive Measures

121. You were told that the 1st, 2nd and 3rd quartiles of female students’ weight at a major university are 95 lbs., 125 lbs., and 138 lbs... What percentage of the students weigh less than 95 lbs...?

ANSWER: 25 percent TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartile 122. You were told that the 1st, 2nd and 3rd quartiles of female students’ weight at a major university are 95 lbs., 125 lbs., and 138 lbs... What percentage of the students weigh between 95 and 138 lbs...?

ANSWER: 50 percent TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartile 123. You were told that the 1st, 2nd and 3rd quartiles of female students’ weight at a major university are 95 lbs., 125 lbs., and 138 lbs. What percentage of the students weigh more than 125 lbs...?

ANSWER: 50 percent TYPE: PR DIFFICULTY: Moderate KEYWORDS: quartile 124. The Z scores can be used to identify outliers.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z scores 125. The larger the Z score, the farther is the distance from the value to the median.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z scores 126. As a rule, a value is considered an extreme value if its Z score is greater than3.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score 127. As a rule, a value is considered an extreme value if its Z score is greater than3.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score Copyright ©2020 Pearson Education, Inc.

Numerical Descriptive Measures

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128. As a rule, a value is considered an extreme value if its Z score is less than3.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score 129. As a rule, a value is considered an extreme value if its Z score is less than3.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z score 130. The Z score of a value can never be negative.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z score SCENARIO 3-7 In a recent academic year, many public universities in the United States raised tuition and fees due to a decrease in state subsidies. The change in the cost of tuition, a shared dormitory room, and the most popular meal plan from the previous academic year for a sample of 10 public universities were as follows: $1,589, $593, $1,223, $869, $423, $1,720, $708, $1425, $922 and $308.

131. Referring to Scenario 3-7, what is the mean and median change in the cost?

ANSWER: $978, $895.5 TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean 132. Referring to Scenario 3-7, what is the five-number summary of the change in the cost?

ANSWER: $308, $593, $895.5, $1425, and $1720 TYPE: PR DIFFICULTY: Moderate KEYWORDS: five-number summary 133. Referring to Scenario 3-7, what is the standard deviation of the change in the cost?

ANSWER: $491.8 TYPE: PR DIFFICULTY: Moderate KEYWORDS: standard deviation 134. Referring to Scenario 3-7, what is the interquartile range of the change in the cost?

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Numerical Descriptive Measures

ANSWER: $832 TYPE: PR DIFFICULTY: Moderate KEYWORDS: interquartile range 135. Referring to Scenario 3-7, what is the coefficient of variation of the change in cost?

ANSWER: 50.29% TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of variation 136. Referring to Scenario 3-7, what is the skewness statistic of the change in the cost?

ANSWER: 0.22 TYPE: PR DIFFICULTY: Moderate KEYWORDS: skewness, shape

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Numerical Descriptive Measures

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137. Referring to Scenario 3-7, is the change in the cost right- or left-skewed?

ANSWER: Right-skewed TYPE: PR DIFFICULTY: Easy KEYWORDS: skewness, shape 138. Referring to Scenario 3-7, what is the kurtosis statistic of the change in the cost?

ANSWER: -1.32 TYPE: PR DIFFICULTY: Moderate KEYWORDS: kurtosis, shape 139. Referring to Scenario 3-7, is the change in the cost leptokurtic or platykurtic?

ANSWER: platykurtic TYPE: PR DIFFICULTY: Easy KEYWORDS: skewness, shape 140. Referring to Scenario 3-7, what are the (absolute values of) the Z scores of the change in cost?

ANSWER: 1.24, 0.78, 0.50, 0.22, 1.13, 1.51, 0.55, 0.91, 0.11, 1.36 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Z scores 141. Referring to Scenario 3-7, are the data skewed? If so, how?

ANSWER: skewed to the right TYPE: PR DIFFICULTY: Moderate KEYWORDS: shape

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Numerical Descriptive Measures

SCENARIO 3-8 The following table represents the assets in billions of dollars of the five largest bond funds sometime in the past.

Bond Fund PIMCO Total Return Fund Vanguard Total Bond Market Index Fund Templeton Global Bond Fund Vanguard Total Bond Market Index Fund II Vanguard Inflation-Protected Securities

Assets (Billions $) 246 110 57 56 43

142. Referring to Scenario 3-8, what is the mean for this population of the five largest bond funds?

ANSWER: $102.4 billions TYPE: PR DIFFICULTY: Easy KEYWORDS: population mean 143. Referring to Scenario 3-8, what are the variance and standard deviation for this population?

ANSWER: 5,684.24 squared billion dollars, $75.39 billion dollars, respectively TYPE: PR DIFFICULTY: Moderate KEYWORDS: population variance, population standard deviation SCENARIO 3-10 The population of eight analysts at a software firm were asked to estimate the reuse rate when developing a new software system. The following data are given as a percentage of the total code written for a software system that is part of the reuse database.

50, 62.5, 37.5, 75.0, 45.0, 47.5, 15.0, 25.0 144. Referring to Scenario 3-10, what is the mean percentage of the total code that is part of the reuse database?

ANSWER: 44.69 TYPE: PR DIFFICULTY: Easy KEYWORDS: population mean 145. Referring to Scenario 3-10, what are the variance and standard deviation of the total code that is part of the reuse database?

ANSWER: 324.12 and 18.00, respectively TYPE: PR DIFFICULTY: Moderate KEYWORDS: population variance, population standard deviation

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Numerical Descriptive Measures

3-31

SCENARIO 3-11 Given below are the closing prices for the Dow Jones Industrial Average (DJIA) and the Standard & Poor’s (S&P) 500 Index over 10-weeks sometime in the past.

Dow Jones

10,421

10,110

9,862

10,475

9,920

10,592

11,213

10,933

11,134

10,316

S&P 500

1,379

1,356

1,343

1,410

1,389

1,463

1,529

1,499

1,516

1,355

146. Referring to Scenario 3-11, what is the sample covariance between the DJIA and the S&P 500 index?

ANSWER: 31594.7333 TYPE: PR DIFFICULTY: Easy KEYWORDS: covariance 147. Referring to Scenario 3-11, what is the sample correlation coefficient between the DJIA and the S&P 500 index?

ANSWER: 0.9274 TYPE: PR DIFFICULTY: Easy KEYWORDS: coefficient of correlation 148. Referring to Scenario 3-11, how will you classify the linear relationship between the DJIA and the S&P 500 index? a) Weak b) Moderate c) Strong d) No relationship ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation 149. Referring to Scenario 3-11, for the week when the DJIA is high, you will expect the S&P index in that week to a) be about the same value as the DJIA b) be low c) be high d) have no relationship with the DJIA value ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation

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Numerical Descriptive Measures

150. Referring to Scenario 3-11, you will expect an increase in the DJIA to be associated with a) an increase in the S&P 500 index b) a decrease in the S&P 500 index c) no predictable change in the DJIA d) no predictable change in the S&P 500 index ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation SCENARIO 3-12 Given below are the rating and performance scores of 15 laptop computers.

Performance Score

115

191

153

194

236

184

184

216

Overall Rating

74

78

79

80

84

76

77

92

Performance Score

185

183

189

202

192

141

187

Overall Rating

83

78

77

78

78

73

77

151. Referring to Scenario 3-12, what is the sample covariance between the performance scores and the rating?

ANSWER: 88.8905 TYPE: PR DIFFICULTY: Moderate KEYWORDS: covariance 152. Referring to Scenario 3-12, what is the sample correlation coefficient between the performance scores and the rating?

ANSWER: 0.6629 TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of correlation

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Numerical Descriptive Measures

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153. Referring to Scenario 3-12, how will you classify the linear relationship between the performance scores and the rating? a) Weak b) Moderate c) Strong d) No relationship ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation 154. Referring to Scenario 3-12, for a laptop computer that has a high rating, you will expect its performance score to a) be about the same as its rating b) be low c) be high d) have no relationship with its rating ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation 155. Referring to Scenario 3-12, you will expect a decrease in the performance score of one laptop computer to be associated with a) an increase in its rating b) a decrease in its rating c) no predictable change in its rating d) no predictable change in the performance score of another laptop computer ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation

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Numerical Descriptive Measures

SCENARIO 3-13 Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the current leader in the energy drink market. Given below are the exam scores and the number of 12ounce energy drinks consumed within a week prior to the exam of 10 college students.

Exam Scores

75

92

84

64

64

86

81

61

73

93

Number of Drinks

5

3

2

4

2

7

3

0

1

0

156. Referring to Scenario 3-13, what is the sample covariance between the exam scores and the number of energy drinks consumed?

ANSWER: 3.7667 TYPE: PR DIFFICULTY: Moderate KEYWORDS: covariance 157. Referring to Scenario 3-13, what is the sample correlation coefficient between the exam scores and the number of energy drinks consumed?

ANSWER: 0.1450 TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of correlation 158. Referring to Scenario 3-13, how will you classify the linear relationship between the exam scores and the number of energy drinks consumed? a) Weak b) Moderate c) Strong d) No relationship ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation 159. Referring to Scenario 3-13, for a student who has consumed a high number of energy drinks within the week prior to the exam, you will expect his/her exam score to a) be noticeably higher than the exam score had he/she not consume as much energy drink. b) be noticeably lower than the exam score had he/she not consume as much energy drink. c) not be noticeably different from the amount of energy drinks that he/she consumed. d) not be noticeably different from the exam score had he/she not consumed as much.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of correlation, interpretation

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Numerical Descriptive Measures

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160. Referring to Scenario 3-13, you will expect a decrease in the amount of energy drink consumed within the week prior to the exam to be associated with a) no predictable change in the amount of energy drink consumed after the exam b) an increase in the exam score c) a decrease in the exam score d) no predictable change in the exam score ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation 161. Which of the following measures is used to determine where the data is clustering? a) Variance b) Standard deviation c) Mean d) Combination of mean and standard deviation ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Measures of variation, measures of central tendency

161. Which of the following measures is used to determine variation relative to the mean? a) Variance b) Standard deviation c) Range d) Coefficient of variation ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Coefficient of variation

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Numerical Descriptive Measures

162. A positive kurtosis measure means a sample distribution is ______ peaked than a ________ distribution.

ANSWER: more, Normal TYPE: FI Difficulty: Easy KEYWORDS: kurtosis, normal distribution

163. In a right skewed distribution, the distance from X smallest to Q1 is ______ than the distance from Q3 to X largest.

ANSWER: less TYPE: FI Difficulty: Moderate KEYWORDS: Skew, five number summary

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Basic Probability

4-1

CHAPTER 4: BASIC PROBABILITY 1. If two events are collectively exhaustive, what is the probability that one or the other occurs? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: collectively exhaustive 2. If two events are collectively exhaustive, what is the probability that both occur at the same time? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are mutually exclusive.

3. If two events are mutually exclusive, what is the probability that one or the other occurs? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are collectively exhaustive.

4. If two events are mutually exclusive, what is the probability that both occur at the same time? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mutually exclusive

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4-2

Basic Probability 5. If two events are mutually exclusive and collectively exhaustive, what is the probability that both occur? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: collective exhaustive, mutually exclusive 6. If two events are mutually exclusive and collectively exhaustive, what is the probability that one or the other occurs? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: collectively exhaustive, mutually exclusive 7. If events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are equally likely events.

8. If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: b TYPE: MC DIFFICULTY: easy KEYWORDS: collectively exhaustive, mutually exclusive

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Basic Probability

4-3

9. If two equally likely events A and B are mutually exclusive, what is the probability that event A occurs? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are collectively exhaustive.

10. If two equally likely events A and B are collectively exhaustive, what is the probability that event A occurs? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: collectively exhaustive, mutually exclusive EXPLANATION: We do not know if they are mutually exclusive.

11. Selection of raffle tickets from a large bowl is an example of a) simple probability. b) sampling without replacement. c) subjective probability. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling with replacement, sampling without replacement 12. If two events are independent, what is the probability that they both occur? a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: statistical independence

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4-4

Basic Probability 13. If the outcome of event A is not affected by event B, then events A and B are said to be a) mutually exclusive. b) independent. c) collectively exhaustive. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence 14. If event A and event B cannot occur at the same time, then events A and B are said to be a) mutually exclusive. b) independent. c) collectively exhaustive. d) None of the above.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mutually exclusive 15. If either event A or event B must occur, then events A and B are said to be a) mutually exclusive. b) independent. c) collectively exhaustive. d) None of the above.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: collectively exhaustive 16. The collection of all possible events is called a) a simple probability. b) a sample space. c) a joint probability. d) the null set.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample space

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Basic Probability

4-5

17. All the events in the sample space that are not part of the specified event are called a) simple events. b) joint events. c) the sample space. d) the complement of the event.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample space, complement 18. Simple probability is also called a) marginal probability. b) joint probability. c) conditional probability. d) Bayes' theorem.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability 19. When using the general multiplication rule, P (A and B) is equal to a) P(A|B)P(B). b) P(A)P(B). c) P(B)/P(A). d) P(A)/P(B).

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: multiplication rule 20. A business venture can result in the following outcomes (with their corresponding chance of occurring in parentheses): Highly Successful (10%), Successful (25%), Break Even (25%), Disappointing (20%), and Highly Disappointing (?). If these are the only outcomes possible for the business venture, what is the chance that the business venture will be considered Highly Disappointing? a) 10% b) 15% c) 20% d) 25% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability

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4-6

Basic Probability 21. A survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment) on a certain date in the past.

Interest Rate

Probability

3.20% to 3.29% 0.12

3.30% to 3.39% 0.23

3.40% to 3.49% 0.24

3.50% to 3.59% 0.35

3.60% and above 0.06

If a bank is selected at random from this distribution, what is the chance that the interest rate charged on a home loan will exceed 3.49%? a) 0.06 b) 0.41 c) 0.59 d) 1.00 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: marginal probability, addition rule 22. The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is single or has a college degree is: a) 0.10 b) 0.25 c) 0.667 d) 0.733 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: addition rule 23. The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company is married and has a college degree is: a) 0.0667 b) 0.567 c) 0.667 d) 0.833 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability

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Basic Probability

4-7

24. The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company does not have a college degree is: a) 0.10 b) 0.33 c) 0.67 d) 0.75 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: complement 25. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is: a) 0.10 b) 0.185 c) 0.705 d) 0.90 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability 26. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that neither house sales nor interest rates will increase during the next 6 months is: a) 0.10 b) 0.195 c) 0.89 d) 0.90 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, complement

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4-8

Basic Probability 27. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that house sales will increase but interest rates will not during the next 6 months is: a) 0.065 b) 0.15 c) 0.51 d) 0.89 ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: joint probability, marginal probability, complement EXPLANATION: P(H and I) = P(H) + P(I) – P(H or I); P(H and I) + P(H and Not I) = P(H); P(H and Not I) = P(H) – P(H and I) 28. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events increase in house sales and increase in interest rates in the next 6 months are a) independent. b) mutually exclusive. c) collectively exhaustive. d) None of the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, statistical independence EXPLANATION: They are not statistically independent.

29. The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The events increase in house sales and no increase in house sales in the next 6 months are a) independent. b) mutually exclusive. c) collectively exhaustive. d) (b) and (c) ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: mutually exclusive, collectively exhaustive, complement

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Basic Probability

4-9

30. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. If the two events are independent, the probability that the cost is kept within budget and the campaign will increase sales is: a) 0.20 b) 0.32 c) 0.40 d) 0.88 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, joint probability, multiplication rule 31. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. If the two events are independent, the probability that the cost is kept within budget or the campaign will increase sales is: a) 0.20 b) 0.32 c) 0.68 d) 0.88 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, addition rule 32. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. If the two events are independent, the probability that the cost is not kept within budget or the campaign will not increase sales is: a) 0.12 b) 0.32 c) 0.68 d) 0.88 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, addition rule, complement

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4-10

Basic Probability

33. The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. If the two events are independent, the probability that neither the cost is kept within budget nor the campaign will increase sales is: a) 0.12 b) 0.32 c) 0.68 d) 0.88 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule, joint probability, complement 34. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income over $50,000 a year is: a) 0.12 b) 0.18 c) 0.22 d) 0.48 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: joint probability, conditional probability 35. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $50,000 a year is: a) 0.12 b) 0.18 c) 0.22 d) 0.48 ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: joint probability, complement, multiplication rule, conditional probability

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Basic Probability

4-11

36. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that the residents of a household own 2 cars and have an income less than or equal to $50,000 a year is: a) 0.12 b) 0.18 c) 0.22 d) 0.48 ANSWER: ( was not able to get the book answer to this one) c TYPE: MC DIFFICULTY: Difficult KEYWORDS: joint probability, complement, multiplication rule, conditional probability 37. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that annual household income is over $50,000 if the residents of a household own 2 cars is: a) 0.42 b) 0.48 c) 0.50 d) 0.69 ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability 38. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that annual household income is over $50,000 if the residents of a household do not own 2 cars is: a) 0.12 b) 0.18 c) 0.40 d) 0.70 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability, complement

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Basic Probability

39. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. The probability that the residents do not own 2 cars if annual household income is not over $50,000 is: a) 0.12 b) 0.18 c) 0.45 d) 0.70 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: conditional probability, complement 40. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given that a widget was produced by the new machine, what is the probability it is not defective? a) 0.06 b) 0.50 c) 0.92 d) 0.94 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: conditional probability, complement 41. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. What is the probability that a randomly chosen widget produced by the company is defective? a) 0.078 b) 0.1175 c) 0.156 d) 0.310 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: marginal probability

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42. A company has 2 machines that produce widgets. An older machine produces 23% defective widgets, while the new machine produces only 8% defective widgets. In addition, the new machine produces 3 times as many widgets as the older machine does. Given a randomly chosen widget was tested and found to be defective, what is the probability it was produced by the new machine? a) 0.08 b) 0.15 c) 0.489 d) 0.511 ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability SCENARIO 4-1 Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed.

Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Did alcohol play a role?

Yes No Totals

Number of Vehicles Involved 1 2 3 50 100 20 25 175 30 75 275 50

Totals 170 230 400

43. Referring to Scenario 4-1, what proportion of accidents involved more than one vehicle? a) 50/400 or 12.5% b) 75/400 or 18.75% c) 275/400 or 68.75% d) 325/400 or 81.25% ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule

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44. Referring to Scenario 4-1, what proportion of accidents involved alcohol and a single vehicle? a) 25/400 or 6.25% b) 50/400 or 12.5% c) 195/400 or 48.75% d) 245/400 or 61.25% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, joint probability 45. Referring to Scenario 4-1, what proportion of accidents involved alcohol or a single vehicle? a) 25/400 or 6.25% b) 50/400 or 12.5% c) 195/400 or 48.75% d) 245/400 or 61.25% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule 46. Referring to Scenario 4-1, given alcohol was involved, what proportion of accidents involved a single vehicle? a) 50/75 or 66.67% b) 50/170 or 29.41% c) 120/170 or 70.59% d) 120/400 or 30% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, marginal probability 47. Referring to Scenario 4-1, given that multiple vehicles were involved, what proportion of accidents involved alcohol? a) 120/170 or 70.59% b) 120/230 or 52.17% c) 120/325 or 36.92% d) 120/400 or 30% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, addition rule

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48. Referring to Scenario 4-1, given that 3 vehicles were involved, what proportion of accidents involved alcohol? a) 20/30 or 66.67% b) 20/50 or 40% c) 20/170 or 11.77% d) 20/400 or 5% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability 49. Referring to Scenario 4-1, given that alcohol was not involved, what proportion of the accidents were single vehicle? a) 50/75 or 66.67% b) 25/230 or 10.87% c) 50/170 or 29.41% d) 25/75 or 33.33% ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, complement 50. Referring to Scenario 4-1, given that alcohol was not involved, what proportion of the accidents were multiple vehicle? a) 50/170 or 29.41% b) 120/170 or 70.59% c) 205/230 or 89.13% d) 25/230 or 10.87% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability, complement

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SCENARIO 4-2 An alcohol awareness task force at a Big-Ten university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following result was obtained.

Studying for Exam Went Bar Hopping

Did Well on Midterm 80 30

Did Poorly on Midterm 20 70

51. Referring to Scenario 4-2, what is the probability that a randomly selected student who went bar hopping did well on the midterm? a) 30/100 or 30% b) 30/110 or 27.27% c) 30/200 or 15% d) (100/200) *(110/200) or 27.50% ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, conditional probability 52. Referring to Scenario 4-2, what is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm? a) 30/200 or 15% b) (80+30)/200 or (30+80)/200 or 55% c) (30+70)/200 or (70+30)/200 or 50% d) (80+30+70)/200 or (110+100-30)/200 or 90% ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, addition rule 53. Referring to Scenario 4-2, what is the probability that a randomly selected student did well on the midterm and went bar hopping the weekend before the midterm? a) 30/200 or 15% b) (80+30)/200 or 55% c) (30+70)/200 or 50% d) (80+30+70)/200 or 90% ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, joint probability

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54. Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are a) dependent. b) mutually exclusive. c) collective exhaustive. d) None of the above.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, contingency table, empirical classical probability, joint probability 55. Referring to Scenario 4-2, the events "Did Well on Midterm" and "Studying for Exam" are a) not dependent. b) not mutually exclusive. c) collective exhaustive. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, empirical classical probability, mutually exclusive, joint probability 56. Referring to Scenario 4-2, the events "Did Well on Midterm" and "Did Poorly on Midterm" are a) dependent. b) mutually exclusive. c) collective exhaustive. d) All the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence, mutually exclusive, collective exhaustive, contingency table, empirical classical probability, joint probability 57. True or False: When A and B are mutually exclusive, P (A or B) can be found by adding P(A) and P(B).

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive, addition rule 58. True or False: The collection of all the possible events is called a sample space.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sample space

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59. True or False: If A and B cannot occur at the same time they are called mutually exclusive.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive 60. True or False: If either A or B must occur they are called mutually exclusive.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive, collective exhaustive 61. True or False: If either A or B must occur they are called collectively exhaustive.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: collective exhaustive 62. True or False: If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: collective exhaustive, mutually exclusive 63. True or False: If P(A) = 0.4 and P(B) = 0.6, then A and B must be mutually exclusive.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: mutually exclusive 64. True or False: If P (A or B) = 1.0, then A and B must be mutually exclusive.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: mutually exclusive, collective exhaustive 65. True or False: If P (A or B) = 1.0, then A and B must be collectively exhaustive.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: collective exhaustive

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66. True or False: If P (A and B) = 0, then A and B must be mutually exclusive.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mutually exclusive 67. True or False: If P (A and B) = 0, then A and B must be collectively exhaustive.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: collectively exhaustive, mutually exclusive 68. True or False: If P (A and B) = 1, then A and B must be collectively exhaustive.

ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: collective exhaustive 69. True or False: If P (A and B) = 1, then A and B must be mutually exclusive.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: mutually exclusive, collective exhaustive 70. Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P (A and B) = __________.

ANSWER: 0.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: statistical independence, multiplication rule 71. Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P (A and B) = __________.

ANSWER: 0 TYPE: FI DIFFICULTY: Easy KEYWORDS: mutually exclusive, joint probability, multiplication rule 72. Suppose A and B are mutually exclusive events where P(A) = 0.4 and P(B) = 0.5. Then P (A or B) = __________.

ANSWER: 0.9 TYPE: FI DIFFICULTY: Easy KEYWORDS: mutually exclusive, addition rule

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Basic Probability

73. Suppose A and B are independent events where P(A) = 0.4 and P(B) = 0.5. Then P (A or B) = __________.

ANSWER: 0.7 TYPE: FI DIFFICULTY: Easy KEYWORDS: statistical independence, addition rule 74. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P (A and B) = 0.1.

Then P (A or B) = __________.

ANSWER: 0.8 TYPE: FI DIFFICULTY: Easy KEYWORDS: addition rule 75. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P (A and B) = 0.1.

Then P(A|B) = __________.

ANSWER: 0.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability 76. Suppose A and B are events where P(A) = 0.4, P(B) = 0.5, and P (A and B) = 0.1.

Then P(B|A) = __________.

ANSWER: 0.25 TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability SCENARIO 4-3 A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger.

77. Referring to Scenario 4-3, the probability that a randomly selected individual is an adult is __________.

ANSWER: 125/200 or 62.5% TYPE: FI DIFFICULTY: Moderate KEYWORDS: marginal probability, empirical probability

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78. Referring to Scenario 4-3, the probability that a randomly selected individual is an adult, or a child is __________.

ANSWER: 200/200 or 100% TYPE: FI DIFFICULTY: Moderate KEYWORDS: addition rule, empirical probability 79. Referring to Scenario 4-3, the probability that a randomly selected individual is a child and prefers chicken is __________.

ANSWER: 20/200 or 10% TYPE: FI DIFFICULTY: Moderate KEYWORDS: joint probability, multiplication rule, empirical probability 80. Referring to Scenario 4-3, the probability that a randomly selected individual is an adult and prefers chicken is __________.

ANSWER: 60/200 or 30% TYPE: FI DIFFICULTY: Moderate KEYWORDS: joint probability, multiplication rule, empirical probability 81. Referring to Scenario 4-3, the probability that a randomly selected individual is a child or prefers hamburger is __________.

ANSWER: 140/200 or 70% TYPE: FI DIFFICULTY: Moderate KEYWORDS: empirical probability, addition rule 82. Referring to Scenario 4-3, assume we know the person is a child. The probability that this individual prefers hamburger is __________.

ANSWER: 55/75 or 73.33% TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability, empirical probability 83. Referring to Scenario 4-3, assume we know that a person prefers chicken. The probability that this individual is an adult is __________.

ANSWER: 60/80 or 75% TYPE: FI DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, empirical classical probability, conditional probability

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84. Referring to Scenario 4-3, assume we know that a person prefers hamburger. The probability that this individual is a child is __________.

ANSWER: 55/120 or 45.83% TYPE: FI DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, conditional probability, empirical classical probability SCENARIO 4-4 Suppose that patrons of a restaurant were asked whether they preferred water or whether they preferred soda. 70% said that they preferred water. 60% of the patrons were male. 80% of the males preferred water.

85. Referring to Scenario 4-4, the probability a randomly selected patron prefers soda is __________.

ANSWER: 0.30 TYPE: FI DIFFICULTY: Moderate KEYWORDS: addition rule, multiplication rule, marginal probability 86. Referring to Scenario 4-4, the probability a randomly selected patron is a female is __________.

ANSWER: 0.40 TYPE: FI DIFFICULTY: Moderate KEYWORDS: addition rule, multiplication rule, marginal probability 87. Referring to Scenario 4-4, the probability a randomly selected patron is a female who prefers soda is __________.

ANSWER: 0.18 TYPE: FI DIFFICULTY: Difficult KEYWORDS: joint probability, multiplication rule, addition rule 88. Referring to Scenario 4-4, the probability a randomly selected patron is a female who prefers water is __________.

ANSWER: 0.22 TYPE: FI DIFFICULTY: Difficult KEYWORDS: joint probability, addition rule, multiplication rule

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89. Referring to Scenario 4-4, suppose a randomly selected patron prefers soda. Then the probability the patron is a male is __________.

ANSWER: 0.40 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability, addition rule, multiplication rule 90. Referring to Scenario 4-4, suppose a randomly selected patron prefers water. Then the probability the patron is a male is __________.

ANSWER: 0.69 TYPE: FI DIFFICULTY: Difficult KEYWORDS: addition rule, multiplication rule, conditional probability 91. Referring to Scenario 4-4, suppose a randomly selected patron is a female. Then the probability the patron prefers water is __________.

ANSWER: 0.55 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, addition rule, multiplication rule, conditional probability 92. True or False: Referring to Scenario 4-4, the two events "preferring water" and "preferring soda" are independent.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: statistical independence, addition rule, multiplication rule 93. True or False: Referring to Scenario 4-4, the two events "preferring water" and “being a male” are independent.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: statistical independence, addition rule, multiplication rule

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SCENARIO 4-5 In a meat packaging plant Machine A accounts for 60% of the plant's output, while Machine B accounts for 40% of the plant's output. In total, 4% of the packages are improperly sealed. Also, 3% of the packages are from Machine A and are improperly sealed.

94. Referring to Scenario 4-5, if a package is selected at random, the probability that it will be properly sealed is ________.

ANSWER: 0.96 TYPE: FI DIFFICULTY: Moderate KEYWORDS: addition rule, marginal probability 95. Referring to Scenario 4-5, if a package selected at random is improperly sealed, the probability that it came from machine A is ________.

ANSWER: 0.75 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability 96. Referring to Scenario 4-5, if a package selected at random came from Machine A, the probability that it is improperly sealed is ________.

ANSWER: 0.05 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability 97. Referring to Scenario 4-5, if a package selected at random came from Machine B, the probability that it is properly sealed is ________.

ANSWER: 0.975 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, addition rule 98. Referring to Scenario 4-5, if a package selected at random came from Machine B, the probability that it is improperly sealed is ________.

ANSWER: 0.025 TYPE: FI DIFFICULTY: Difficult KEYWORDS: conditional probability, complement, addition rule

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SCENARIO 4-6 At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out-of-state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-staters have passed the ELM. 99. Referring to Scenario 4-6, the probability that a randomly selected student is someone from northern Texas who has not passed the ELM is ________.

ANSWER: 0.09 TYPE: FI DIFFICULTY: Difficult KEYWORDS: joint probability, multiplication rule 100. Referring to Scenario 4-6, the probability that a randomly selected student has passed the ELM is ________.

ANSWER: 0.66 TYPE: FI DIFFICULTY: Difficult KEYWORDS: marginal probability, multiplication rule, addition rule 101. Referring to Scenario 4-6, if a randomly selected student has passed the ELM, the probability the student is from out-of-state is ________.

ANSWER: 0.136 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability 102. Referring to Scenario 4-6, if a randomly selected student has not passed the ELM, the probability the student is from southern Texas is ________.

ANSWER: 0.706 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability, complement 103. Referring to Scenario 4-6, the probability that a randomly selected student is not from southern Texas and has not passed the ELM is ________.

ANSWER: 0.10 TYPE: FI DIFFICULTY: Difficult KEYWORDS: joint probability, complement, multiplication rule, addition

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104. Referring to Scenario 4-6, if a randomly selected student has not passed the ELM, the probability the student is not from northern Texas is ________.

ANSWER: 0.735 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability, complement, addition rule, multiplication rule 105. Referring to Scenario 4-6, if a randomly selected student is not from southern Texas, the probability the student has not passed the ELM is ________.

ANSWER: 0.25 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability, complement, addition rule, multiplication rule 106. Referring to Scenario 4-6, if a randomly selected student is not from out-of-state, the probability the student has passed the ELM is ________.

ANSWER: 0.633 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability, complement, addition rule, multiplication rule SCENARIO 4-7 The next state lottery will have the following payoffs possible with their associated probabilities.

Payoff Probability $2.00 0.0500 $25.00 0.0100 $100.00 0.0050 $500.00 0.0010 $5,000.00 0.0005 $10,000.00 0.0001 You buy a single ticket.

107. Referring to Scenario 4-7, the probability that you win any money is ________.

ANSWER: 0.0666 TYPE: FI DIFFICULTY: Easy KEYWORDS: addition rule, empirical probability

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108. Referring to Scenario 4-7, the probability that you win at least $100.00 is ________.

ANSWER: 0.0066 TYPE: FI DIFFICULTY: Easy KEYWORDS: addition rule, empirical probability 109. Referring to Scenario 4-7, if you have a winning ticket, the probability that you win at least $100.00 is ________.

ANSWER: 0.10 TYPE: FI DIFFICULTY: Moderate KEYWORDS: conditional probability, addition rule, empirical probability 110. The closing price of a company’s stock tomorrow can be lower, higher or the same as today’s closed. Without any prior information that may affect the price of the stock tomorrow, the probability that it will close higher than today’s close is 1/3. This is an example of using which of the following probability approach? a) A priori probability b) Empirical probability c) Subjective probability d) Conditional probability ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: a priori probability, empirical probability, subjective probability 111. The closing price of a company’s stock tomorrow can be lower, higher or the same as today’s closing price. Based on the closing price of the stock collected over the last month, 25% of the days the closing price was higher than previous day’s closing price, 45% was lower than previous day’s and 30% was the same as previous day’s. Based on this information, the probability that tomorrow’s closing price will be higher than today’s is 25%. This is an example of using which of the following probability approach? a) A priori probability b) Empirical probability c) Subjective probability d) Conditional probability ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: a priori probability, empirical probability, subjective probability

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112. The closing price of a company’s stock tomorrow can be lower, higher or the same as today’s closing price. After evaluating all the information available on the company’s fundamentals and the economic environment, an analyst has determined that the probability that tomorrow’s closing price will be higher than today’s is determined to be 25%. This is an example of using which of the following probability approach? a) A priori probability b) Empirical probability c) Subjective probability d) Conditional probability ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: a priori probability, empirical probability, subjective probability SCENARIO 4-8 According to the record of the registrar’s office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior and the rest are senior. Among the freshmen, sophomores, juniors and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30% and 20%.

113. Referring to Scenario 4-8, what is the probability that a randomly selected student is a freshman who lives in a dormitory?

ANSWER: 0.28 TYPE: PR DIFFICULTY: Easy KEYWORDS: joint probability, multiplication rule 114. Referring to Scenario 4-8, what is the probability that a randomly selected student is a sophomore who does not live in a dormitory?

ANSWER: 0.1 TYPE: PR DIFFICULTY: Easy KEYWORDS: joint probability, multiplication rule, complement 115. Referring to Scenario 4-8, what is the probability that a randomly selected student is a junior who does not live in a dormitory?

ANSWER: 0.112 TYPE: PR DIFFICULTY: Easy KEYWORDS: joint probability, multiplication rule, complement

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116. Referring to Scenario 4-8, what is the probability that a randomly selected student is a junior or senior who lives in a dormitory?

ANSWER: 0.096 TYPE: PR DIFFICULTY: Moderate KEYWORDS: joint probability, multiplication rule, addition rule 117. Referring to Scenario 4-8, what proportion of the students live in a dormitory?

ANSWER: 0.526 TYPE: PR DIFFICULTY: Easy KEYWORDS: marginal probability, multiplication rule, addition rule 118. Referring to Scenario 4-8, what proportion of the students do not live in a dormitory?

ANSWER: 0.474 TYPE: PR DIFFICULTY: Easy KEYWORDS: marginal probability, multiplication rule, addition rule 119. Referring to Scenario 4-8, if a randomly selected student lives in the dormitory, what is the probability that the student is a freshman?

ANSWER: 0.532 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, conditional probability 120. Referring to Scenario 4-8, if a randomly selected student lives in the dormitory, what is the probability that the student is not a freshman?

ANSWER: 0.468 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, conditional probability, complement, addition rule 121. Referring to Scenario 4-8, if a randomly selected student does not live in the dormitory, what is the probability that the student is a junior or a senior?

ANSWER: 0.641 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, conditional probability, complement, addition rule

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122. Referring to Scenario 4-8, determine whether the class status of a student and whether the student lives in a dormitory are independent.

ANSWER: Not independent TYPE: PR DIFFICULTY: Easy KEYWORDS: statistical independence SCENARIO 4-9 A survey conducted by the Segal Company of New York found that in a sample of 189 large companies, 40 offered stock options to their board members as part of their non-cash compensation packages. For small- to mid-sized companies, 43 of the 180 surveyed indicated that they offer stock options as part of their noncash compensation packages to their board members.

123. Referring to Scenario 4-9, set up a contingency table.

ANSWER: Large Stock Options

Yes No

Company Size Small-to-midsized 40 43 149 137 189 180

83 286 369

TYPE: PR DIFFICULTY: Moderate KEYWORDS: contingency table 124. Referring to Scenario 4-9, if a company is selected at random, what is the probability that the company offered stock options to their board members?

ANSWER: 83/369 = 0.2249 or 22.49% TYPE: PR DIFFICULTY: Easy KEYWORDS: marginal probability, contingency table 125. Referring to Scenario 4-9, if a company is selected at random, what is the probability that the company is small to mid-sized and did not offer stock options to their board members?

ANSWER: 137/369 = 0.3713 or 37.13% TYPE: PR DIFFICULTY: Easy KEYWORDS: joint probability, contingency table 126. Referring to Scenario 4-9, if a company is selected at random, what is the probability that the company is small to mid-sized or offered stock options to their board members?

ANSWER: 220/369 = 0.5962 or 59.62% TYPE: PR DIFFICULTY: Easy KEYWORDS: addition rule, contingency table

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127. Referring to Scenario 4-9, if a randomly selected company is a large company, what is the probability that it offered stock options to their board members?

ANSWER: 40/189 = 0.2116 or 21.16% TYPE: PR DIFFICULTY: Easy KEYWORDS: conditional probability, contingency table 128. Referring to Scenario 4-9, if a randomly selected company offered stock options to their board members, what is the probability that it is a large company?

ANSWER: 40/83 = 0.4819 or 48.19% TYPE: PR DIFFICULTY: Easy KEYWORDS: conditional probability, contingency table 129. Referring to Scenario 4-9, is the size of the company independent of whether stock options are offered to their board members and why?

ANSWER: No, because P(stock option) is not equal to P(stock option | large) TYPE: PR DIFFICULTY: Moderate KEYWORDS: statistical independence, conditional probability, contingency table SCENARIO 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were black and 10% are other races. Given that a worker was white, the probability that the worker had claimed bias was 30%. Given that a worker was black, the probability that the worker had claimed bias was 40%. Given that a worker was other race, the probability that the worker had claimed bias was 0%.

130. Referring to Scenario 4-10, what is the probability that a randomly selected worker had not claimed bias?

ANSWER: 0.7 or 70% TYPE: PR DIFFICULTY: Moderate KEYWORDS: complement, marginal probability, multiplication rule 131. Referring to Scenario 4-10, if a randomly selected worker had claimed bias, what is the probability that the worker is white?

ANSWER: 0.6 or 60% TYPE: PR DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, conditional probability

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132. Referring to Scenario 4-10, if a randomly selected worker had not claimed bias, what is the probability that the worker is white?

ANSWER: 0.6 or 60% TYPE: PR DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, conditional probability 133. Referring to Scenario 4-10, what is the probability that a randomly selected worker is white and had claimed bias?

ANSWER: 0.18 or 18% TYPE: PR DIFFICULTY: Moderate KEYWORDS: joint probability, multiplication rule 134. Referring to Scenario 4-10, what is the probability that a randomly selected worker is black and had not claimed bias?

ANSWER: 0.18 or 18% TYPE: PR DIFFICULTY: Moderate KEYWORDS: joint probability, multiplication rule 135. Referring to Scenario 4-10, what is the probability that a randomly selected worker is black and had not claimed bias or is white and has claimed bias?

ANSWER: 0.36 or 36% TYPE: PR DIFFICULTY: Moderate KEYWORDS: joint probability, multiplication rule, addition rule 136. Referring to Scenario 4-10, what is the probability that a randomly selected worker is not black and had not claimed bias?

ANSWER: 0.52 or 52% TYPE: PR DIFFICULTY: Moderate KEYWORDS: joint probability, multiplication rule, addition rule 137. Referring to Scenario 4-10, when a randomly selected worker was not white, what is the probability that the worker had not claimed bias?

ANSWER: 0.7 or 70% TYPE: PR DIFFICULTY: Moderate KEYWORDS: conditional probability, multiplication rule, addition rule

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138. You know that the probability of a randomly selected student will cheat on an exam is 1%. You also know that the probability of a randomly selected student will cheat on an exam knowing that his/her fellow classmate is cheating on the exam is also 1%. Which of the following is true about the event of "the randomly selected student cheating on an exam" and "his/her classmate is cheating on the exam"? a) They are mutually exclusive. b) They are collectively exhaustive. c) They are independent. d) None of the above.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: statistical independence 139. True or False: To ethically advertise a school lottery scheme to try to raise money for the athletic department, the organizer of the lottery does not need to explicitly specify the probability of each of the prize in the lottery.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issues 140. True or False: An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of exceptionally high gain. It is an unethical practice to tell the clienteles the probability of a loss in her recommendations.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issues 141. True or False: An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of gain. It is an ethical practice to explain to the clienteles what the basis of her probability estimate is.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issues 142. True or False: An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of gain. It is an ethical practice to explain to the clienteles what the meaning of probability is.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issues

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143. True or False: An investment consultant is recommending a certain class of mutual funds to the clienteles based on its exceptionally high probability of gain. It is an unethical practice not to also recommend a class of mutual funds with an exceptionally high probability of loss.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: ethical issues SCENARIO 4-11 A sample of 300 adults is selected. The contingency table below shows their registration status and their preferred source of information on current events.

Preferred source of information Voting registration status

Television

Newspapers

Radio

Internet

Registered

45

30

45

36

Not registered

35

44

45

20

144. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she prefers to get his/her current information from the internet?

ANSWER: 56/300 = 0.1867 or 18.67% TYPE: PR DIFFICULTY: Easy KEYWORDS: marginal probability, contingency table 145. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter?

ANSWER: 156/300 = 0.52 or 52% TYPE: PR DIFFICULTY: Easy KEYWORDS: marginal probability, contingency table 146. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter and prefers to get his/her current information from the television?

ANSWER: 45/300 = 0.15 or 15% TYPE: PR DIFFICULTY: Easy KEYWORDS: joint probability, contingency table

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147. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter who does not prefer to get his/her current information from the internet?

ANSWER: 120/300 = 0.4 or 40% TYPE: PR DIFFICULTY: Moderate KEYWORDS: joint probability, complement, and addition rule, contingency table 148. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter or prefers to get his/her current information from radio?

ANSWER: 201/300 = 0.67 or 67% TYPE: PR DIFFICULTY: Easy KEYWORDS: addition rule, contingency table 149. Referring to Scenario 4-11, if an adult is selected at random, what is the probability that he/she is a not a registered voter or does not prefer to get his/her current information from the internet?

ANSWER: 264/300 = 0.88 or 88% TYPE: PR DIFFICULTY: Moderate KEYWORDS: addition rule, contingency table 150. Referring to Scenario 4-11, if a randomly selected adult is a registered voter, what is the probability that he/she prefers to get his/her current information from the newspapers?

ANSWER: 30/156 = 0.1923 or 19.23% TYPE: PR DIFFICULTY: Easy KEYWORDS: conditional probability, contingency table 151. Referring to Scenario 4-11, what is the probability that an adult who prefers to get his/her current information from the internet will be a registered voter?

ANSWER: 36/56 = 0.6429 or 64.29% TYPE: PR DIFFICULTY: Easy KEYWORDS: conditional probability, contingency table 152. Referring to Scenario 4-11, is the preferred source of current information independent of the voting registration status?

ANSWER: No, because P(registered) is not equal to P(registered | television) TYPE: PR DIFFICULTY: Moderate KEYWORDS: statistical independence, conditional probability

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SCENARIO 4-12 Jake woke up late in the morning on the day that he has to go to school to take an important test. He can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice.

153. Referring to Scenario 4-12, if Jake, in fact, gets to the test on time, what is the probability that he took the bus?

ANSWER: 0.5714 or 57.14% TYPE: PR DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability, complement rule 154. Referring to Scenario 4-12, if Jake, in fact, gets to the test on time, what is the probability that he rode his motorcycle?

ANSWER: 0.4286 or 42.86% TYPE: PR DIFFICULTY: Difficult KEYWORDS: Bayes’ theorem, conditional probability, complement rule 155. Referring to Scenario 4-12, if Jake is late to the test, what is the probability that he rode his motorcycle?

ANSWER: 0.6667 or 66.67% TYPE: PR DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, conditional probability 156. Referring to Scenario 4-12, if Jake is late to the test, what is the probability that he took the bus?

ANSWER: 0.3333 or 33.33% TYPE: PR DIFFICULTY: Moderate KEYWORDS: Bayes’ theorem, conditional probability 157. A new model car from Ford Motor Company offers a keyless entry system that utilizes a fourletter code. How many different possible outcomes are there for the code?

ANSWER: 456,976 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule

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Basic Probability

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158. At the International Pancakes Hut, there are 4 different ways to have an egg cooked, 7 different choices of pancakes, 5 different types of syrups and 8 different beverages. How many different ways are there to order an egg, a pancake with a choice of syrup and a beverage?

ANSWER: 1,120 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule 159. There are 10 finalists at a national dog show. How many different orders of finishing can there be for all the 10 finalists?

ANSWER: 3,628,800 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, permutation 160. Eleven freshmen are to be assigned to eleven empty rooms in a student dormitory. Each room is considered unique so that it matters who is being assigned to which room. How many different ways can those eleven freshmen be allocated?

ANSWER: 39,916,800 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, permutation 161. There are only 4 empty rooms available in a student dormitory for eleven new freshmen. Each room is considered unique so that it matters who is being assigned to which room. How many different ways can those 4 empty rooms be filled one student per room?

ANSWER: 7,920 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, permutation 162. There are only 4 empty rooms available in a student dormitory for eleven new freshmen. All the rooms are considered as homogenous so that it does not matter who is being assigned to which room. How many different ways can those 4 empty rooms be filled one student per room?

ANSWER: 330 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, combination

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163. Four freshmen are to be assigned to eleven empty rooms in a student dormitory. All the rooms are considered as homogenous so that it does not matter who is being assigned to which room.

How many different ways can those 4 freshmen be assigned?

ANSWER: 330 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, combination 164. There are 47 contestants at a national dog show. How many different ways can contestants fill the first place, second place, and third place positions?

ANSWER: 97,290 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, permutation 165. Seven passengers are on a waiting list for an overbooked flight. As a result of cancellations, 3 seats become available. How many ways can those 3 available seats be filled regardless of the order?

ANSWER: 35 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, combination 166. A high school debate team of 4 is to be chosen from a class of 35. How many possible ways can the team be formed?

ANSWER: 52,360 TYPE: PR DIFFICULTY: Easy KEYWORDS: counting rule, combination 167. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.

How many possible ways can the team be formed which will include only one of the twin brothers?

ANSWER: 10,912 TYPE: PR DIFFICULTY: Difficult KEYWORDS: counting rule, combination 168. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.

How many possible ways can the team be formed which will not include any of the twin brothers?

ANSWER: 40,920 TYPE: PR DIFFICULTY: Moderate KEYWORDS: counting rule, combination

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169. A debate team of 4 is to be chosen from a class of 35. There are two twin brothers in the class.

How many possible ways can the team be formed which will include both of the twin brothers?

ANSWER: 528 TYPE: PR DIFFICULTY: Moderate KEYWORDS: counting rule, combination 170. An exploration team of 2 women and 3 men is to be chosen from a candidate pool of 6 women and 7 men. How many different ways can this team of 5 be formed?

ANSWER: 525 TYPE: PR DIFFICULTY: Moderate KEYWORDS: counting rule, combination, multiply the combinations from each gender.

171. Twelve students in a Business Statistics class are to be formed into three teams of four. How many different ways can this be done?

ANSWER: 5,775 TYPE: PR DIFFICULTY: Difficult EXPLANATION:

 12!/  4!8!  8!/  4!4!  / 3!

KEYWORDS: counting rule, combination 172. True or False The events “rolling a single die and getting four or greater” and “rolling a single die and getting a valueless than or equal to five” are mutually exclusive.

ANSWER: False TYPE: TF DIFFICULTY: moderate KEYWORDS: mutually exclusive EXPLANATION: Rolling a five is common to both events

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Discrete Probability Distributions

5-1

CHAPTER 5: DISCRETE PROBABILITY DISTRIBUTIONS 1. Thirty-six of the staff of 80 teachers at a local intermediate school are certified in CardioPulmonary Resuscitation (CPR). In 180 days of school, about how many days can we expect that the teacher on bus duty will likely be certified in CPR? a) 5 days b) 45 days c) 65 days d) 81 days ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, mean 2. A campus program evenly enrolls undergraduate and graduate students. If a random sample of 4 students is selected from the program to be interviewed about the introduction of a new fast food outlet on the ground floor of the campus building, what is the probability that all 4 students selected are undergraduate students? a) 0.0256 b) 0.0625 c) 0.16 d) 1.00 ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution 3. A probability distribution is an equation that a) associates a probability of occurrence with each outcome. b) measures outcomes and assigns values of X to the simple events. c) assigns a value to the variability of the set of events. d) assigns a value to the center of the set of events.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: probability distribution 4. The connotation "expected value" or "expected gain" from playing roulette at a casino means a) the amount you expect to "gain" on a single play. b) the amount you expect to "gain" in the long run over many plays. c) the amount you need to "break even" over many plays. d) the amount you should expect to gain if you are lucky.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: expected value Copyright ©2020 Pearson Education, Inc.

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Discrete Probability Distributions 5. Which of the following about the binomial distribution is not a true statement? a) The probability of the event of interest must be constant from trial to trial. b) Each outcome is independent of the other. c) Each outcome may be classified as either "event of interest" or "not event of interest." d) The variable of interest is continuous.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, properties 6. In a binomial distribution a) the variable X is continuous. b) the probability of event of interest  is stable from trial to trial. c) the number of trials n must be at least 30. d) the results of one trial are dependent on the results of the other trials.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, properties 7.

Whenever  = 0.5, the binomial distribution will a) always be symmetric. b) be symmetric only if n is large. c) be right-skewed. d) be left-skewed.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 8. Whenever  = 0.1 and n is small, the binomial distribution will be a) symmetric. b) right-skewed. c) left-skewed. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties

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Discrete Probability Distributions

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9. If n = 10 and  = 0.70, then the mean of the binomial distribution is a) 0.07 b) 1.45. c) 7.00 d) 14.29 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, mean 10. If n = 10 and  = 0.70, then the standard deviation of the binomial distribution is a) 0.07 b) 1.45 c) 7.00 d) 14.29 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: binomial distribution, standard deviation 11. If the outcomes of a variable follow a Poisson distribution, then them a) mean equals the standard deviation. b) median equals the standard deviation. c) mean equals the variance. d) median equals the variance.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Poisson distribution, mean, standard deviation, properties 12. What type of probability distribution will the consulting firm most likely employ to analyze the insurance claims in the following problem?

An insurance company has called a consulting firm to determine if the company has an unusually high number of false insurance claims. It is known that the industry proportion for false claims is 3%. The consulting firm has decided to randomly and independently sample 100 of the company’s insurance claims. They believe the number of these 100 that are false will yield the information the company desires. a) binomial distribution. b) Poisson distribution. c) Either of the above d) none of the above.

ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution, properties

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Discrete Probability Distributions

13. What type of probability distribution will most likely be used to analyze warranty repair needs on new cars in the following problem?

The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold. a) binomial distribution. b) Poisson distribution. c) Either of the above d) none of the above.

ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: binomial distribution, properties 14. What type of probability distribution will most likely be used to analyze the number of blue chocolate chips per bag in the following problem?

The quality control manager of a candy plant is inspecting a batch of chocolate chip bags.

When the production process is in control, the mean number of blue chocolate chips per bag is 6.0. The manager is interested in analyzing the probability that any bag being inspected has fewer than 5.0 blue chocolate chips. a) binomial distribution. b) Poisson distribution. c) Either of the above d) none of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties

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Discrete Probability Distributions

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15. A professor receives, on average, 24.7 e-mails from students the day before the midterm exam.

To compute the probability of receiving at least 10 e-mails on such a day, he will use what type of probability distribution? a) binomial distribution. b) Poisson distribution. c) Either of the above d) none of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties 16. A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.025. To find the probability that exactly 20 of the computers will require repair on a given day, one will use what type of probability distribution? a) binomial distribution. b) Poisson distribution. c) Either of the above d) none of the above.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 17. The portfolio expected return of two investments a) will be higher when the covariance is zero. b) will be higher when the covariance is negative. c) will be higher when the covariance is positive. d) does not depend on the covariance.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: portfolio, mean 18. n the average, 1.8 customers per minute arrive at any one of the checkout counters of a grocery store. What type of probability distribution can be used to find out the probability that there will be no customer arriving at a checkout counter? a) binomial distribution. b) Poisson distribution. c) Either of the above d) none of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties Copyright ©2020 Pearson Education, Inc.

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Discrete Probability Distributions 19. A multiple-choice test has 30 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What type of probability distribution can be used to figure out his chance of getting at least 20 questions right? a) binomial distribution. b) Poisson distribution. c) Either of the above d) none of the above.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 20. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value. a) Most of the weeks resulted in rat costs of $13.00. b) The median cost for the distribution of rat costs is $13.00. c) The expected or mean cost for all weekly rat purchases is $13.00. d) The rat cost that occurs more often than any other is $13.00.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mean (expected value), probability distribution A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution: Price: $10.00 $12.50 $15.00 Probability: 0.35 0.40 0.25 How much should the lab budget for next year’s rat orders be, assuming this distribution does not change? e) $520 f) $637 g) $650 h) $780 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean (expected value), probability distribution

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Discrete Probability Distributions

5-7

21. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean. a) The number of tickets that is written most often is 6.5 tickets per day. b) Half of the days have less than 6.5 tickets written, and half of the days have more than 6.5 tickets written. c) If we sampled all days, the arithmetic average or expected number of tickets written would be 6.5 tickets per day. d) The mean has no interpretation since 0.5 ticket can never be written.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mean (expected value), Poisson distribution 22. True or False: The Poisson distribution can be used to model a continuous random variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, properties 23. True or False: Another name for the mean of a probability distribution is its expected value.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mean (expected value) True or False: The number of customers arriving at a department store in a 5-minute period has a binomial distribution.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, properties 24. True or False: The number of customers arriving at a department store in a 5-minute period has a Poisson distribution.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, properties

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Discrete Probability Distributions

25. True or False: The diameters of 10 randomly selected bolts have a binomial distribution.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: binomial distribution, properties 26. True or False: The largest value that a Poisson random variable X can have is n.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties 27. True or False: In a Poisson distribution, the mean and standard deviation are equal.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties 28. True or False: In a Poisson distribution, the mean and variance are equal.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Poisson distribution, properties 29. True or False: If  remains constant in a binomial distribution, an increase in n will increase the variance.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 30. True or False: If  remains constant in a binomial distribution, an increase in n will not change the mean.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: binomial distribution, properties 31. True or False: Suppose that a judge’s decisions follow a binomial distribution and that his verdict is incorrect 10% of the time. In his next 10 decisions, the probability that he makes fewer than 2 incorrect verdicts is 0.736.

ANSWER: True Copyright ©2020 Pearson Education, Inc.

Discrete Probability Distributions

5-9

TYPE: TF DIFFICULTY: Moderate KEYWORDS: binomial distribution, probability 32. True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The mean number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.05041.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Poisson distribution, probability SCENARIO 5-1 The probability that a smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have 2 such alarms in your home and they operate independently.

33. Referring to Scenario 5-1, the probability that both sound an alarm in the presence of smoke is ________.

ANSWER: 0.64 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 34. Referring to Scenario 5-1, the probability that neither sound an alarm in the presence of smoke is ________.

ANSWER: 0.04 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 35. Referring to Scenario 5-1, the probability that at least one sounds an alarm in the presence of smoke is ________.

ANSWER: 0.96 TYPE: FI DIFFICULTY: Difficult KEYWORDS: binomial distribution SCENARIO 5-2 A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete, so it is reasonable to believe that their relative successes would be independent).

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Discrete Probability Distributions

36. Referring to Scenario 5-2, the probability that all 3 businesses succeed is ________.

ANSWER: 0.216 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 37. Referring to Scenario 5-2, the probability that all 3 businesses fail is ________.

ANSWER: 0.064 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 38. Referring to Scenario 5-2, the probability that at least 1 business succeeds is ________.

ANSWER: 0.936 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 39. Referring to Scenario 5-2, the probability that exactly 1 business succeeds is ________.

ANSWER: 0.288 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 40. If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________ .

ANSWER: 0.4116 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution 41. If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________ .

ANSWER: 0.3483 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 42. If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________ .

ANSWER: 0.0729 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution Copyright ©2020 Pearson Education, Inc.

Discrete Probability Distributions 43. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 1 prefers brand C is ________.

ANSWER: 0.0768 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution 44. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that at least 1 prefers brand C is ________.

ANSWER: 0.9898 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 45. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 3 prefer brand C is ________.

ANSWER: 0.3456 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution 46. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that exactly 4 prefer brand C is ________.

ANSWER: 0.2592 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution 47. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that 2 or fewer prefer brand C is ________.

ANSWER: 0.3174 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 48. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that more than 3 prefer brand C is ________.

ANSWER: 0.3370 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution

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Discrete Probability Distributions

49. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The probability that fewer than 2 prefer brand C is ________.

ANSWER: 0.0870 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 50. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The mean number that you would expect to prefer brand C is ________.

ANSWER: 3 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution, mean 51. Suppose that history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The variance of the number that prefer brand C is ________.

ANSWER: 1.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution, variance SCENARIO 5-3 The following table contains the probability distribution for X = the number of retransmissions necessary to successfully transmit a 1024K data package through a network.

X 0 1 2 3 P(X) 0.35 0.35 0.25 0.05 52. Referring to Scenario 5-3, the probability of no retransmissions is ________.

ANSWER: 0.35 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution 53. Referring to Scenario 5-3, the probability of at least one retransmission is ________.

ANSWER: 0.65 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution

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Discrete Probability Distributions

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54. Referring to Scenario 5-3, the mean or expected value for the number of retransmissions is ________.

ANSWER: 1.0 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, mean (expected value), 55. Referring to Scenario 5-3, the variance for the number of retransmissions is ________.

ANSWER: 0.80 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, variance 56. Referring to Scenario 5-3, the standard deviation of the number of retransmissions is ________.

ANSWER: 0.894 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, standard deviation 57. In a game called Taxation and Evasion, a player rolls a pair of dice. If, on any turn, the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she does not get audited is ________.

ANSWER: 0.2373 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 58. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited once is ________.

ANSWER: 0.3955 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 59. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited at least once is ________.

ANSWER: 0.7627 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution

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5-14

Discrete Probability Distributions

60. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The probability that she gets audited no more than 2 times is ________.

ANSWER: 0.8965 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution 61. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The expected number of times she will be audited is ________.

ANSWER: 1.25 TYPE: FI DIFFICULTY: Easy KEYWORDS: binomial distribution, mean (expected value) 62. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The variance of the number of times she will be audited is ________.

ANSWER: 0.9375 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution, variance 63. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice. The standard deviation of the number of times she will be audited is ________.

ANSWER: 0.968 TYPE: FI DIFFICULTY: Moderate KEYWORDS: binomial distribution, standard deviation SCENARIO 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in a small city in the Midwest.

X 0 1 2 3 4 5 P(X) 0.10 0.20 0.45 0.15 0.05 0.05 64. Referring to Scenario 5-4, the probability of 3 accidents is ________.

ANSWER: 0.15 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution Copyright ©2020 Pearson Education, Inc.

Discrete Probability Distributions

5-15

65. Referring to Scenario 5-4, the probability of at least 1 accident is ________.

ANSWER: 0.90 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution 66. Referring to Scenario 5-4, the mean or expected value of the number of accidents is ________.

ANSWER: 2.0 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, mean 67. Referring to Scenario 5-4, the variance of the number of accidents is ________.

ANSWER: 1.4 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, variance 68. Referring to Scenario 5-4, the standard deviation of the number of accidents is ________.

ANSWER: 1.18 TYPE: FI DIFFICULTY: Easy KEYWORDS: probability distribution, standard deviation 69. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be exactly 3 power outages in a year is ____________.

ANSWER: 0.0892 TYPE: FI DIFFICULTY: Easy KEYWORDS: Poisson distribution 70. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be at least 3 power outages in a year is ____________.

ANSWER: 0.9380 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Poisson distribution

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5-16

Discrete Probability Distributions

71. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be at least 1 power outage in a year is ____________.

ANSWER: 0.9975 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Poisson distribution 72. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be no more than 1 power outage in a year is ____________.

ANSWER: 0.0174 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Poisson distribution 73. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The probability that there will be between 1 and 3 inclusive power outages in a year is ____________.

ANSWER: 0.1487 TYPE: FI DIFFICULTY: Difficult KEYWORDS: Poisson distribution 74. The number of power outages at a nuclear power plant has a Poisson distribution with a mean of 6 outages per year. The variance of the number of power outages is ____________.

ANSWER: 6 TYPE: FI DIFFICULTY: Easy KEYWORDS: Poisson distribution 75. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.

The probability of seven 911 calls in a day is ____________.

ANSWER: 0.0901 TYPE: FI DIFFICULTY: Easy KEYWORDS: Poisson distribution 76. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.

The probability of seven or eight 911 calls in a day is ____________.

ANSWER: 0.2027 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Poisson distribution Copyright ©2020 Pearson Education, Inc.

Discrete Probability Distributions

5-17

77. The number of 911 calls in a small city has a Poisson distribution with a mean of 10 calls a day.

The probability of 2 or more 911 calls in a day is ____________.

ANSWER: 0.9995 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Poisson distribution 78. The number of 911 calls in a small city has a Poisson distribution with a mean of 10.0 calls a day.

The standard deviation of the number of 911 calls in a day is ____________.

ANSWER: 3.16 TYPE: FI DIFFICULTY: Easy KEYWORDS: Poisson distribution 79. The Department of Commerce in a state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that more than 3 bankruptcies occur next month.

ANSWER: 0.8811 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 80. The Department of Commerce in a state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that exactly 5 bankruptcies occur next month.

ANSWER: 0.1487 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 81. Current estimates suggest that 75% of the home-based computers in a foreign country have access to on-line services. Suppose 20 people with home-based computers were randomly and independently sampled. Find the probability that fewer than 10 of those sampled currently have access to on-line services.

ANSWER: 0.0039 TYPE: PR DIFFICULTY: Moderate KEYWORDS: binomial distribution

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5-18

Discrete Probability Distributions

82. Current estimates suggest that 75% of the home-based computers in a foreign country have access to on-line services. Suppose 20 people with home-based computers were randomly and independently sampled. Find the probability that more than 9 of those sampled currently do not have access to on-line services.

ANSWER: 0.0139 TYPE: PR DIFFICULTY: Difficult KEYWORDS: binomial distribution 83. A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability all the hotels in the sample offered hairdryers in the bathrooms.

ANSWER: 0.0008 TYPE: PR DIFFICULTY: Moderate KEYWORDS: binomial distribution 84. A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that more than 7 but less than 13 of the hotels in the sample offered hairdryers in the bathrooms.

0.2264 TYPE: PR DIFFICULTY: Moderate KEYWORDS: binomial distribution 85. A national trend predicts that women will account for half of all business travelers in the next 3 years. To attract these women business travelers, hotels are providing more amenities that women particularly like. A recent survey of American hotels found that 70% offer hairdryers in the bathrooms. Consider a random and independent sample of 20 hotels. Find the probability that at least 9 of the hotels in the sample do not offer hairdryers in the bathrooms.

ANSWER: 0.1133 TYPE: PR DIFFICULTY: Difficult KEYWORDS: binomial distribution 86. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day. Find the probability that less than 6 tickets are written on a randomly selected day from this population.

ANSWER: 0.3837 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution Copyright ©2020 Pearson Education, Inc.

Discrete Probability Distributions

5-19

87. The local police department must write, on average, 5 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.4 tickets per day. Find the probability that exactly 6 tickets are written on a randomly selected day from this population.

ANSWER: 0.1586 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution SCENARIO 5-5 The quality control manager of Green Bulbs Inc. is inspecting a batch of energy saving compact fluorescent light bulbs. When the production process is in control, the mean number of bad bulbs per shift is 6.0.

88. Referring to Scenario 5-6, what is the probability that any shift being inspected has produced 4.0 bad bulbs.

ANSWER: 0.1339 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 89. Referring to Scenario 5-6, what is the probability that any shift being inspected has produced fewer than 5.0 bad bulbs.

ANSWER: 0.2851 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 90. Referring to Scenario 5-6, what is the probability that any shift being inspected has produced at least 6.0 bad bulbs.

ANSWER: 0.5543 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 91. Referring to Scenario 5-6, what is the probability that any shift being inspected has produced between 5.0 and 8.0 inclusive bad bulbs.

ANSWER: 0.5622 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution

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5-20

Discrete Probability Distributions

92. Referring to Scenario 5-6, what is the probability that any shift being inspected has less than 5.0 or more than 8.0 bad bulbs.

ANSWER: 0.4378 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Poisson distribution SCENARIO 5-9 A major hotel chain keeps a record of the number of mishandled bags per 1,000 customers. In a recent year, the hotel chain had 4.06 mishandled bags per 1,000 customers. Assume that the number of mishandled bags has a Poisson distribution.

93. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have no mishandled bags?

ANSWER: 0.0172 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution

Referring to Scenario 5-9, what is the probability that in the next 1,000 custoers, the chain will have at least one mishandled bag?

ANSWER: 0.9828 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 94. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have at least two mishandled bags?

ANSWER: 0.9127 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 95. Referring to Scenario 5-9, what is the probability that in the next 1,000 customer, the hotel chain will have no more than three mishandled bags?

ANSWER: 0.4218 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution

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Discrete Probability Distributions

5-21

96. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have no more than four mishandled bags?

ANSWER: 0.6171 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 97. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have fewer than six mishandled bags?

ANSWER: 0.7757 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 98. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have fewer than eight mishandled bags?

ANSWER: 0.9452 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 99. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have more than eight mishandled bags?

ANSWER: 0.02320 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 100. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have more than ten mishandled bags?

ANSWER: 0.003172 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 101. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have between two and four inclusive mishandled bags?

ANSWER: 0.5298 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution

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5-22

Discrete Probability Distributions

102. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have more than five but less than eight mishandled bags?

ANSWER: 0.1695 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 103. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have less than two or more than eight mishandled bags?

ANSWER: 0.1105 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 104. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have no more than two or at least eight mishandled bags?

ANSWER: 0.2842 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 105. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have less than two and more than eight mishandled bags?

ANSWER: 0 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Poisson distribution 106. Referring to Scenario 5-9, what is the probability that in the next 1,000 customers, the hotel chain will have no more than two and at least eight mishandled bags?

ANSWER: 0 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Poisson distribution SCENARIO 5-11 Subscribers to Investment Advice White Letters perform security transactions at the rate of five trades per month. Assume that one of the subscribers performs transactions at this rate and the probability of a transaction for any two months is the same and the number of transactions in one month is independent of the number of transactions in another month.

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Discrete Probability Distributions

5-23

107. Referring to Scenario 5-11, what is mean number of transactions per month for this subscriber?

ANSWER: 5 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 108. Referring to Scenario 5-11, what is variance of the number of transactions per month for this subscriber?

ANSWER: 5 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 109. Referring to Scenario 5-11, what is probability that exactly ten security transactions will be conducted in one month?

ANSWER: 0.0181 TYPE: PR DIFFICULTY: Easy KEYWORDS: Poisson distribution 110. Referring to Scenario 5-11, what is probability that at least five security transactions will be conducted in one month?

ANSWER: 0.5595 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 111. Referring to Scenario 5-11, what is probability that no more than five security transactions will be conducted in one month?

ANSWER: 0.6160 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 112. Referring to Scenario 5-11, what is probability that no security transaction will be conducted in one month?

ANSWER: 0.0067 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution

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5-24

Discrete Probability Distributions

113. Referring to Scenario 5-11, what is probability that more than two security transactions will be conducted in one month?

ANSWER: 0.8753 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 114. Referring to Scenario 5-11, what is probability that fewer than two security transactions will be conducted in one month?

ANSWER: 0.0404 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution SCENARIO 5-12 Phone calls arrive at the rate of 50 per hour at the reservation desk for Queen City Airways. The desk manager has asked you for an analysis of the call rates and probabilities to better understand the operation and determine if more call desk workers are needed.

115. Using Scenario 5-12, What is the expected number of calls when calculating the probability of receiving three calls in a 6-minute period?

ANSWER: 5 calls TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution, proportions 116.. Using Scenario 5-12, What is the probability of receiving exactly three calls in a 6 minute period?

ANSWER: 0.1404 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution 117. Using Scenario 5-12, What is the expected number of calls when calculating the probability of receiving nine calls in a 12-minute period?

ANSWER: 10 calls TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution, proportions

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Discrete Probability Distributions

5-25

118. Using Scenario 5-12, What is the probability of receiving exactly 10 calls in a 12-minute period?

ANSWER: 0.1251 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Poisson distribution

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The Normal Distribution 6-1

CHAPTER 6: THE NORMAL DISTRIBUTION 1. In its standardized form, the normal distribution a) has a mean of 0 and a standard deviation of 1. b) has a mean of 1 and a variance of 0. c) has an area equal to 0.5. d) cannot be used to approximate discrete probability distributions.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: standardized normal distribution, properties 2. Which of the following about the normal distribution is not true? a) Theoretically, the mean, median, and mode are the same. b) About 2/3 of the observations fall within  1 standard deviation from the mean. c) It is a discrete probability distribution. d) Its parameters are the mean,  , and standard deviation,  .

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: normal distribution, properties 3. If a set of data is approximately normally distributed, we would find that approximately a) 2 of every 3 observations would fall between  1 standard deviation around the mean. b) 4 of every 5 observations would fall between  1.28 standard deviations around the mean. c) 19 of every 20 observations would fall between  2 standard deviations around the mean. d) All the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: normal distribution, properties 4. The value of the cumulative standardized normal distribution at Z is 0.8770. The value of Z is a) 0.18 b) 0.81 c) 1.16 d) 1.47 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value

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6-2

The Normal Distribution 5. For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. The value of Z is a) – 0.81 b) – 0.31 c) 0.31 d) 1.96 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 6. For some value of Z, the value of the cumulative standardized normal distribution is 0.8340. The value of Z is a) 0.07 b) 0.37 c) 0.97 d) 1.06 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 7. The value of the cumulative standardized normal distribution at Z is 0.6255. The value of Z is a) 0.99 b) 0.40 c) 0.32 d) 0.16 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: standard normal distribution, value 8. The value of the cumulative standardized normal distribution at 1.5X is 0.9332. The value of X is a) 0.10 b) 0.50 c) 1.00 d) 1.50 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: normal distribution, value

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The Normal Distribution 6-3 9. Given that X is a normally distributed variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.

ANSWER: 0.9104 TYPE: PR DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 10. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75?

ANSWER: 0.0228 TYPE: PR DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 11. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients die before they reach the standard retirement age of 65?

ANSWER: 0.1957 using Excel or 0.1949 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, probability 12. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.

ANSWER: 71.78 years old TYPE: PR DIFFICULTY: Difficult KEYWORDS: standardized normal distribution, value

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6-4

The Normal Distribution 13. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes. a) 0.3551 b) 0.3085 c) 0.2674 d) 0.1915 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 14. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will take between 2 and 4.5 minutes to find a parking spot in the library parking lot. a) 0.0919 b) 0.2255 c) 0.4938 d) 0.7745 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 15. If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot? a) 2.8 minutes b) 3.2 minutes c) 3.4 minutes d) 4.2 minutes ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 16. The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is _______?

ANSWER: 0.0668 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability Copyright ©2020 Pearson Education, Inc.

The Normal Distribution 6-5 17. The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh between 3 and 5 pounds is _______?

ANSWER: 0.5865 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 18. The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top 2% in weight.

Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the citation designation be established? a) 1.56 pounds b) 4.84 pounds c) 5.20 pounds d) 7.36 pounds ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 19. The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above what weight (in pounds) do 89.80% of the weights occur?

ANSWER: 2.184 pounds TYPE: PR DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 20. The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh less than 2.2 pounds is _______?

ANSWER: 0.1056 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability 21. A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces.

ANSWER: 0.8944 TYPE: PR DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability Copyright ©2020 Pearson Education, Inc.

6-6

The Normal Distribution

22. A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall above 10.95 ounces.

ANSWER: 0.0668 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 23. True or False: The probability that a standard normal variable, Z, falls between – 1.50 and 0.81 is 0.7242.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 24. True or False: The probability that a standard normal variable, Z, is between 1.50 and 2.10 is the same as the probability Z is between – 2.10 and – 1.50.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 25. True or False: The probability that a standard normal variable, Z, is below 1.96 is 0.4750.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 26. True or False: The probability that a standard normal variable, Z, is between 1.00 and 3.00 is 0.1574.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 27. True or False: The probability that a standard normal variable, Z, falls between –2.00 and –0.44 is 0.6472.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability Copyright ©2020 Pearson Education, Inc.

The Normal Distribution 6-7 28. True or False: The probability that a standard normal variable, Z, is less than 5.0 is approximately 0.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 29. True or False: A worker earns $15 per hour at a plant in China and is told that only 2.5% of all workers make a higher wage. If the wage is assumed to be normally distributed and the standard deviation of wage rates is $5 per hour, the mean wage for the plant is $7.50 per hour.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, mean 30. True or False: Theoretically, the mean, median, and the mode are all equal for a normal distribution.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: normal distribution, properties 31. True or False: Any set of normally distributed data can be transformed to its standardized form.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: normal distribution, properties 32. True or False: The "middle spread," that is the middle 50% of the normal distribution, is equal to plus or minus one standard deviation.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, value 33. True or False: A normal probability plot may be used to assess the assumption of normality for a set of data.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: normal probability plot

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6-8

The Normal Distribution 34. True or False: If a data set is approximately normally distributed, its normal probability plot would be S-shaped.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: normal probability plot 35. The probability that a standard normal variable Z is positive is ________.

ANSWER: 0.50 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 36. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. What is the probability that a randomly selected can will contain between 100 and 110 grams of tea leaves?

ANSWER: 0.1554 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 37. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. What is the probability that a randomly selected can will contain between 82 and 100 grams of tea leaves?

ANSWER: 0.2132 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 38. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. What is the probability that a randomly selected can will contain at least 100 grams of tea leaves?

ANSWER: 0.6554 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 39. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. What is the probability that a randomly selected can will contain between 100 and 120 grams of tea leaves?

ANSWER: 0.3108 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability Copyright ©2020 Pearson Education, Inc.

The Normal Distribution 6-9

40. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. What is the probability that a randomly selected can will contain less than 100 grams of tea leaves?

ANSWER: 0.3446 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 41. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. What is the probability that a randomly selected can will contain less than 100 grams or more than 120 grams of tea leaves?

ANSWER: 0.6892 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 42. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. Approximately 83% of the can will have at least how many grams of tea leaves?

ANSWER: 86.15 using Excel or 86.25 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value 43. The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be between 121 and 124 inches?

ANSWER: 0.8186 using Excel or 0.8185 using Table E.2 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 44. The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be over 125 inches in length?

ANSWER: 0.0228 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability

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6-10

The Normal Distribution

45. The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be less than 124 inches?

ANSWER: 0.8413 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 46. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time elapsed between two consecutive trades will be longer than 17 seconds?

ANSWER: 7% or 0.07 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 47. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time elapsed between two consecutive trades will be between 13 and 14 seconds?

ANSWER: 13% or 0.13 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 48. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time elapsed between two consecutive trades will be between 15 and 16 seconds?

ANSWER: 30% or 0.30 TYPE: PR DIFFICULTY: Difficult KEYWORDS: normal distribution, probability, asymmetry

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The Normal Distribution 6-11 49. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time elapsed between two consecutive trades will be between 14 and 15 seconds?

ANSWER: 30% or 0.30 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 50. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time elapsed between two consecutive trades will be between 13 and 16 seconds?

ANSWER: 73% or 0.73 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 51. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time elapsed between two consecutive trades will be between 14 and 17 seconds?

ANSWER: 73% or 0.73 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 52. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. The probability is 20% that the time elapsed will be shorter how many seconds?

ANSWER: 14 seconds TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability

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6-12

The Normal Distribution

53. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. The probability is 80% that the time elapsed will be longer than how many seconds?

ANSWER: 14 seconds TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 54. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. The middle 60% of the time elapsed will fall between which two numbers?

ANSWER: 14 seconds and 16 seconds TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 55. You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%. The middle 86% of the time elapsed will fall between which two numbers?

ANSWER: 13 seconds and 17 seconds TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 56. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 90 and 95?

ANSWER: 4.41% or 0.0441 TYPE: PR DIFFICULTY: Difficult KEYWORDS: normal distribution, probability

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The Normal Distribution 6-13 57. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score greater than 95?

ANSWER: 2.27% or 0.0227 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 58. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score lower than 55?

ANSWER: 2.27% or 0.0227 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 59. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 75 and 90?

ANSWER: 43.32% or 0.4332 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 60. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 60 and 75?

ANSWER: 43.32% or 0.4332 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 61. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 60 and 95?

ANSWER: 91.05% or 0.9105 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability

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6-14

The Normal Distribution

62. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 55 and 90?

ANSWER: 91.05% or 0.9105 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 63. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 55 and 95?

ANSWER: 95.46% or 0.9546 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 64. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. The middle 86.64% of the students will score between which two scores?

ANSWER: 60 and 90 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 65. You were told that the mean score on a statistics exam is 75 with the scores normally distributed.

In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. The middle 95.46% of the students will score between which two scores?

ANSWER: 55 and 95 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability 66. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than 1.15 is __________.

ANSWER: 0.8749 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability

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The Normal Distribution 6-15 67. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than 0.77 is __________.

ANSWER: 0.2206 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 68. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than -2.20 is __________.

ANSWER: 0.0139 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 69. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than -0.98 is __________.

ANSWER: 0.8365 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 70. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -2.33 and 2.33 is __________.

ANSWER: 0.9802 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 71. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -2.89 and -1.03 is __________.

ANSWER: 0.1496 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability 72. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is between -0.88 and 2.29 is __________.

ANSWER: 0.7996 TYPE: FI DIFFICULTY: Easy KEYWORDS: standardized normal distribution, probability

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6-16

The Normal Distribution

73. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z values are larger than __________ is 0.3483.

ANSWER: 0.39 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, probability 74. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z values are larger than __________ is 0.6985.

ANSWER: -0.52 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, probability 75. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So, 27% of the possible Z values are smaller than __________.

ANSWER: -0.61 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 76. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So, 85% of the possible Z values are smaller than __________.

ANSWER: 1.04 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 77. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So, 96% of the possible Z values are between __________ and __________ (symmetrically distributed about the mean).

ANSWER: -2.05 and 2.05 or -2.06 and 2.06 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value 78. Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So, 50% of the possible Z values are between __________ and __________ (symmetrically distributed about the mean).

ANSWER: -0.67 and 0.67 or -0.68 and 0.68 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standardized normal distribution, value

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The Normal Distribution 6-17 79. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled in less than 12 minutes.

ANSWER: 0.0668 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability 80. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled in between 14 and 16 minutes.

ANSWER: 0.3829 using Excel or 0.3830 using Table E.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability 81. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled in between 10 and 12 minutes.

ANSWER: 0.0606 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability 82. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled in between 15 and 21 minutes.

ANSWER: 0.49865 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability 83. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled in between 16 and 21 minutes.

ANSWER: 0.30719 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability

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6-18

The Normal Distribution

84. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled in more than 11 minutes.

ANSWER: 0.9772 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability 85. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled in more than 19 minutes.

ANSWER: 0.0228 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability 86. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is __________ that a product is assembled in less than 20 minutes.

ANSWER: 0.9938 TYPE: FI DIFFICULTY: Easy KEYWORDS: normal distribution, probability 87. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 15% of the products require more than __________ minutes for assembly.

ANSWER: 17.0729 using Excel or 17.08 using Table E.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: normal distribution, value 88. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 90% of the products require more than __________ minutes for assembly.

ANSWER: 12.44 TYPE: FI DIFFICULTY: Moderate KEYWORDS: normal distribution, value

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The Normal Distribution 6-19 89. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 60% of the products would be assembled within __________ and __________ minutes (symmetrically distributed about the mean).

ANSWER: 13.32 and 16.68 or 13.31 and 16.69 TYPE: FI DIFFICULTY: Difficult KEYWORDS: normal distribution, value 90. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 17% of the products would be assembled within __________ minutes.

ANSWER: 13.1 TYPE: FI DIFFICULTY: Moderate KEYWORDS: normal distribution, value 91. The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 70% of the products would be assembled within __________ minutes.

ANSWER: 16.0488 using Excel or 16.04 using Table E.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: normal distribution, value SCENARIO 6-1 The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches.

92. Referring to Scenario 6-1, for a randomly chosen Monday, what is the probability there will be less than 340 column inches of classified advertisement?

ANSWER: 0.8413 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 93. Referring to Scenario 6-1, for a randomly chosen Monday, what is the probability there will be between 280 and 360 column inches of classified advertisement?

ANSWER: 0.9545 using Excel or 0.9544 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability Copyright ©2020 Pearson Education, Inc.

6-20

The Normal Distribution

94. Referring to Scenario 6-1, for a randomly chosen Monday the probability is 0.1 that there will be less than how many column inches of classified advertisements?

ANSWER: 294.4 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value

95. Referring to Scenario 6-1, a single Monday is chosen at random. State in which of the following ranges the number of column inches of classified advertisement is most likely to be: a) 300 --320 b) 310 --330 c) 320 -- 340 d) 330 -- 350 ANSWER: b TYPE: MC Difficulty: Moderate KEYWORDS: normal distribution, probability SCENARIO 6-2 John has two jobs. For daytime work at a jewelry store he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with mean $10,000 and standard deviation $2000. At night he works occasionally as a waiter, for which his monthly income is normally distributed with mean $1,000 and standard deviation $300. John's income levels from these two sources are independent of each other.

96. Referring to Scenario 6-2, for a given month, what is the probability that John's commission from the jewelry store is less than $13,000?

ANSWER: 0.9332 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 97. Referring to Scenario 6-2, for a given month, what is the probability that John's commission from the jewelry store is no more than $8,000?

ANSWER: 0.1587 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability

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The Normal Distribution 6-21 98. Referring to Scenario 6-2, for a given month, what is the probability that John's commission from the jewelry store is at least $12,000?

ANSWER: 0.1587 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 99. Referring to Scenario 6-2, for a given month, what is the probability that John's commission from the jewelry store is more than $9,500?

ANSWER: 0.5987 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 100. Referring to Scenario 6-2, for a given month, what is the probability that John's commission from the jewelry store is between $11,000 and $12,000?

ANSWER: 0.1499 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 101. Referring to Scenario 6-2, for a given month, what is the probability that John's commission from the jewelry store is between $5,000 and $7,000?

ANSWER: 0.0606 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 102. Referring to Scenario 6-2, for a given month, what is the probability that John's commission from the jewelry store is between $9,000 and $11,000?

ANSWER: 0.3829 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 103. Referring to Scenario 6-2, the probability is 0.75 that John's commission from the jewelry store is less than how much in a given month?

ANSWER: $ 11348.98 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value 104. Referring to Scenario 6-2, the probability is 0.95 that John's commission from the jewelry store is at least how much in a given month?

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6-22

The Normal Distribution

ANSWER: $6710.29 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value 105. Referring to Scenario 6-2, John's commission from the jewelry store will be between what two values symmetrically distributed around the population mean 80% of the time?

ANSWER: $7436.90 and $12563.10 TYPE: PR DIFFICULTY: Difficult KEYWORDS: normal distribution, value 106. Referring to Scenario 6-2, John's commission from the jewelry store will be between what two values symmetrically distributed around the population mean 90% of the time?

ANSWER: $6710.29 and $13289.71 TYPE: PR DIFFICULTY: Difficult KEYWORDS: normal distribution, value 107. Referring to Scenario 6-2, the probability is 0.10 that John's commission from the jewelry store is more than how much in a given month?

ANSWER: $12563.10 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value 108. Referring to Scenario 6-2, the probability is 0.30 that John's commission from the jewelry store is no more than how much in a given month?

ANSWER: $8951.20 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value 109. Referring to Scenario 6-2, for a given month, what is the probability that John's income as a waiter is between $700 and $1600?

ANSWER: 0.8186 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability

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The Normal Distribution 6-23 110. Referring to Scenario 6-2, for a given month, what is the probability that John's income as a waiter is between $1,200 and $1,600?

ANSWER: 0.2297 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 111. Referring to Scenario 6-2, for a given month, what is the probability that John's income as a waiter is between $800 and $900?

ANSWER: 0.1169 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 112. Referring to Scenario 6-2, for a given month, what is the probability that John's income as a waiter is no more than $300?

ANSWER: 0.0098 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 113. Referring to Scenario 6-2, for a given month, what is the probability that John's income as a waiter is less than $1300?

ANSWER: 0.8413 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 114. Referring to Scenario 6-2, for a given month, what is the probability that John's income as a waiter is at least $1400?

ANSWER: 0.0912 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability 115. Referring to Scenario 6-2, for a given month, what is the probability that John's income as a waiter is more than $900?

ANSWER: 0.6306 TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability

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6-24

The Normal Distribution

116. Referring to Scenario 6-2, the probability is 0.25 that John's income as a waiter is no more than how much in a given month?

ANSWER: $797.65 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value 117. Referring to Scenario 6-2, the probability is 0.45 that John's income as a waiter is more than how much in a given month?

ANSWER: $1,037.70 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value 118. Referring to Scenario 6-2, the probability is 0.35 that John's income as a waiter is no less than how much in a given month?

ANSWER: $1,115.60 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value 119. Referring to Scenario 6-2, John's income as a waiter will be between what two values symmetrically distributed around the population mean 80% of the time?

ANSWER: $615.53 and $1,384.47 TYPE: PR DIFFICULTY: Difficult KEYWORDS: normal distribution, value 120. Referring to Scenario 6-2, John's income as a waiter will be between what two values symmetrically distributed around the population mean 90% of the time?

ANSWER: $506.54 and $1493.46 TYPE: PR DIFFICULTY: Difficult KEYWORDS: normal distribution, value 121. Referring to Scenario 6-2, the probability is 0.9 that John's income as a waiter is less than how much in a given month?

ANSWER: $1,384.47 TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, value

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The Normal Distribution 6-25 122. The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The probability that a randomly selected catfish will weigh between 2.6 and 3.6 pounds is ______.

ANSWER: 50% or 0.5 TYPE: FI DIFFICULTY: Difficult KEYWORDS: normal distribution, probability, symmetry properties 123. The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The middle 40% of the catfish will weigh between ______ pounds and ______ pounds.

ANSWER: 2.8 and 3.6 TYPE: FI DIFFICULTY: Difficult KEYWORDS: normal distribution, probability, symmetry properties

SCENARIO 6-3 A company producing orange juice buys all its oranges from a large orange orchard. The amount of juice that can be squeezed from each of these oranges is approximately normally distributed with a mean of 4.7 ounces and some unknown standard deviation. The company’s production manager knows that the probability is 30.85% that a randomly selected orange will contain less than 4.5 ounces of juice. Also, the probability is 10.56% that a randomly selected orange will contain more than 5.2 ounces of juice. Answer the following questions without the help of a calculator, statistical software or statistical table.

124. Referring to Scenario 6-5, what is the probability that a randomly selected orange will contain between 4.5 and 5.2 ounces of juices?

ANSWER: 0.5859 or 58.59% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties 125. Referring to Scenario 6-3, what is the probability that a randomly selected orange will contain between 4.2 and 4.9 ounces of juices?

ANSWER: 0.5859 or 58.59% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, properties

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6-26

The Normal Distribution

126. Referring to Scenario 6-3, what is the probability that a randomly selected orange will contain at least 4.9 ounces of juices?

ANSWER: 0.3085 or 30.85% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties 127. Referring to Scenario 6-3, what is the probability that a randomly selected orange will contain no more than 4.9 ounces of juices?

ANSWER: 0.6915 or 69.15% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties 128. Referring to Scenario 6-3, what is the probability that a randomly selected orange will contain no more than 4.2 ounces of juices?

ANSWER: 0.1056 or 10.56% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties 129. Referring to Scenario 6-3, what is the probability that a randomly selected orange will contain more than 4.2 ounces of juices?

ANSWER: 0.8944 or 89.44% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties SCENARIO 6-4 According to Investment Digest, the arithmetic mean of the annual return for common stocks over an 85-year period was 9.5% but the value of the variance was not mentioned. Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%. The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric. Assume that this distribution is normal with the mean given above. Answer the following questions without the help of a calculator, statistical software or statistical table.

130. Referring to Scenario 6-4, find the probability that the annual return of a random year will be less than 11.5%.

ANSWER: 0.90 or 90% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties

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The Normal Distribution 6-27 131. Referring to Scenario 6-4, find the probability that the annual return of a random year will be more than 11.5%.

ANSWER: 0.10 or 10% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties 132. Referring to Scenario 6-4, find the probability that the annual return of a random year will be between 7.5% and 11%.

ANSWER: 0.65 or 65% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, properties 133. Referring to Scenario 6-4, find the probability that the annual return of a random year will be less than 7.5%.

ANSWER: 0.10 or 10% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties 134. Referring to Scenario 6-4, find the probability that the annual return of a random year will be more than 7.5%.

ANSWER: 0.90 or 90% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, probability, properties 135. Referring to Scenario 6-4, what is the value above which will account for the highest 25% of the possible annual returns?

ANSWER: 11% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, properties 136. Referring to Scenario 6-4, 75% of the annual returns will be lower than what value?

ANSWER: 11% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, properties

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6-28

The Normal Distribution

137. Referring to Scenario 6-4, find the two values that will bound the middle 50% of the annual returns?

ANSWER: 8% and 11% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, properties 138. Referring to Scenario 6-4, find the two values that will bound the middle 80% of the annual returns?

ANSWER: 7.5% and 11.5% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, properties 139. Referring to Scenario 6-4, 10% of the annual returns will be less than what amount?

ANSWER: 7.5% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, properties 140 . Referring to Scenario 6-4, 10% of the annual returns will be at least what amount?

ANSWER: 11.5% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, probability, properties SCENARIO 6-5 Ball bearings are manufactured with a mean diameter of 6 millimeters (mm). Because of the inherent manufacturing process variability, the lots of bearings are approximately normally distributed with a standard deviation of 0.03 mm.

141. Using Scenario 6-5, what proportion of ball bearings has a diameter of greater than 6 mm?

NEW QUESTION ANSWER: 0.50 or 50% TYPE: PR DIFFICULTY: Easy KEYWORDS: normal distribution, symmetry property

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The Normal Distribution 6-29 142. Using Scenario 6-5, what proportion of ball bearings has a diameter of more than 6.03 mm?

ANSWER: 0.1587 or 15.87% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, complement rule 143. Using Scenario 6-5, any bearing having a diameter of less than 5.95 mm or greater than 6.05 mm are discarded. What proportion of the bearings will be discarded?

ANSWER: 0.09558 or 9.558% TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, complement rule 144. Using Scenario 6-5 and the result of the previous question, if 40,000 ball bearings were to be manufactured, how many would the manager have to discard?

ANSWER: 3,823 bearings TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, complement rule 145. Using Scenario 6-5, if there is an order for 60,000 ball bearings and it states the bearing diameters must be between 5.96 and 6.04 mm, how many should the manager manufacture?

ANSWER: 73,387.5 or 73,388 bearings TYPE: PR DIFFICULTY: Moderate KEYWORDS: normal distribution, complement rule, Excel normal distribution function.

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Sampling Distributions 7-1

CHAPTER 7: SAMPLING DISTRIBUTIONS 1. Sampling distributions describe the distribution of a) parameters. b) statistics. c) both parameters and statistics. d) neither parameters nor statistics.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: statistics, sampling distribution 2. The standard error of the mean a) is never larger than the standard deviation of the population. b) decreases as the sample size increases. c) measures the variability of the mean from sample to sample. d) All the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: standard error, mean 3. The Central Limit Theorem is important in statistics because a) for a large n, it says the population is approximately normal. b) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. c) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. d) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: central limit theorem 4. If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic a) unbiased. b) minimum variance. c) biased. d) random.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: unbiased

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7-2

Sampling Distributions 5. For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. a) Distribution is right skewed with mean = 10 minutes and standard error = 0.8 minutes. b) Distribution is right skewed with mean = 10 minutes and standard error = 8 minutes. c) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. d) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: central limit theorem 6. Which of the following statements about the sampling distribution of the sample mean is incorrect? a) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large ( n  30 ). b) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means. c) The mean of the sampling distribution of the sample mean is equal to  . d) The standard deviation of the sampling distribution of the sample mean is equal to  .

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling distribution, properties, mean 7. Which of the following is true about the sampling distribution of the sample mean? a) The mean of the sampling distribution is always  . b) The standard deviation of the sampling distribution is always  . c) The shape of the sampling distribution is always approximately normal. d) All the above are true.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, properties, mean

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Sampling Distributions 7-3 8. True or False: The amount of time it takes to complete an examination has a left skewed distribution with a mean of 65 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, central limit theorem 9. Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect? a) The mean of the sampling distribution is equal to 23 years. b) The standard deviation of the sampling distribution is equal to 3 years. c) The shape of the sampling distribution is approximately normal. d) The standard error of the sampling distribution is equal to 0.3 years.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling distribution, central limit theorem 10. Why is the Central Limit Theorem so important to the study of sampling distributions? a) It allows us to disregard the size of the sample selected when the population is not normal. b) It allows us to disregard the shape of the sampling distribution when the size of the population is large. c) It allows us to disregard the size of the population we are sampling from. d) It allows us to disregard the shape of the population when n is large.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: central limit theorem 11. A sample that does not provide a good representation of the population from which it was collected is referred to as a (n) sample.

ANSWER: biased TYPE: FI DIFFICULTY: Moderate KEYWORDS: unbiased

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7-4

Sampling Distributions 12. True or False: The Central Limit Theorem is considered powerful in statistics because it works for any population distribution provided the sample size is sufficiently large and the population mean, and standard deviation are known.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: central limit theorem 13. Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with  = 6 ounces and  = 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected? a) The mean of the sampling distribution is 6 ounces. b) The standard deviation of the sampling distribution is 2.5 ounces. c) The shape of the sampling distribution is approximately normal. d) All the above are correct.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, unbiased 14. The mean score of all pro golfers for a course has a mean of 70 and a standard deviation of 3.0.

Suppose 36 pro golfers played the course today. Find the probability that the mean score of the 36 pro golfers exceeded 71.

ANSWER: 0.0228 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 15. The distribution of the number of loaves of bread sold per week by a large bakery over the past 5 years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of n = 40 weeks has been selected. What is the approximate probability that the mean number of loaves sold in the sampled weeks exceeds 7,895 loaves?

ANSWER: Approximately 0 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem

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Sampling Distributions 7-5 16. Sales prices of baseball cards from the 1960s are known to possess a right skewed distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards. a) Right skewed with a mean of $5.25 and a standard error of $2.80 b) Normal with a mean of $5.25 and a standard error of $0.28 c) Right skewed with a mean of $5.25 and a standard error of $0.28 d) Normal with a mean of $5.25 and a standard error of $2.80 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling distribution, central limit theorem 17. Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary? a) $0.012 million b) $0.12 million c) $12 million d) $1,200.0 million ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error, mean 18. Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $3.5 million. a) Approximately 0 b) 0.0228 c) 0.9772 d) Approximately 1 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem

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7-6

Sampling Distributions 19. Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $4.0 million. a) Approximately 0 b) 0.0228 c) 0.9772 d) Approximately 1 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 20. Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million. a) Approximately 0 b) 0.0151 c) 0.9849 d) Approximately 1 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 21. Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was less than $2.5 million. a) Approximately 0 b) 0.0151 c) 0.9849 d) Approximately 1 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 22. At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the standard error for the sample mean? a) 0.029 b) 0.050 c) 0.091 d) 0.120 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: standard error, mean Copyright ©2020 Pearson Education, Inc.

Sampling Distributions 7-7 23. At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

ANSWER: 0.2710 using Excel or 0.2736 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 24. At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be below 0.95 centimeters?

ANSWER: 0.0416 using Excel or 0.0418 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 25. At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. Above what value do 2.5% of the sample means fall?

ANSWER: 1.057 TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value 26. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 16 fish is taken, what would the standard error of the mean weight equal? a) 0.003 b) 0.050 c) 0.200 d) 0.800 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: standard error, mean

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7-8

Sampling Distributions 27. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation? a) 18.750 b) 2.500 c) 1.875 d) 0.750 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling distribution, mean 28. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger? a) 0.0001 b) 0.0013 c) 0.0228 d) 0.4987 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 29. The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds? a) 84% b) 67% c) 29% d) 16% ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 30. For sample size 16, the sampling distribution of the mean will be approximately normally distributed a) regardless of the shape of the population. b) if the shape of the population is symmetrical. c) if the sample standard deviation is known. d) if the sample is normally distributed.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, central limit theorem Copyright ©2020 Pearson Education, Inc.

Sampling Distributions 7-9 31. The standard error of the mean for a sample of 100 is 30. To cut the standard error of the mean to 15, we would a) increase the sample size to 200. b) increase the sample size to 400. c) decrease the sample size to 50. d) decrease the sample to 25.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error, mean 32. Which of the following is true regarding the sampling distribution of the mean for a large sample size? a) It has the same shape, mean, and standard deviation as the population. b) It has a normal distribution with the same mean and standard deviation as the population. c) It has the same shape and mean as the population but has a smaller standard deviation. d) It has a normal distribution with the same mean as the population but with a smaller standard deviation.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, central limit theorem 33. For sample sizes greater than 30, the sampling distribution of the mean will be approximately normally distributed a) regardless of the shape of the population. b) only if the shape of the population is symmetrical. c) only if the standard deviation of the samples are known. d) only if the population is normally distributed.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem 34. For sample size 1, the sampling distribution of the mean will be normally distributed a) regardless of the shape of the population. b) only if the shape of the population is symmetrical. c) only if the population values are positive. d) only if the population is normally distributed.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, central limit theorem

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7-10

Sampling Distributions

35. The standard error of the population proportion will become larger a) as population proportion approaches 0. b) as population proportion approaches 0.50. c) as population proportion approaches 1.00. d) as the sample size increases.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error, proportion 36. True or False: As the sample size increases, the standard error of the mean increases.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: standard error, mean 37. True or False: If the population distribution is symmetric, the sampling distribution of the mean can be approximated by the normal distribution if the samples contain 15 observations.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem 38. True or False: If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem 39. True or False: If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons, then 99.73% of all cars will purchase between 3 and 27 gallons.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability

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Sampling Distributions 7-11 40. True or False: If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be between 13 and 17 gallons.

ANSWER: False TYPE: TF DIFFICULTY: Moderate EXPLANATION: The sample is too small for the normal approximation.

KEYWORDS: sampling distribution, mean, probability 41. True or False: If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and it is assumed that the amount of gasoline purchased per car is symmetric, there is approximately a 68.26% chance that a random sample of 16 cars will have a sample mean between 14 and 16 gallons.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 42. True or False: If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between 14 and 16 gallons.

ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, probability 43. True or False: As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean 44. True or False: If the population distribution is skewed, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem

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7-12

Sampling Distributions

45. True or False: A sampling distribution is a distribution for a statistic.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution 46. True or False: Suppose  = 50 and  = 10 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 47. True or False: Suppose  = 80 and  = 20 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall above 76.08.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 48. True or False: Suppose  = 50 and  = 10 for a population. In a sample where n = 100 is randomly taken, 90% of all possible sample means will fall between 49 and 51.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 49. True or False: The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: central limit theorem 50. True or False: The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: standard error, mean

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Sampling Distributions 7-13 51. True or False: A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution 52. True or False: As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: standard error, properties 53. True or False: For distributions such as the normal distribution, the arithmetic mean is considered more stable from sample to sample than other measures of central tendency.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean 54. True or False: The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, standard error 55. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be between 100 and 120 grams?

ANSWER: 0.9545 using Excel or 0.9544 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 56. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be less than 100 grams?

ANSWER: 0.0228 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability

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7-14

Sampling Distributions

57. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be greater than 100 grams?

ANSWER: 0.9772 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 58. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. A sample of 25 cans is to be selected. So, 95% of all sample means will be greater than how many grams?

ANSWER: 101.7757 TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value 59. The amount of tea leaves in a can from a production line is normally distributed with  = 110 grams and  = 25 grams. A sample of 25 cans is to be selected. So, the middle 70% of all sample means will fall between what two values?

ANSWER: 104.8 and 115.2 TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value 60. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the standard error of the mean?

ANSWER: 2.5 minutes TYPE: PR DIFFICULTY: Easy KEYWORDS: standard error, mean 61. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean is between 45 and 52 minutes?

ANSWER: 0.4974 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability

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Sampling Distributions 7-15 62. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. What is the probability that the sample mean will be between 39 and 48 minutes?

ANSWER: 0.8767 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 63. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. 95% of all sample means will fall between what two values?

ANSWER: 40.1 and 49.9 minutes TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, probability 64. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. 90% of the sample means will be greater than what value?

ANSWER: 41.8 minutes TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, probability 65. True or False: The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean has a mean of 36 oz.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, unbiased 66. True or False: The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean has a standard error of 0.15.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, standard error

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7-16

Sampling Distributions

67. True or False: The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The sampling distribution of the sample mean will be approximately normal only if the population sampled is normal.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, central limit theorem 68. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample exceeds 36.01 oz. is __________.

ANSWER: 0.3446 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 69. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is less than 36.03 is __________.

ANSWER: 0.8849 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 70. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.94 and 36.06 oz. is __________.

ANSWER: 0.9836 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 71. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. The probability that the mean of the sample is between 35.95 and 35.98 oz. is __________.

ANSWER: 0.1891 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem

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Sampling Distributions 7-17 72. The amount of bleach a machine pours into bottles has a mean of 36 oz. with a standard deviation of 0.15 oz. Suppose we take a random sample of 36 bottles filled by this machine. So, the middle 95% of the sample means based on samples of size 36 will be between __________ and __________.

ANSWER: 35.951 and 36.049 ounces TYPE: FI DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value, central limit theorem 73. A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The mean of the sampling distribution of the sample mean is __________ minutes.

ANSWER: 80 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, unbiased 74. A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The standard deviation of the sampling distribution of the sample mean is __________ minutes.

ANSWER: 5 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, standard error 75. A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be less than 82 minutes is __________.

ANSWER: 0.6554 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 76. A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be between 77 and 89 minutes is __________.

ANSWER: 0.6898 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem

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7-18

Sampling Distributions

77. A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. The probability that the sample mean will be greater than 88 minutes is __________.

ANSWER: 0.0548 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability, central limit theorem 78. A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken. So, the middle 95% of the sample means based on samples of size 64 will be between __________ and __________.

ANSWER: 70.2 and 89.8 minutes TYPE: FI DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value, central limit theorem 79. To use the normal distribution to approximate the binomial distribution, we need ______ and ______ to be at least 5.

ANSWER: n and n 1    TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, central limit theorem 80. True or False: The sample mean is an unbiased estimate of the population mean.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mean, unbiased 81. True or False: The sample proportion is an unbiased estimate of the population proportion.

ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: proportion, unbiased 82. True or False: The mean of the sampling distribution of a sample proportion is the population proportion,  ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion

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Sampling Distributions 7-19 83. True or False: The standard error of the sampling distribution of a sample proportion is

p 1  p  where p is the sample proportion. n ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion 84. True or False: The standard deviation of the sampling distribution of a sample proportion is

 1    n

where  is the population proportion.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion 85. True or False: A sample of size 25 provides a sample variance of 400. The standard error, in this case equal to 4, is best described as the estimate of the standard deviation of means calculated from samples of size 25.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: standard error, mean 86. True or False: An unbiased estimator will have a value, on average across samples, equal to the population parameter value.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: unbiased, mean 87. True or False: In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mean, standard error 88. True or False: The sample proportion is an unbiased estimator for the population proportion.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: unbiased, proportion Copyright ©2020 Pearson Education, Inc.

7-20

Sampling Distributions

89. True or False: The sample mean is an unbiased estimator for the population mean.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: unbiased, mean 90. Assume that house prices in a neighborhood are normally distributed with a standard deviation of $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than $5,000?

ANSWER: 0.3173 using Excel or 0.3174 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability SCENARIO 7-1 The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours. A random sample of 4 students was taken to estimate the mean study time for the population of all students.

91. Referring to Scenario 7-1, what is the probability that the sample mean exceeds the population mean by more than 2 hours?

ANSWER: 0.3085 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 92. Referring to Scenario 7-1, what is the probability that the sample mean is more than 3 hours below the population mean?

ANSWER: 0.2266 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 93. Referring to Scenario 7-1, what is the probability that the sample mean differs from the population mean by less than 2 hours?

ANSWER: 0.3829 using Excel or 0.3830 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability

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Sampling Distributions 7-21 94. Referring to Scenario 7-1, what is the probability that the sample mean differs from the population mean by more than 3 hours?

ANSWER: 0.4533 using Excel or 0.4532 using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability SCENARIO 7-2 The mean selling price of new homes in a small town over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new home sales from this city was taken.

95. Referring to Scenario 7-2, what is the probability that the sample mean selling price was more than $110,000?

ANSWER: 0.9772 TYPE: PR DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, probability, central limit theorem 96. Referring to Scenario 7-2, what is the probability that the sample mean selling price was between $113,000 and $117,000?

ANSWER: 0.5763 using Excel or 0.5762 using Table E.2 TYPE: PR DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, probability, central limit theorem 97. Referring to Scenario 7-2, what is the probability that the sample mean selling price was between $114,000 and $116,000?

ANSWER: 0.3108 TYPE: PR DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, probability, central limit theorem 98. Referring to Scenario 7-2, without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie? a) $113,000 -- $115,000 b) $114,000 -- $116,000 c) $115,000 -- $117,000 d) $116,000 -- $118,000 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, probability, central limit theorem

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7-22

Sampling Distributions

SCENARIO 7-3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken.

99. Referring to Scenario 7-3, what is the probability that the sample mean lifetime is more than 1,550 hours?

ANSWER: 0.8413 TYPE: PR DIFFICULTY: Easy KEYWORDS: sampling distribution, mean, probability 100. Referring to Scenario 7-3, the probability is 0.15 that the sample mean lifetime is more than how many hours?

ANSWER: 1,651.82 hours using Excel or 1,652 hours using Table E.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling distribution, mean, probability 101. Referring to Scenario 7-3, the probability is 0.20 that the sample mean lifetime differs from the population mean lifetime by at least how many hours?

ANSWER: 64.08 hours using Excel or 64 hours using Table E.2 TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, mean, value SCENARIO 7-4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase. Random samples of size 50 are selected.

102. Referring to Scenario 7-4, the mean of all the sample proportions of customers who will make a purchase after visiting the web site is _______.

ANSWER: 0.15 or 15% TYPE: FI DIFFICULTY: Moderate KEYWORDS: Sampling distributions, proportion, mean 103. Referring to Scenario 7-4, the standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is ________.

ANSWER: 0.05050 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, proportion, standard error Copyright ©2020 Pearson Education, Inc.

Sampling Distributions 7-23 104. True or False: Referring to Scenario 7-4, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, central limit theorem 105. Referring to Scenario 7-4, what proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

ANSWER: 0.1596 TYPE: PR DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, probability 106. Referring to Scenario 7-4, what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

ANSWER: 0.5 TYPE: PR DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, probability 107. Referring to Scenario 7-4, what is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site?

ANSWER: 0.0015 TYPE: PR DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, probability 108. Referring to Scenario 7-4, 90% of the samples will have less than what percentage of customers who will make a purchase after visiting the web site?

ANSWER: 21.47% TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, proportion, value 109. Referring to Scenario 7-4, 90% of the samples will have more than what percentage of customers who will make a purchase after visiting the web site?

ANSWER: 8.528% using Excel or 8.536% using Table E.2 TYPE: PR DIFFICULTY: Difficult KEYWORDS: sampling distribution, proportion, value

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7-24

Sampling Distributions

110. A study at a college in the west coast reveals that, historically, 45% of the students are minority students. The expected percentage of minority students in their next group of freshmen is _______.

ANSWER: 45% TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, proportion, means 111. A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, the standard error of the proportion of students in the samples who are minority students is _________.

ANSWER: 0.05745 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, proportion, standard error 112. A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is _______ that between 30% and 50% of the students in the sample will be minority students.

ANSWER: 0.8034 using Excel or 0.8033 using Table E.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, probability 113. A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is _______ that more than half of the students in the sample will be minority students.

ANSWER: 0.1920 using Excel or 0.1922 using Table E.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, probability 114. A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ______% of minority students.

ANSWER: 49.83 TYPE: FI DIFFICULTY: Difficult KEYWORDS: sampling distribution, proportion, value

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Sampling Distributions 7-25 115. A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If random samples of size 75 are selected, 95% of the samples will have more than ______% of minority students.

ANSWER: 35.55 TYPE: FI DIFFICULTY: Difficult KEYWORDS: sampling distribution, proportion, value SCENARIO 7-5 According to an article, 19% of the entire population in a developing country has high-speed access to the Internet. Random samples of size 200 are selected from the country’s population.

116. Referring to Scenario 7-5, the population mean of all the sample proportions is ______.

ANSWER: 19% or 0.19 TYPE: FI DIFFICULTY: Easy KEYWORDS: proportion, mean, sampling distribution, central limit theorem 117. Referring to Scenario 7-5, the standard error of all the sample proportions is ______.

ANSWER: 0.0277 TYPE: FI DIFFICULTY: Easy KEYWORDS: proportion, standard error, sampling distribution, central limit theorem 118. Referring to Scenario 7-5, among all the random samples of size 200, ______ % will have between 14% and 24% who have high-speed access to the Internet.

ANSWER: 92.85 using Excel or 92.82 using Table E.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, central limit theorem 119. Referring to Scenario 7-5, among all the random samples of size 200, ______ % will have between 9% and 29% who have high-speed access to the Internet.

ANSWER: 99.97 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, central limit theorem

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7-26

Sampling Distributions

120. Referring to Scenario 7-5, among all the random samples of size 200, ______ % will have more than 30% who have high-speed access to the Internet.

ANSWER: 0.0000 or virtually zero TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, central limit theorem 121. Referring to Scenario 7-5, among all the random samples of size 200, ______ % will have less than 20% who have high-speed access to the Internet.

ANSWER: 64.08 using Excel or 64.06 using Table E.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, central limit theorem 122. Referring to Scenario 7-5, among all the random samples of size 200, 90 % will have less than _____% that has high-speed access to the Internet.

ANSWER: 22.56 using Excel or 22.55 using Table E.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, proportion, central limit theorem 123. Referring to Scenario 7-5, among all the random samples of size 200, 90 % will have more than _____% who have high-speed access to the Internet.

ANSWER: 15.45 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, proportion, central limit theorem SCENARIO 7-6 Online customer service is a key element to successful online retailing. According to a marketing survey, 37.5% of online customers take advantage of the online customer service. Random samples of 200 customers are selected.

124. Referring to Scenario 7-6, the population mean of all possible sample proportions is ______.

ANSWER: 0.375 or 37.5% TYPE: FI DIFFICULTY: Easy KEYWORDS: proportion, mean, sampling distribution, central limit theorem

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Sampling Distributions 7-27 125. Referring to Scenario 7-6, the standard error of all possible sample proportions is ______.

ANSWER: 0.0342 TYPE: FI DIFFICULTY: Easy KEYWORDS: proportion, standard error, sampling distribution, central limit theorem 126. Referring to Scenario 7-6, ____ % of the samples are likely to have between 35% and 40% who take advantage of online customer service.

ANSWER: 53.48 using Excel or 53.46 using Table E.2 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, central limit theorem 127. Referring to Scenario 7-6, ____ % of the samples are likely to have less than 37.5% who take advantage of online customer service.

ANSWER: 50 TYPE: FI DIFFICULTY: Easy KEYWORDS: sampling distribution, proportion, central limit theorem, properties of normal distribution 128. Referring to Scenario 7-6, 90% of the samples proportions symmetrically around the population proportion will have between _____% and _____% of the customers who take advantage of online customer service.

ANSWER: 31.87 and 43.13 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, proportion, central limit theorem 129. Referring to Scenario 7-6, 95% of the samples that proportion symmetrically around the population proportion will have between _____% and _____% of the customers who take advantage of online customer service.

ANSWER: 30.79 and 44.21 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sampling distribution, proportion, central limit theorem

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Confidence Interval Estimation

8-1

CHAPTER 8: CONFIDENCE INTERVAL ESTIMATION 1. True or False: A point estimate consists of a single sample statistic that is used to estimate the true population parameter.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: point estimate 2. True or False: The sample mean is a point estimate of the population mean.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: point estimate, mean 3. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress? a) 740 b) 830 c) 920 d) 1,660 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: point estimate, mean 4. Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. What value will be used as the point estimate for the mean endowment of all private colleges in the United States? a) $1,447.8 b) $180.975 c) $143.042 d) $8 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: point estimate, mean

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8-2

Confidence Interval Estimation

5. True or False: A population parameter is used to estimate a confidence interval.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: point estimate, confidence interval 6. True or False: For a given data set, the confidence interval will be wider for 95% confidence than for 90% confidence.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: width, confidence interval, properties 7. True or False: Holding the sample size fixed, increasing the level of confidence in a confidence interval will necessarily lead to a wider confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: trade-off, confidence interval, properties, width 8. True or False: Holding the level of confidence fixed, increasing the sample size will lead to a wider confidence interval.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: trade-off, confidence interval, properties, width 9. True or False: Holding the width of a confidence interval fixed, increasing the level of confidence can be achieved with a lower sample size.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: trade-off, confidence interval, properties, width

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Confidence Interval Estimation

8-3

10. Suppose a 95% confidence interval for  turns out to be (1,000, 2,100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? a) Increase the sample size. b) Increase the confidence level. c) Increase the population mean. d) Increase the sample mean.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: width, confidence interval, properties 11. Suppose a 95% confidence interval for  has been constructed. If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would . (Assume that the sample statistics gathered would not change very much for the new sample.) a) be larger than the current interval width b) be narrower than the current interval width c) be the same as the current interval width d) be unknown until actual sample sizes and reliability levels were determined ANSWER: TYPE: MC DIFFICULTY: Moderate KEYWORDS: width, confidence interval, properties 12. In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to an interval. a) narrower b) wider c) less significant d) biased ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: width, confidence interval, properties 13. True or False: Other things being equal, as the confidence level for a confidence interval increases, the width of the interval increases.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: trade-off, confidence interval, properties

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8-4

Confidence Interval Estimation

14. True or False: The confidence interval obtained will always correctly estimate the population parameter.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, interpretation 15. True or False: Other things being equal, the confidence interval for the mean will be wider for 95% confidence than for 90% confidence.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, properties, width 16. True or False: The difference between the upper limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 17. True or False: The difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 18. True or False: Sampling error equals half the width of a confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 19. True or False: The width of a confidence interval equals twice the sampling error.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error

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Confidence Interval Estimation

8-5

20. True or False: The sampling error can either be positive or negative.

ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: sampling error 21. True or False: The difference between the sample mean and the population mean is called the sampling error.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: sampling error 22. True or False: The difference between the sample proportion and the population proportion is called the sampling error.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: sampling error 23. True or False: The difference between the sample size and the population size is called the sampling error.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sampling error 24. True or False: The confidence interval estimate of the population mean is constructed around the sample mean.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean

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8-6

Confidence Interval Estimation

25. A 99% confidence interval estimate can be interpreted to mean that a) if all possible samples of size n are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. b) we have 99% confidence that we have selected a sample whose interval does include the population mean. c) Both above. d) None of the above.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, confidence interval 26. An economist is interested in studying the incomes of consumers in a country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What is the upper end in a 99% confidence interval for the average income? a) $15,052 b) $15,141 c) $15,330 d) $15,364 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: confidence interval, mean, standardized normal distribution 27. An economist is interested in studying the incomes of consumers in a country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What is the width of the 90% confidence interval? a) $232.60 b) $364.30 c) $465.23 d) $728.60 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: width, confidence interval, means, standardized normal distribution 28. True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, standardized normal distribution

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Confidence Interval Estimation

8-7

29. True or False: A sample size of 5 provides a sample mean of 9.6. If the population variance is known to be 5 and the population distribution is assumed to be normal, the lower limit for a 90% confidence interval is 7.96.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, standardized normal distribution 30. The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: t distribution, standardized normal distribution, degrees of freedom 31. True or False: The t distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 32. True or False: For a t distribution with 12 degrees of freedom, the area between – 2.6810 and 2.1788 is 0.980.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: t distribution, degrees of freedom 33. If you were constructing a 99% confidence interval of the population mean based on a sample of n=25 where the standard deviation of the sample S = 0.05, the critical value of t will be a) 2.7969 b) 2.7874 c) 2.4922 d) 2.4851 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: critical value, t distribution

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8-8

Confidence Interval Estimation

34. Which of the following is not true about the Student’s t distribution? a) It has more area in the tails and less in the center than does the normal distribution. b) It is used to construct confidence intervals for the population mean when the population standard deviation is known. c) It is bell shaped and symmetrical. d) As the number of degrees of freedom increases, the t distribution approaches the normal distribution.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t distribution, properties 35. True or False: The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, standard deviation unknown 36. The t distribution a) assumes the population is normally distributed. b) approaches the normal distribution as the sample size increases. c) has more area in the tails than does the normal distribution. d) All the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: t distribution, properties 37. It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct? a) 95% of the sampled total compensation values fell between $2,181,260 and $5,836,180. b) We are 95% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180. c) In the population of Service industry CEOs, 95% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180. d) We are 95% confident that the mean total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180.

ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: confidence interval, mean, interpretation

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Confidence Interval Estimation

8-9

38. It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the mean total compensation of CEOs in the Service industry is more than $3,000,000? a) Yes, and I am 95% confident of it. b) Yes, and I am 78% confident of it. c) I am 95% confident that the mean compensation is $3,000,000. d) I cannot conclude that the mean exceeds $3,000,000 at the 95% confidence level.

ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: confidence interval, mean, interpretation 39. Suppose a 95% confidence interval for  turns out to be (1,000, 2,100). Give a definition of what it means to be “95% confident” as an inference. a) In repeated sampling, the population parameter would fall in the given interval 95% of the time. b) In repeated sampling, 95% of the intervals constructed would contain the population mean. c) 95% of the observations in the entire population fall in the given interval. d) 95% of the observations in the sample fall in the given interval.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 40. A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X  $50.50 and S  20 , S being the standard deviation. Assuming the distribution of the amount spent on their first visit is normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for  ? a) Approximately normal with a mean of $50.50 b) A standard normal distribution c) A t distribution with 15 degrees of freedom d) A t distribution with 14 degrees of freedom ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution, degrees of freedom

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8-10

Confidence Interval Estimation

41. A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain’s new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X  $50.50 and S  20 , S being the standard deviation. Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain’s new store in the mall if the amount spent follows a normal distribution. a) $50.50  $9.09 b) $50.50  $10.12 c) $50.50  $11.00 d) $50.50  $11.08 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 42. Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield X  180.975 and S  143.042 . Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments. a) $180.975  $94.066 b) $180.975  $99.123 c) $180.975  $116.621 d) $180.975  $119.586 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution Note: The value of the sample mean is the correct answer for the previous question.

43. As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, X  396 and S = 100. Which of the following assumptions is necessary for a confidence interval to be valid? a) The population sampled from has an approximate normal distribution. b) The population sampled from has an approximate t distribution. c) The mean of the sample equals the mean of the population. d) None of these assumptions are necessary.

ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: confidence interval, mean, t distribution

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Confidence Interval Estimation

8-11

44. As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, X  396 and S = 100. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.

ANSWER: 396  24.9793 or 371.0207    420.9793 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 45. True or False: In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be 6 degrees of freedom.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution, degrees of freedom 46. True or False: A race car driver tested his car for time from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 mean time is 4.52 seconds to 5.18 seconds.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 47. True or False: Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 48. True or False: A random sample of 50 provides a sample mean of 31 with a standard deviation of S = 14. The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution

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Confidence Interval Estimation

49. True or False: In forming a 90% confidence interval for a population mean from a sample size of 22, the number of degrees of freedom from the t distribution equals 22.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution, degrees of freedom 50. True or False: The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 51. True or False: The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 52. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 90% confidence interval to estimate the true proportion of students who receive financial aid.

ANSWER: 0.59  0.057 or 0.533    0.647 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 53. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for  is 0.59  0.07. Interpret this interval. a) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66. b) 95% of the students get between 52% and 66% of their tuition paid for by financial aid. c) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid. d) We are 95% confident that 59% of the students are on some sort of financial aid.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation

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Confidence Interval Estimation

8-13

54. The county clerk wants to estimate the proportion of voters who will need special election facilities.

No information is available from past data. The clerk wants to construct a 95% confidence interval for the population proportion which extends at most 0.07 to either side of the sample proportion. How large a sample must be taken to assure these conditions are met?

ANSWER: 196 TYPE: PR DIFFICULTY: Difficult KEYWORDS: sample size determination, proportion EXPLANATION: Since no sample proportion is available from past data, assume π=0.5 55. The county clerk wants to estimate the proportion of voters who will need special election facilities.

Suppose a sample of 400 voters was taken. If 150 need special election facilities, calculate a 90% confidence interval for the population proportion.

ANSWER: 0.3352 to 0.4148 TYPE: PR DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 56. A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 300 items, 27 are defective. A 90% confidence interval for the proportion of defectives from this production line would go from __________ to __________.

ANSWER: 0.063 to 0.117 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 57. A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A confidence interval will be obtained for the proportion of cases of recidivism. Part of this calculation includes the estimated standard error of the sample proportion. For this sample, the estimated standard error is __________.

ANSWER: 0.028 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 58. A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A 99% confidence interval for the proportion of cases of recidivism would go from __________ to __________.

ANSWER: 0.189 to 0.331 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion

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8-14

Confidence Interval Estimation

59. True or False: A sample of 100 fuses from a very large shipment is found to have 10 that are defective. The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 60. True or False: The confidence interval estimate of the population proportion is constructed around the sample proportion.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 61. True or False: The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, t distribution 62. True or False: The standardized normal distribution is used to develop a confidence interval estimate of the population proportion regardless of whether the population standard deviation is known.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, standardized normal distribution 63. True or False: The standardized normal distribution is used to develop a confidence interval estimate of the population proportion when the sample size is sufficiently large.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, standardized normal distribution 64. The width of a confidence interval estimate for a proportion will be a) narrower for 99% confidence than for 95% confidence. b) wider for a sample size of 100 than for a sample size of 50. c) narrower for 90% confidence than for 95% confidence. d) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, properties, width

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Confidence Interval Estimation

8-15

65. When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that  is estimated to be, the sample size required __________. a) is smaller b) is larger c) is not affected d) can be smaller, larger or unaffected ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, properties 66. A confidence interval was used to estimate the proportion of statistics students who are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60? a) No, and we are 90% sure of it. b) No. The proportion is 54.17%. c) Maybe. 0.60 is a believable value of the population proportion based on the information above. d) Yes, and we are 90% sure of it.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, testing 67. When determining the sample size necessary for estimating the true population mean, which factor is not considered when sampling with replacement? a) The population size. b) The population standard deviation. c) The level of confidence desired in the estimate. d) The allowable or tolerable sampling error.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: sample size determination, mean 68. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, approximately how large a sample did her assistant use to determine the interval estimate? a) 2 b) 3 c) 12 d) It cannot be determined from the information given.

ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: sample size determination, mean Copyright ©2020 Pearson Education, Inc.

8-16

Confidence Interval Estimation

69. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant for a 95% confidence interval, approximately how large a sample did her assistant use to determine the interval estimate? a) 125 b) 13 c) 11 d) 4 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: sample size determination, mean 70. The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant to use 25 days of data to construct the interval estimate, what confidence level can she attach to the interval estimate? a) 99.7% b) 99.0% c) 98.0% d) 95.4% ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: sample size determination, mean 71. An economist is interested in studying the incomes of consumers in a country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100? a) n = 1537 b) n = 385 c) n = 40 d) n = 20 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample size determination, mean

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Confidence Interval Estimation

8-17

72. As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, X  396 and S = 100. Using the sample standard deviation as an estimate for the population standard deviation, what size sample should the director choose if she wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability?

ANSWER: n = 166 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sample size determination, mean Note: The answer is computed using Z = 2.575 from Table E.2 or Z = 2.5758293 using PHStat.

73. Suppose a department store wants to estimate the mean age of the customers of its contemporary apparel department, correct to within 2 years, with level of confidence equal to 95%. Management believes that the standard deviation is 8 years. The sample size they should take is ________.

ANSWER: 62 TYPE: FI DIFFICULTY: Easy KEYWORDS: sample size determination, mean 74. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled? a) n = 1,844 b) n = 1,784 c) n = 1,503 d) n = 1,435 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample size determination, proportion Note: The answer is computed using Z = 2.575 from Table E.2 or Z = 2.5758293 using PHStat.

75. A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within 0.08 using 95% confidence? a) 105 b) 150 c) 420 d) 597 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sample size determination, proportion Copyright ©2020 Pearson Education, Inc.

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Confidence Interval Estimation

76. A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Currently, the students pay $400 per credit hour. The university system administrators are contemplating charging each student a set fee of $7,000 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation. How large a total sample would they need to take?

ANSWER: n = 2033 TYPE: PR DIFFICULTY: Easy KEYWORDS: sample size determination, mean SCENARIO 8-1 The managers of a company are worried about the morale of their employees. To determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points.

77. Referring to Scenario 8-1, they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.

ANSWER: 63 TYPE: FI DIFFICULTY: Easy KEYWORDS: sample size determination, mean 78. Referring to Scenario 8-1, due to financial limitations, the managers decide to take a sample of 45 employees. This yields a mean score of 88.0 points. A 90% confidence interval would go from ________ to ________.

ANSWER: 82.12 to 93.88 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, standardized normal distribution 79. True or False: Referring to Scenario 8-1, this confidence interval is only valid if the scores on the Fortunato test are normally distributed.

ANSWER: False TYPE: TF DIFFICULTY: Difficult EXPLANATION: With a sample size of 45, this confidence interval will still be valid if the scores are not normally distributed due to the central limit theorem.

KEYWORDS: confidence interval, mean, standardized normal distribution, central limit theorem

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Confidence Interval Estimation

8-19

SCENARIO 8-2 A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine.

80. Referring to Scenario 8-2, the critical value to use in obtaining the confidence interval is ________.

ANSWER: 2.58 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, mean, standardized normal distribution 81. Referring to Scenario 8-2, the confidence interval goes from ________ to ________.

ANSWER: 12.09 to 12.19 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, standardized normal distribution 82. True or False: Referring to Scenario 8-2, the confidence interval indicates that the machine is not working properly.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, standardized normal distribution, interpretation 83. True or False: Referring to Scenario 8-2, the confidence interval is valid only if the lengths cut are normally distributed.

ANSWER: False TYPE: TF DIFFICULTY: Moderate EXPLANATION: With a sample size of 70, this confidence interval will still be valid if the lengths cut are not normally distributed due to the central limit theorem.

KEYWORDS: confidence interval, mean, standardized normal distribution, central limit theorem 84. Referring to Scenario 8-2, suppose the engineer had decided to estimate the mean length to within 0.03 with 99% confidence. Then the sample size would be ________.

ANSWER: 165.8724 rounds up to 166 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sample size determination, mean Note: The answer is computed using Z = 2.575 from Table E.2 or Z = 2.5758293 using PHStat.

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8-20

Confidence Interval Estimation

SCENARIO 8-3 To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program.

85. Referring to Scenario 8-3, the mean of the sample is __________, while the standard deviation of the sample is __________.

ANSWER: 6.0; 2.0 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, mean 86. Referring to Scenario 8-3, the confidence interval will be based on __________ degrees of freedom.

ANSWER: 7 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution, degrees of freedom 87. Referring to Scenario 8-3, the critical value used in constructing a 90% confidence interval is __________.

ANSWER: 1.8946 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 88. Referring to Scenario 8-3, a 90% confidence interval for the mean score of actuarial students in the special program is from __________ to __________.

ANSWER: 4.66 to 7.34 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 89. True or False: Referring to Scenario 8-3, for the confidence interval to be valid, it is necessary that test scores of students in the special study program on the actuarial exam be normally distributed.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution

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Confidence Interval Estimation

8-21

90. True or False: Referring to Scenario 8-3, it is possible that the confidence interval obtained will not contain the mean score for all actuarial students in the special study program.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 91. True or False: Referring to Scenario 8-3, if we use the same sample information to obtain a 95% confidence interval, the resulting interval would be narrower than the one obtained here with 90% confidence.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Widths, confidence interval, mean, properties SCENARIO 8-4 The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64, 11.84, 12.13, 11.99, and 11.77.

92. Referring to Scenario 8-4, a confidence interval for this sample would be based on the t distribution with __________ degrees of freedom.

ANSWER: 6 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution, degrees of freedom 93. Referring to Scenario 8-4, the critical value for a 99% confidence interval for this sample is __________.

ANSWER: 3.7074 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution 94. Referring to Scenario 8-4, a 99% confidence interval for the mean voltage of the power packs is from __________ to __________.

ANSWER: 11.6367 to 12.0891 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution

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8-22

Confidence Interval Estimation

95. True or False: Referring to Scenario 8-4, a 95% confidence interval for the mean voltage of the power pack is wider than a 99% confidence interval.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, properties, width 96. True or False: Referring to Scenario 8-4, a 99% confidence interval will contain 99% of the voltages for all such power packs.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 97. True or False: Referring to Scenario 8-4, a confidence interval estimate of the population mean would only be valid if the distribution of voltages is normal.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, t distribution 98. True or False: Referring to Scenario 8-4, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, properties, width 99. True or False: Referring to Scenario 8-4, it is possible that the 99% confidence interval calculated from the data will not contain the mean voltage for the sample.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, interpretation 100. True or False: Referring to Scenario 8-4, it is possible that the 99% confidence interval calculated from the data will not contain the mean voltage for the entire population.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, interpretation

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Confidence Interval Estimation

8-23

SCENARIO 8-5 A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61.

101. True or False: Referring to Scenario 8-5, 95% of the time, the sample mean salary offer to management majors will fall between 47.19 and 52.61.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 102. True or False: Referring to Scenario 8-5, 95% of the salary offers are between 47.19 and 52.61.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 103. True or False: Referring to Scenario 8-5, it is possible that the mean of the population is between 47.19 and 52.61.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 104. True or False: Referring to Scenario 8-5, it is possible that the mean of the population is not between 47.19 and 52.61.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 105. True or False: Referring to Scenario 8-5, 95% of the sample means will fall between 47.19 and 52.61.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 106. True or False: Referring to Scenario 8-5, 95% of all confidence intervals constructed similarly to this one with a sample size of 10 will contain the mean of the population.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation Copyright ©2020 Pearson Education, Inc.

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Confidence Interval Estimation

107. True or False: Referring to Scenario 8-5, a 99% confidence interval for the mean of the population from the same sample would be wider than 47.19 to 52.61.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, properties, width 108. True or False: Referring to Scenario 8-5, the confidence interval obtained is valid only if the distribution of the population of salary offers is normal.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, t distribution SCENARIO 8-6 After an extensive advertising campaign, the manager of a company wants to estimate the proportion of potential customers that recognize a new product. She samples 120 potential consumers and finds that 54 recognize this product. She uses this sample information to obtain a 95% confidence interval that goes from 0.36 to 0.54.

109. True or False: Referring to Scenario 8-6, the parameter of interest to the manager is the proportion of potential customers in this sample that recognize the new product.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, parameter 110. True or False: Referring to Scenario 8-6, the parameter of interest is 54/120 = 0.45.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, parameter 111. True or False: Referring to Scenario 8-6, this interval requires the use of the t distribution to obtain the confidence coefficient.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, t distribution

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Confidence Interval Estimation

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112. True or False: Referring to Scenario 8-6, this interval requires the assumption that the distribution of the number of people recognizing the product has a normal distribution.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 113. True or False: Referring to Scenario 8-6, 95% of the time, the proportion of people that recognize the product will fall between 0.36 and 0.54.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation 114. True or False: Referring to Scenario 8-6, 95% of the time, the sample proportion of people that recognize the product will fall between 0.36 and 0.54.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation 115. True or False: Referring to Scenario 8-6, 95% of the people will recognize the product between 36% and 54% of the time.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, proportion, interpretation 116. True or False: Referring to Scenario 8-6, it is possible that the true proportion of people that recognize the product is between 0.36 and 0.54.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation 117. True or False: Referring to Scenario 8-6, it is possible that the true proportion of people that recognize the product is not between 0.36 and 0.54.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation

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118. The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. Suppose there is no information about the proportion of students who might choose the option. What size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

ANSWER: 97 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sample size determination, proportion 119. The head of a computer science department is interested in estimating the proportion of students entering the department who will choose the new computer engineering option. A preliminary sample indicates that the proportion will be around 0.25. Therefore, what size sample should the department head take if she wants to be 95% confident that the estimate is within 0.10 of the true proportion?

ANSWER: 72 TYPE: PR DIFFICULTY: Easy KEYWORDS: sample size determination, proportion SCENARIO 8-7 A hotel chain wants to estimate the mean number of rooms rented daily in a given month. The population of rooms rented daily is assumed to be normally distributed for each month with a standard deviation of 240 rooms. During February, a sample of 25 days has a sample mean of 370 rooms.

120. True or False: Referring to Scenario 8-7, the parameter of interest is the mean number of rooms rented daily in a given month.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, parameter 121. True or False: Referring to Scenario 8-7, the parameter of interest is the proportion of the rooms rented daily in a given month.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, parameter

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122. Referring to Scenario 8-7, the critical value for a 99% confidence interval for this sample is __________.

ANSWER: 2.5758 or 2.58 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, mean 123. Referring to Scenario 8-7, a 99% confidence interval for the mean number of rooms rented daily in a given month is from __________ to __________.

ANSWER: 246.3602 to 493.6398 or 246.36 to 493.64 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, mean 124. Referring to Scenario 8-7, the sampling error of a 99% confidence interval for the mean number of rooms rented daily in a given month is __________.

ANSWER: 123.6398 or 123.64 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, sampling error 125. True or False: Referring to Scenario 8-7, a 95% confidence interval for the mean number of rooms rented daily in a given month is narrower than a 99% confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, properties, width 126. True or False: Referring to Scenario 8-7, a 99% confidence interval will contain 99% of the sample mean number of rooms rented daily in a given month.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, mean, interpretation 127. True or False: Referring to Scenario 8-7, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Widths, confidence interval, mean, properties

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128. True or False: Referring to Scenario 8-7, it is possible that the 99% confidence interval calculated from the data will not contain the sample mean number of rooms rented daily in a given month.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, interpretation 129. True or False: Referring to Scenario 8-7, it is possible that the 99% confidence interval calculated from the data will not contain the population mean number of rooms rented daily in a given month.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, interpretation 130. True or False: Referring to Scenario 8-7, we are 99% confident that between 246.36% and 493.64% of the rooms will be rented daily in a given month.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, interpretation 131. True or False: Referring to Scenario 8-7, we are 99% confident that the average number of rooms rented daily in a given month is somewhere between 246.36 and 493.64.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, mean, interpretation SCENARIO 8-8 The president of a university would like to estimate the proportion of the student population that owns a personal computer. In a sample of 500 students, 417 own a personal computer.

132. True or False: Referring to Scenario 8-8, the parameter of interest is the mean number of students in the population who own a personal computer.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, parameter

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133. True or False: Referring to Scenario 8-8, the parameter of interest is the proportion of the student population who own a personal computer.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, parameter 134. Referring to Scenario 8-8, the critical value for a 99% confidence interval for this sample is __________.

ANSWER: 2.5758 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 135. Referring to Scenario 8-8, a 99% confidence interval for the proportion of the student population who own a personal computer is from __________ to __________.

ANSWER: 0.7911 to 0.8769 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 136. Referring to Scenario 8-8, the sampling error of a 99% confidence interval for the proportion of the student population who own a personal computer is __________.

ANSWER: 0.04286 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, sampling error 137. True or False: Referring to Scenario 8-8, a 95% confidence interval for the proportion of the student population who own a personal computer is narrower than a 99% confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, properties, width 138. True or False: Referring to Scenario 8-8, a 99% confidence interval will contain 99% of the student population who own a personal computer.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation

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139. True or False: Referring to Scenario 8-8, a confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who own a personal computer is normal.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 140. True or False: Referring to Scenario 8-8, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: width, confidence interval, proportion, properties 141. True or False: Referring to Scenario 8-8, it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who own a personal computer.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, interpretation 142. True or False: Referring to Scenario 8-8, it is possible that the 99% confidence interval calculated from the data will not contain the proportion of the student population who own a personal computer.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, interpretation 143. True or False: Referring to Scenario 8-8, we are 99% confident that the mean numbers of student population who own a personal computer is between 0.7911 and 0.8769.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, interpretation 144. True or False: Referring to Scenario 8-8, we are 99% confident that between 79.11% and 87.69% of the student population own a personal computer.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, interpretation

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SCENARIO 8-9 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered “Yes” and 1,456 answered “no”.

145. True or False: Referring to Scenario 8-9, the parameter of interest is the total number of students in the population who feel comfortable reporting cheating by their fellow students.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, parameter 146. True or False: Referring to Scenario 8-9, the parameter of interest is the proportion of the student population who feel comfortable reporting cheating by their fellow students.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, parameter 147. Referring to Scenario 8-9, the critical value for a 99% confidence interval for this sample is __________.

ANSWER: 2.5758 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 148. Referring to Scenario 8-9, a 99% confidence interval for the proportion of the student population who feel comfortable reporting cheating by their fellow students is from __________ to __________.

ANSWER: 0.4557 to 0.5043 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 149. Referring to Scenario 8-9, the sampling error of a 99% confidence interval for the proportion of student population who feel comfortable reporting cheating by their fellow students is __________.

ANSWER: 0.0243 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, sampling error

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150. True or False: Referring to Scenario 8-9, a 95% confidence interval for the proportion of the student population who feel comfortable reporting cheating by their fellow students is narrower than a 99% confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: width, confidence interval, proportion, properties 151. True or False: Referring to Scenario 8-9, a 99% confidence interval will contain 99% of the student population who feel comfortable reporting cheating by their fellow students.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation 152. True or False: Referring to Scenario 8-9, a confidence interval estimate of the population proportion would only be valid if the distribution of the number of students who feel comfortable reporting cheating by their fellow students is normal.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 153. True or False: Referring to Scenario 8-9, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: width, confidence interval, proportion, properties 154. True or False: Referring to Scenario 8-9, it is possible that the 99% confidence interval calculated from the data will not contain the sample proportion of students who feel comfortable reporting cheating by their fellow students.

ANSWER: False TYPE: TF DIFFICULTY: Moderate EXPLANATION: The confidence interval always contains the sample proportion.

KEYWORDS: confidence interval, proportion, interpretation 155. True or False: Referring to Scenario 8-9, it is possible that the 99% confidence interval calculated from the data will not contain the proportion of the student population who feel comfortable reporting cheating by their fellow students.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, interpretation Copyright ©2020 Pearson Education, Inc.

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156. True or False: Referring to Scenario 8-9, we are 99% confident that the total number of the student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, proportion, interpretation 157. True or False: Referring to Scenario 8-9, we are 99% confident that between 45.57% and 50.43% of the student population feel comfortable reporting cheating by their fellow students.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, interpretation SCENARIO 8-10 A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report, 50% have caught salespeople working a second job on company time, 22% have caught salespeople listing a “strip bar” as a restaurant on an expense report, and 19% have caught salespeople giving a kickback to a customer.

158. Referring to Scenario 8-10, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report.

ANSWER: 0.5116 to 0.6484 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 159. Referring to Scenario 8-10, the critical value for a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is __________.

ANSWER: 1.96 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 160. Referring to Scenario 8-10, the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report is __________.

ANSWER: 0.0684 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, sampling error Copyright ©2020 Pearson Education, Inc.

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161. True or False: Referring to Scenario 8-10, a 95% confidence interval will contain 95% of the population proportion of managers who have caught salespeople cheating on an expense report.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation 162. True or False: Referring to Scenario 8-10, it is possible that the 95% confidence interval calculated from the data will not contain the sample proportion of managers who have caught salespeople cheating on an expense report.

ANSWER: False TYPE: TF DIFFICULTY: Moderate EXPLANATION: The confidence interval always contains the sample proportion.

KEYWORDS: confidence interval, proportion, interpretation 163. True or False: Referring to Scenario 8-10, it is possible that the 95% confidence interval calculated from the data will not contain the population proportion of managers who have caught salespeople cheating on an expense report.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, interpretation 164. True or False: Referring to Scenario 8-10, we are 95% confident that the population mean number of managers who have caught salespeople cheating on an expense report is between 0.5116 to 0.6484.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, proportion, interpretation 165. True or False: Referring to Scenario 8-10, we are 95% confident that between 51.16% and 64.84% of managers in the population have caught salespeople cheating on an expense report.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, interpretation 166. Referring to Scenario 8-10, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time.

ANSWER: 0.4307 to 0.5693 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion

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167. Referring to Scenario 8-10, the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople working a second job on company time is __________.

ANSWER: 0.0693 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, sampling error 168. Referring to Scenario 8-10, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople listing a “strip bar” as a restaurant on an expense report.

ANSWER: 0.1626 to 0.2774 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 169. Referring to Scenario 8-10, the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople listing a “strip bar” as a restaurant on an expense report is __________.

ANSWER: 0.05741 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, sampling error 170. Referring to Scenario 8-10, construct a 95% confidence interval estimate of the population proportion of managers who have caught salespeople giving a kickback to a customer.

ANSWER: 0.1356 to 0.2444 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion 171. Referring to Scenario 8-10, the sampling error of a 95% confidence interval estimate of the population proportion of managers who have caught salespeople giving a kickback to a customer is __________.

ANSWER: 0.05437 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, sampling error

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172. Referring to Scenario 8-10, determine the sample size needed to estimate the proportion of managers who have caught salespeople working a second job on company time to within ±0.02 with 95% confidence.

ANSWER: 2401 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sample size determination, confidence interval, proportion SCENARIO 8-11 A poll was conducted by the marketing department of a video game company to determine the popularity of a new game that was targeted to be launched in three months. Telephone interviews with 1,500 young adults were conducted which revealed that 49% said they would purchase the new game. The margin of error was ±3 percentage points.

173. True or False: Referring to Scenario 8-11, the report contains all the essential components for an ethical reporting of poll results.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, ethical issues EXPLANATION: The level of confidence is missing.

174. True or False: Referring to Scenario 8-11, the size of the population is 1,500.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 175. Referring to Scenario 8-11, 1,500 is the size of the a) population b) sample c) frame d) proportion ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: confidence interval, proportion 176. True or False: Referring to Scenario 8-11, you are 99% confidence that the percentage of the targeted young adults who will purchase the new game is somewhere between 46% and 52%.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, proportion, interpretation

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177. True or False: Referring to Scenario 8-11, the standard error is 3%.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, sampling error 178. True or False: Referring to Scenario 8-11, the sampling error is 3%.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, proportion, sampling error 179. Referring to Scenario 8-11, what is the needed sample size to obtain a 95% confidence interval estimate of the percentage of the targeted young adults who will purchase the new game by allowing the same level of margin of error?

ANSWER: 1067 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sample size determination, confidence interval, proportion 180. Referring to Scenario 8-11, what is the needed sample size to obtain a 90% confidence interval estimate of the percentage of the targeted young adults who will purchase the new game by allowing the same level of margin of error?

ANSWER: 752 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sample size determination, confidence interval, proportion 181. Referring to Scenario 8-11, what is the needed sample size to obtain a 95% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within ±5%?

ANSWER: 384 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sample size determination, confidence interval, proportion 182. Referring to Scenario 8-11, what is the needed sample size to obtain a 95% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within ±5% if you do not have the information on the 49% in the interviews who said that they would purchase the new game?

ANSWER: 385 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sample size determination, confidence interval, proportion

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183. Referring to Scenario 8-11, what is the needed sample size to obtain a 99% confidence interval in estimating the percentage of the targeted young adults who will purchase the new game to within ±5% if you do not have the information on the 49% in the interviews who said that they would purchase the new game?

ANSWER: 664 using Z = 2.5758 or 666 using Z = 2.58 TYPE: PR DIFFICULTY: Moderate KEYWORDS: sample size determination, confidence interval, proportion SCENARIO 8-12 The Three Brothers Energy Drink Company bottles and distributes a popular drink for athletes and exercise enthusiasts. Because of its marketing successes the company has installed an additional filling machine and the managers are eager to use it in daily operations. The machine is set to fill bottles at 16 oz.

However, we know there is inherent machine variability and quality control has determined through testing a mean of 16.2 oz. and a standard deviation of 0.3 oz. using a 100 bottle sample.

184. Refer to Scenario 8-12.

In calculating a 90% confidence interval for the population what would be the sampling error?

ANSWER: 0.04935 oz.

TYPE: PR DIFFICULTY: Moderate KEYWORDS: t distribution, confidence interval, sampling error 185. Refer to Scenario 8-12.

Find a 90% confidence interval for the mean volume of the filled bottle contents.

ANSWER: 16.1507 to 16.24935 TYPE: PR DIFFICULTY: Moderate KEYWORDS: t distribution, confidence interval, sampling error 186. Refer to Scenario 8-12.

True or False: If we select using a 95% confidence interval in lieu of a 90% one for the mean fill volume, the new interval would be narrower.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, critical value 187. Refer to Scenario 8-12 True or False: It is possible that a 90% confidence interval will not include the mean fill volume.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval Copyright ©2020 Pearson Education, Inc.

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188. Refer to Scenario 8-12. Suppose you want to estimate the population mean fill with 95% confidence and 0.04 oz. sampling error rate. What should be your sample size?

ANSWER: 216.09 or 217 bottles TYPE: PR DIFFICULTY: Moderate KEYWORDS: sampling error, sample size 189. Which of the following statements is(are) correct concerning a 95% confidence interval? a. There is a 0.95 probability that the population parameter of interest is contained within the interval. b. In computing confidence intervals from 20 samples, 19 of the intervals would contain the population mean. c. If you were to produce all possible confidence intervals using the sample mean of each sample of a given size from the population, then 95% of the intervals would contain the population mean. d. There is a 0.05 probability the population parameter of interest is not contained within the interval.

ANSWER: c TYPE: PR DIFFICULTY: Difficult EXPLANATION: Alternatives are wrong because we only define probabilities for random events, the parameter being a fixed value.

KEYWORDS: confidence interval interpretation

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Fundamentals of Hypothesis Testing: One-Sample Tests

CHAPTER 9: FUNDAMENTALS OF HYPOTHESIS TESTING: ONE-SAMPLE TESTS 1. Which of the following would be an appropriate null hypothesis? a) The mean of a population is equal to 55. b) The mean of a sample is equal to 55. c) The mean of a population is greater than 55. d) Only (a) and (c) are appropriate.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, form of hypothesis 2. Which of the following would be an appropriate null hypothesis? a) The population proportion is less than 0.65. b) The sample proportion is less than 0.65. c) The population proportion is not less than 0.65. d) The sample proportion is no less than 0.65.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, form of hypothesis 3. Which of the following would be an appropriate alternative hypothesis? a) The mean of a population is equal to 55. b) The mean of a sample is equal to 55. c) The mean of a population is greater than 55. d) The mean of a sample is greater than 55.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, form of hypothesis 4. Which of the following would be an appropriate alternative hypothesis? a) The population proportion is less than 0.65. b) The sample proportion is less than 0.65. c) The population proportion is not less than 0.65. d) The sample proportion is not less than 0.65.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, form of hypothesis

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5. A Type II error is committed when a) you reject a null hypothesis that is true. b) you don't reject a null hypothesis that is true. c) you reject a null hypothesis that is false. d) you don't reject a null hypothesis that is false.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, Type II error 6. A Type I error is committed when a) you reject a null hypothesis that is true. b) you don't reject a null hypothesis that is true. c) you reject a null hypothesis that is false. d) you don't reject a null hypothesis that is false.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, Type I error 7. The power of a test is measured by its capability of a) rejecting a null hypothesis that is true. b) not rejecting a null hypothesis that is true. c) rejecting a null hypothesis that is false. d) not rejecting a null hypothesis that is false.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, power 8. If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000 a) either a one-tail or two-tail test could be used with equivalent results. b) a one-tail test should be utilized. c) a two-tail test should be utilized. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: one-tail test

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Fundamentals of Hypothesis Testing: One-Sample Tests

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9. If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000 a) either a one-tail or two-tail test could be used with equivalent results. b) a one-tail test should be utilized. c) a two-tail test should be utilized. d) None of the above.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, two-tail test 10. If the p-value is less than  in a two-tail test, a) the null hypothesis should not be rejected. b) the null hypothesis should be rejected. c) a one-tail test should be used. d) no conclusion should be reached.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, p-value, level of significance 11. If a test of hypothesis has a Type I error probability (  ) of 0.01, it means that a) if the null hypothesis is true, you don't reject it 1% of the time. b) if the null hypothesis is true, you reject it 1% of the time. c) if the null hypothesis is false, you don't reject it 1% of the time. d) if the null hypothesis is false, you reject it 1% of the time.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, Type I error, level of significance 12. If the Type I error (  ) for a given test is to be decreased, then for a fixed sample size n a) the Type II error (  ) will also decrease. b) the Type II error (  ) will increase. c) the power of the test will increase. d) a one-tail test must be utilized.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, Type I error, Type II error, sample size

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13. True or False: For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type I error will increase.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: level of significance, sample size, type I error 14. True or False: For a given level of significance, if the sample size is increased but the summary statistics remain the same, the probability of committing a Type II error will increase.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: level of significance, sample size, type II error 15. True or False: For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: sample size, type I error, type II error 16. For a given sample size n, if the level of significance (  ) is decreased, the power of the test a) will increase. b) will decrease. c) will remain the same. d) cannot be determined.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, level of significance, power, sample size 17. For a given level of significance (  ), if the sample size n is increased, the probability of a Type II error (  ) a) will decrease. b) will increase. c) will remain the same. d) cannot be determined.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, level of significance, beta-risk, sample size Copyright ©2020 Pearson Education, Inc.

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18. You know that the level of significance (  ) of a test is 5%, you can tell that the probability of committing a Type II error (  ) is a) 2.5% b) 95%. c) 97.5% d) unknown ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, level of significance, beta-risk 19. You know that the probability of committing a Type II error (  ) is 5%, you can tell that the power of the test is a) 2.5% b) 95%. c) 97.5% d) unknown ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, level of significance, beta-risk, power 20. If a researcher rejects a true null hypothesis, she has made a _______error.

ANSWER: Type I TYPE: FI DIFFICULTY: Easy KEYWORDS: fundamental, Type I error 21. If a researcher does not reject a true null hypothesis, she has made a _______decision.

ANSWER: correct TYPE: FI DIFFICULTY: Easy KEYWORDS: fundamental, decision 22. If a researcher rejects a false null hypothesis, she has made a _______decision.

ANSWER: correct TYPE: FI DIFFICULTY: Easy KEYWORDS: fundamental, decision

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Fundamentals of Hypothesis Testing: One-Sample Tests

23. If a researcher does not reject a false null hypothesis, she has made a _______error.

ANSWER: Type II TYPE: FI DIFFICULTY: Easy KEYWORDS: fundamental, Type II error 24. It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if a) a two-tail test for  is used. b) a one-tail test for  is used. c) Both of the previous statements are true. d) None of the previous statements is true.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, confidence interval, two-tail test 25. The power of a statistical test is a) the probability of not rejecting H0 when it is false. b) the probability of rejecting H0 when it is true. c) the probability of not rejecting H0 when it is true. d) the probability of rejecting H0 when it is false.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, power 26. The symbol for the power of a statistical test is a)  . b) 1 –  . c)  . d) 1 –  .

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, power

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Fundamentals of Hypothesis Testing: One-Sample Tests

27. The symbol for the probability of committing a Type I error of a statistical test is a)  . b) 1 –  . c)  . d) 1 –  .

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, level of significance, probability, type I error 28. The symbol for the level of significance of a statistical test is a)  . b) 1 –  . c)  . d) 1 –  .

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: level of significance, probability, type I error 29. The symbol for the probability of committing a Type II error of a statistical test is a)  . b) 1 –  . c)  . d) 1 –  .

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, probability, type II error 30. The symbol for the confidence coefficient of a statistical test is a)  . b) 1 –  . c)  . d) 1 –  .

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, confidence coefficient

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Fundamentals of Hypothesis Testing: One-Sample Tests

31. Suppose we wish to test H0:   47 versus H1:  > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52? a) We have made a Type I error. b) We have made a Type II error. c) We have made a correct decision d) None of the above are correct.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, conclusion 32. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?

Researchers determined that 60 tissues is the mean number of tissues used during a cold.

Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, S = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60. a) H0 :   60 and H1 :   60. b) H0 :   60 and H1 :   60. c) H0 : X  60 and H1 : X  60. d) H0 : X  52 and H1 : X  52.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean, t test, one-tail test, form of hypothesis, form of hypothesis 33. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?

Researchers determined that 60 tissues is the mean number of tissues used during a cold.

Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, S = 22. Using the sample information provided, calculate the value of the test statistic. a) t   52  60  / 22 b) t   52  60  /  22 / 100  c) t   5 2  6 0  /  2 2 / 1 0 0 2  d) t   52  60  /  22 / 10  ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, t test, one-tail test

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Fundamentals of Hypothesis Testing: One-Sample Tests

9-9

34. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?

Researchers determined that 60 tissues is the mean number of tissues used during a cold.

Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, S = 22. Suppose the alternative you wanted to test was H1 :   60 . State the correct rejection region for  = 0.05. a) Reject H0 if t > 1.6604. b) Reject H0 if t < – 1.6604. c) Reject H0 if t > 1.9842 or Z < – 1.9842. d) Reject H0 if t < – 1.9842.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean, t test, one-tail test, rejection region 35. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?

Researchers determined that 60 tissues is the mean number of tissues used during a cold.

Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, S = 22. Suppose the test statistic does fall in the rejection region at  = 0.05. Which of the following decision is correct? a) At  = 0.05, you do not reject H0. b) At  = 0.05, you reject H0. c) At  = 0.05, you do not reject H0. d) At  = 0.10, you do not reject H0.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, t test, one-tail test, decision 36. How many tissues should the Kimberly Clark Corporation package of Kleenex contain?

Researchers determined that 60 tissues is the mean number of tissues used during a cold.

Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: X = 52, S = 22. Suppose the test statistic does fall in the rejection region at  = 0.05. Which of the following conclusion is correct? a) At  = 0.05, there is not sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues. b) At  = 0.05, there is sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues. c) At  = 0.05, there is insufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues. d) At  = 0.10, there is sufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean, t test, two-tail test, conclusion Copyright ©2020 Pearson Education, Inc.

9-10

Fundamentals of Hypothesis Testing: One-Sample Tests

37. You have created a 95% confidence interval for  with the result 10    15 . What decision will you make if you test H0 :   16 versus H1 :   16 at  = 0.05? a) Reject H0 in favor of H1. b) Do not reject H0 in favor of H1. c) Fail to reject H0 in favor of H1. d) We cannot tell what our decision will be from the information given.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, t test, two-tail test, confidence interval, decision 38. You have created a 95% confidence interval for  with the result 10    15 . What decision will you make if we test H0 :   16 versus H1 :   16 at  = 0.10? a) Reject H0 in favor of H1. b) Do not reject H0 in favor of H1. c) Fail to reject H0 in favor of H1. d) We cannot tell what our decision will be from the information given.

ANSWER: a TYPE: MC DIFFICULTY: Moderate EXPLANATION: The 90% confidence interval is narrower than (10, 15), which still does not contain 16.

KEYWORDS: mean, t test, two-tail test, confidence interval, decision 39. You have created a 95% confidence interval for  with the result 10    15 . What decision will you make if we test H0 :   16 versus H1 :   16 at  = 0.01? a) Reject H0 in favor of H1. b) Do not reject H0 in favor of H1. c) Fail to reject H0 in favor of H1. d) You cannot tell what our decision will be from the information given.

ANSWER: d TYPE: MC DIFFICULTY: Moderate EXPLANATION: The 99% confidence interval is wider than (10, 15), which could have contained 16 or not have contained 16.

KEYWORDS: mean, t test, two-tail test, confidence interval, decision

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Fundamentals of Hypothesis Testing: One-Sample Tests

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40. Suppose you want to test H0 :   30 versus H1 :   30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of H1? a) X = 28, S = 6 b) X = 27, S = 4 c) X = 32, S = 2 d) X = 26, S = 9 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean, one-tail test, rejection region 41. Which of the following statements is not true about the level of significance in a hypothesis test? a) The larger the level of significance, the more likely you are to reject the null hypothesis. b) The level of significance is the maximum risk we are willing to accept in making a Type I error. c) The significance level is also called the  level. d) The significance level is another name for Type II error.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, level of significance 42. If, as a result of a hypothesis test, you reject the null hypothesis when it is false, then you have committed a) a Type II error. b) a Type I error. c) no error. d) an acceptance error.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: fundamental, decision, Type I error, Type II error 43. The value that separates a rejection region from a non-rejection region is called the _______.

ANSWER: critical value TYPE: FI DIFFICULTY: Easy KEYWORDS: fundamental, critical value, rejection region

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9-12

Fundamentals of Hypothesis Testing: One-Sample Tests

44. A is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis. a) significance level b) critical value c) test statistic d) parameter ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: fundamental, test statistic 45. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: a) H0 :   30 versus H1 :   30. b) H0 :   30 versus H1 :   30. c) H0 : X  30 versus H1 : X  30 . d) H0 : X  30 versus H1 : X  30 .

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: one-tail test, mean, form of hypothesis, form of hypothesis 46. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to have a level of significance at 0.01, what rejection region should she use? a) Reject H0 if t < – 2.3263. b) Reject H0 if t < – 2.5758. c) Reject H0 if t > 2.3263. d) Reject H0 if t > 2.5758.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, t test, rejection region

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Fundamentals of Hypothesis Testing: One-Sample Tests

9-13

47. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to have a level of significance at 0.01, what decision should she make? a) Reject H0. b) Reject H1. c) Do not reject H0. d) We cannot tell what her decision should be from the information given.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, decision 48. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to have a level of significance at 0.01 what conclusion can she make? a) There is not sufficient evidence that the mean age of her customers is greater than 30. b) There is sufficient evidence that the mean age of her customers is greater than 30. c) There is not sufficient evidence that the mean age of her customers is not greater than 30. d) There is sufficient evidence that the mean age of her customers is not greater than 30.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, conclusion

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9-14

Fundamentals of Hypothesis Testing: One-Sample Tests

49. The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic? a) 0.3577 b) 0.1423 c) 0.0780 d) 0.02 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, p-value 50. An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $675 with a population standard deviation of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null hypothesis that the daily mean revenue was $675, which test would you use? a) Z-test of a population mean b) Z-test of a population proportion c) t-test of population mean d) t-test of a population proportion ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean, Z test, two-tail test 51. An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $675 with a population standard deviation of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null hypothesis that the daily mean revenue was $675 and decide not to reject the null hypothesis, what can you conclude? a) There is not enough evidence to conclude that the daily mean revenue was $675. b) There is not enough evidence to conclude that the daily mean revenue was not $675. c) There is enough evidence to conclude that the daily mean revenue was $675. d) There is enough evidence to conclude that the daily mean revenue was not $675.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean, Z test, two-tail test, conclusion

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Fundamentals of Hypothesis Testing: One-Sample Tests

9-15

52. A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the auditor should conclude that there is evidence that the mean balance is different from $75, which test would you use? a) Z-test of a population mean b) Z-test of a population proportion c) t-test of population mean d) t-test of a population proportion ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, t test, two-tail test 53. A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65. If you wanted to test whether the mean balance is different from $75 and decided to reject the null hypothesis, what conclusion could you reach? a) There is not evidence that the mean balance is $75. b) There is not evidence that the mean balance is not $75. c) There is evidence that the mean balance is $75. d) There is evidence that the mean balance is not $75.

ANSWER: d TYPE: MC DIFFICULTY: moderate KEYWORDS: mean, t test, two-tail test, conclusion 54. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to: a) – 4.12 b) – 2.33 c) – 1.86 d) – 0.07 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, one-tail test, test statistic

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9-16

Fundamentals of Hypothesis Testing: One-Sample Tests

55. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected.

Suppose that the test statistic is – 2.20. Can you conclude that H0 should be rejected at the (a)  = 0.10, (b)  = 0.05, and (c)  = 0.01 level of Type I error? a) (a) yes; (b) yes; (c) yes b) (a) no; (b) no; (c) no c) (a) no; (b) no; (c) yes d) (a) yes; (b) yes; (c) no ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: proportion, one-tail test, decision 56. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected.

Suppose you reject the null hypothesis. What conclusion can you reach? a) There is not sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90. b) There is sufficient evidence that the proportion of doctors who recommend aspirin is not less than 0.90. c) There is not sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90. d) There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: proportion, one-tail test, conclusion 57. A pizza chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of its brand. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view. State the test of hypothesis that is of interest to the pizza chain. a) H 0 :   0.32 versus H 1 :   0.32 b) H 0 :   0.25 versus H 1 :   0.25 c) H 0 :   5,000 versus H 1 :   5,000 d) H0 :   5,000 versus H1 :   5,000 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, one-tail test, form of hypothesis, form of hypothesis Copyright ©2020 Pearson Education, Inc.

Fundamentals of Hypothesis Testing: One-Sample Tests

9-17

58. A pizza chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view. The value of the test statistic in this problem is approximately equal to: a) 2.80 b) 2.60 c) 1.94 d) 1.30 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, one-tail test, Z test, test statistic 59. A pizza chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view. The p-value associated with the test statistic in this problem is approximately equal to: a) 0.0100 b) 0.0051 c) 0.0026 d) 0.0013 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, one-tail test, Z test, p-value 60. A pizza chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of its brand. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view. The decision on the hypothesis test using a 5% level of significance is: a) to reject H0 in favor of H1. b) to accept H0 in favor of H1. c) to fail to reject H0 in favor of H1. d) we cannot tell what the decision should be from the information given.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, one-tail test, Z test, decision

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9-18

Fundamentals of Hypothesis Testing: One-Sample Tests

61. A pizza chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area have a favorable view of its brain. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have a favorable view. The pizza chain's conclusion from the hypothesis test using a 5% level of significance is: a) to open a new store. b) not to open a new store. c) to delay opening a new store until additional evidence is collected. d) we cannot tell what the decision should be from the information given.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, one-tail test, Z test, conclusion 62. The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a GPS navigation system if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the GPS navigation system. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use? a) Z-test of a population mean b) Z-test of a population proportion c) t-test of population mean d) t-test of a population proportion ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, Z-test, two-tail test

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Fundamentals of Hypothesis Testing: One-Sample Tests

9-19

63. The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a GPS navigation system if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the GPS navigation system. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis, what conclusion could you reach? a) There is sufficient evidence that the proportion is 0.30. b) There is not sufficient evidence that the proportion is 0.30. c) There is sufficient evidence that the proportion is 0.30. d) There is not sufficient evidence that the proportion is not 0.30.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, Z-test two-tail test, conclusion SCENARIO 9-1 Microsoft Excel was used on a set of data involving the number of defective items found in a random sample of 46 cases of light bulbs produced during a morning shift at a plant. A manager wants to know if the mean number of defective bulbs per case is greater than 20 during the morning shift. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 cases: n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: H 0 :   20 ;  = 0.10; df = 45; T Test Statistic = 2.09; One-Tail Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject.

64. Referring to Scenario 9-1, the parameter the manager is interested in is: a) the mean number of defective light bulbs per case produced at the plant. b) the mean number of defective light bulbs per case among the 46 cases. c) the mean number of defective light bulbs per case produced during the morning shift. d) the proportion of cases with defective light bulbs produced at the plant.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, t test, parameter

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Fundamentals of Hypothesis Testing: One-Sample Tests

65. Referring to Scenario 9-1, state the alternative hypothesis for this study.

ANSWER: H1 :   20 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, form of hypothesis 66. Referring to Scenario 9-1, what critical value should the manager use to determine the rejection region? a) 1.6794 b) 1.3011 c) 1.3006 d) 0.6800 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, critical value 67. True or False: Referring to Scenario 9-1, the null hypothesis would be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, decision 68. True or False: Referring to Scenario 9-1, the null hypothesis would be rejected if a 5% probability of committing a Type I error is allowed.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, decision 69. True or False: Referring to Scenario 9-1, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, decision

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Fundamentals of Hypothesis Testing: One-Sample Tests

9-21

70. Referring to Scenario 9-1, the lowest level of significance at which the null hypothesis can be rejected is ______.

ANSWER: 0.021 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, p-value 71. True or False: Referring to Scenario 9-1, the evidence proves beyond a doubt that the mean number of defective bulbs per case is greater than 20 during the morning shift.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, conclusion 72. True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is greater than 20 during the morning shift using a level of significance of 0.10.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, conclusion 73. True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is greater than 20 during the morning shift with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, decision 74. True or False: Referring to Scenario 9-1, the manager can conclude that there is sufficient evidence to show that the mean number of defective bulbs per case is greater than 20 during the morning shift with no more than a 1% probability of incorrectly rejecting the true null hypothesis.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, decision

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Fundamentals of Hypothesis Testing: One-Sample Tests

75. True or False: Referring to Scenario 9-1, if these data were used to perform a two-tail test, the p-value would be 0.042.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, p-value 76. True or False: Suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: mean, t test, p-value, level of significance, decision 77. True or False: Suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: mean, p-value, level of significance, decision 78. True or False: Suppose, in testing a hypothesis about a mean, the Z test statistic is computed to be 2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tail test is used.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: proportion, Z test, test statistic, critical value, decision 79. True or False: In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: pitfalls, testing

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Fundamentals of Hypothesis Testing: One-Sample Tests

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80. True or False: The test statistic measures how close the computed sample statistic has come to the hypothesized population parameter.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: fundamental, test statistic 81. True or False: The statement of the null hypothesis always contains an equality.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: fundamental, form of null hypothesis 82. True or False: The larger the p-value, the more likely you are to reject the null hypothesis.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: fundamental, p-value 83. True or False: The smaller the p-value, the stronger is the evidence against the null hypothesis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: fundamental, p-value 84. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.05.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, two-tail test, decision

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85. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the mean of the population differs from 18, the null hypothesis could be rejected at a level of significance of 0.05.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: fundamental, confidence interval, two-tail test, decision 86. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.10.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: fundamental, confidence interval, two-tail test, decision 87. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.02.

ANSWER: False TYPE: TF DIFFICULTY: Moderate EXPLANATION: We are not sure if 20 will be in the wider confidence interval.

KEYWORDS: fundamental, confidence interval, two-tail test, decision 88. True or False: A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be accepted at a level of significance of 0.01.

ANSWER: False TYPE: TF DIFFICULTY: Moderate EXPLANATION: We are not sure if 20 will be in the wider confidence interval.

KEYWORDS: fundamental, confidence interval, two-tail test, decision

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89. True or False: In testing a hypothesis, you should always raise the question concerning the purpose of the study, survey or experiment.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pitfalls, testing 90. True or False: A proper methodology in performing hypothesis tests is to ask whether a random sample can be selected from the population of interest.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pitfalls, testing 91. True or False: “What conclusions and interpretations can you reach from the results of the hypothesis test?” is not an important question to ask when performing a hypothesis test.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: pitfalls, testing 92. True or False: “Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen?” should be among the questions asked when performing a hypothesis test ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pitfalls, testing 93. True or False: In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this does not prove that the null hypothesis is true.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pitfalls, testing

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94. True or False: In instances in which there is insufficient evidence to reject the null hypothesis, you must make it clear that this has proven that the null hypothesis is true.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: pitfalls, testing 95. True or False: In conducting research, you should document both good and bad results.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pitfalls, testing 96. True or False: You should report only the results of hypothesis tests that show statistical significance and omit those for which there is insufficient evidence in the findings.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: pitfalls, testing SCENARIO 9-2 A student claims that he can correctly identify whether a person is a business major or an agriculture major by the way the person dresses. Suppose in actuality that if someone is a business major, he can correctly identify that person as a business major 87% of the time.

When a person is an agriculture major, the student will incorrectly identify that person as a business major 16% of the time. Presented with one person and asked to identify the major of this person (who is either a business or an agriculture major), he considers this to be a hypothesis test with the null hypothesis being that the person is a business major and the alternative that the person is an agriculture major.

97. Referring to Scenario 9-2, what would be a Type I error? a) Saying that the person is a business major when in fact the person is a business major. b) Saying that the person is a business major when in fact the person is an agriculture major. c) Saying that the person is an agriculture major when in fact the person is a business major. d) Saying that the person is an agriculture major when in fact the person is an agriculture major.

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: fundamental, form of hypothesis, form of hypothesis Copyright ©2020 Pearson Education, Inc.

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98. Referring to Scenario 9-2, what would be a Type II error? a) Saying that the person is a business major when in fact the person is a business major. b) Saying that the person is a business major when in fact the person is an agriculture major. c) Saying that the person is an agriculture major when in fact the person is a business major. d) Saying that the person is an agriculture major when in fact the person is an agriculture major.

ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: fundamental, Type II error 99. Referring to Scenario 9-2, what is the “actual level of significance” of the test? a) 0.13 b) 0.16 c) 0.84 d) 0.87 ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: fundamental, level of significance 100. Referring to Scenario 9-2, what is the “actual confidence coefficient”? a) 0.13 b) 0.16 c) 0.84 d) 0.87 ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: fundamental, confidence coefficient 101. Referring to Scenario 9-2, what is the value of  ? a) 0.13 b) 0.16 c) 0.84 d) 0.87 ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: fundamental, level of significance Copyright ©2020 Pearson Education, Inc.

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102. Referring to Scenario 9-2, what is the value of  ? a) 0.13 b) 0.16 c) 0.84 d) 0.87 ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: fundamental, beta-risk 103. Referring to Scenario 9-2, what is the power of the test? a) 0.13 b) 0.16 c) 0.84 d) 0.87 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: fundamental, power SCENARIO 9-3 An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true.

They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. 104. Referring to Scenario 9-3, the population of interest is a) the power consumption in the 20 microwave ovens. b) the power consumption in all such microwave ovens. c) the mean power consumption in the 20 microwave ovens. d) the mean power consumption in all such microwave ovens.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test

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105. Referring to Scenario 9-3, the parameter of interest is a) the mean power consumption of the 20 microwave ovens. b) the mean power consumption of all such microwave ovens. c) 250 d) 257.3 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, parameter 106. Referring to Scenario 9-3, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are: a) H 0 :   250 versus H 1 :   250 b) H 0 :   250 versus H 1 :   250 c) H 0 :   250 versus H 1 :   250 d) H 0 :   257.3 versus H 1 :   257.3 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, form of hypothesis, form of hypothesis 107. Referring to Scenario 9-3, for a test with a level of significance of 0.05, the critical value would be ________.

ANSWER: Z = 1.645 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, critical value 108. Referring to Table 9.3, the value of the test statistic is ________.

ANSWER: 2.18 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, test statistic 109. Referring to Scenario 9-3, the p-value of the test is ________.

ANSWER: 0.0148 using Excel or 0.0146 using Table E.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, p-value

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110. True or False: Referring to Scenario 9-3, for this test to be valid, it is necessary that the power consumption for microwave ovens has a normal distribution.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, assumptions 111. True or False: Referring to Scenario 9-3, the null hypothesis will be rejected at 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, decision 112. True or False: Referring to Scenario 9-3, the null hypothesis will be rejected at 1% level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, decision 113. True or False: Referring to Scenario 9-3, the consumer group can conclude that there is enough evidence that the manufacturer’s claim is not true when allowing for a 5% probability of committing a Type I error.

ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: one-tail test, mean, Z test, conclusion

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SCENARIO 9-4 A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision.

114. Referring to Scenario 9-4, the appropriate hypotheses are: a) H 0 :   7.4 versus H 1 :   7.4 b) H 0 :   7.4 versus H 1 :   7.4 c) H 0 :   7.4 versus H 1 :   7.4 d) H 0 :   7.4 versus H 1 :   7.4 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, form of hypothesis, form of hypothesis 115. Referring to Scenario 9-4, for a test with a level of significance of 0.10, the critical value would be ________.

ANSWER: -1.28 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, critical value 116. Referring to Scenario 9-4, the value of the test statistic is ________.

ANSWER: -1.50 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, test statistic 117. Referring to Scenario 9-4, the p-value of the test is ________.

ANSWER: 0.0668 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, p-value

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118. True or False: Referring to Scenario 9-4, the null hypothesis will be rejected with a level of significance of 0.10.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, decision 119. True or False: Referring to Scenario 9-4, if the level of significance had been chosen as 0.05, the null hypothesis would be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, decision 120. True or False: Referring to Scenario 9-4, if the level of significance had been chosen as 0.05, the company would market the new anesthetic.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, conclusion SCENARIO 9-5 A bank tests the null hypothesis that the mean age of the bank's mortgage holders is less than or equal to 45 years, versus an alternative that the mean age is greater than 45 years. They take a sample and calculate a p-value of 0.0202.

121. True or False: Referring to Scenario 9-5, the null hypothesis would be rejected at a significance level of  = 0.05.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, decision 122. True or False: Referring to Scenario 9-5, the null hypothesis would be rejected at a significance level of  = 0.01.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, decision

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123. True or False: Referring to Scenario 9-5, the bank can conclude there is insufficient evidence to conclude that the mean age is greater than 45 years at a significance level of  = 0.01.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, conclude 124. Referring to Scenario 9-5, if the same sample was used to test the opposite one-tail test, what would be that test's p-value? a) 0.0202 b) 0.0404 c) 0.9596 d) 0.9798 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, p-value SCENARIO 9-6 The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tail test of the null hypothesis that the mean for the stressed oak furniture is 650 pounds. The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test.

125. True or False: Referring to Scenario 9-6, if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, decision 126. True or False: Referring to Scenario 9-6, if the test is performed with a level of significance of 0.10, the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650 pounds.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, conclusion

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127. True or False: Referring to Scenario 9-6, if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, decision 128. True or False: Referring to Scenario 9-6, if the test is performed with a level of significance of 0.05, the engineer can conclude that the mean amount of force necessary to produce cracks in stressed oak furniture is 650.

ANSWER: False TYPE: TF DIFFICULTY: Moderate EXPLANATION: the engineer can conclude that there is insufficient evidence to show that the mean amount of force needed is not 650 but cannot conclude that there is evidence to show that the force needed is 650.

KEYWORDS: one-tail test, mean, Z test, conclusion 129. True or False: Referring to Scenario 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. Then if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, Z test, decision 130. Referring to Scenario 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650 pounds. What would be the pvalue of this one-tail test? a) 0.040 b) 0.160 c) 0.840 d) 0.960 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, p-value EXPLANATION: Change to a right side one-tail test

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131. Referring to Scenario 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. What would be the p-value of this one-tail test? a) 0.040 b) 0.160 c) 0.840 d) 0.960 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, p-value 132. True or False: Referring to Scenario 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650 pounds.. Then if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, decision SCENARIO 9-7 A major home improvement store conducted its biggest brand recognition campaign in the company’s history. A series of new television advertisements featuring well-known entertainers and sports figures were launched. A key metric for the success of television advertisements is the proportion of viewers who “like the ads a lot”. A study of 1,189 adults who viewed the ads reported that 230 indicated that they “like the ads a lot.” The percentage of a typical television advertisement receiving the “like the ads a lot” score is believed to be 22%. Company officials wanted to know if there is evidence that the series of television advertisements are less successful than the typical ad (i.e. if there is evidence that the population proportion of “like the ads a lot” for the company’s ads is less than 0.22) at a 0.01 level of significance.

133. Referring to Scenario 9-7, the parameter the company officials is interested in is: a) the mean number of viewers who “like the ads a lot”. b) the total number of viewers who “like the ads a lot”. c) the mean number of company officials who “like the ads a lot”. d) the proportion of viewers who “like the ads a lot”.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, Z test, parameter

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134. Referring to Scenario 9-7, state the null hypothesis for this study.

ANSWER: H 0 :   0.22 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, form of hypothesis 135. Referring to Scenario 9-7, state the alternative hypothesis for this study.

ANSWER: H 1 :   0.22 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, form of hypothesis 136. Referring to Scenario 9-7, what critical value should the company officials use to determine the rejection region?

ANSWER: 2.3263 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, critical value 137. Referring to Scenario 9-7, the null hypothesis will be rejected if the test statistic is a) greater than 2.3263 b) less than 2.3263 c) greater than -2.3263 d) less than -2.3263 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, rejection region 138. True or False: Referring to Scenario 9-7, the null hypothesis would be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, decision 139. Referring to Scenario 9-7, the lowest level of significance at which the null hypothesis can be rejected is ______.

ANSWER: 0.0135 or 0.0136 using Table E.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, proportion, Z test, p-value Copyright ©2020 Pearson Education, Inc.

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140. Referring to Scenario 9-7, the largest level of significance at which the null hypothesis will not be rejected is ______.

ANSWER: 0.0135 or 0.0136 using Table E.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, proportion, Z test, p-value 141. True or False: Referring to Scenario 9-7, the company officials can conclude that there is sufficient evidence to show that the series of television advertisements are less successful than the typical ad using a level of significance of 0.01.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, conclusion 142. True or False: Referring to Scenario 9-7, the company officials can conclude that there is sufficient evidence to show that the series of television advertisements are less successful than the typical ad using a level of significance of 0.05.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, decision 143. True or False: Referring to Scenario 9-7, the value of  is 0.90.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, beta-risk 144. Referring to Scenario 9-7, what will be the p-value if these data were used to perform a two-tail test?

ANSWER: 0.027 TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, proportion, Z test, p-value

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SCENARIO 9-8 One of the biggest issues facing e-retailers is the ability to turn browsers into buyers. This is measured by the conversion rate, the percentage of browsers who buy something in their visit to a site. The conversion rate for a company’s website was 10.1%. The website at the company was redesigned in an attempt to increase its conversion rates. A sample of 200 browsers at the redesigned site was selected. Suppose that 24 browsers made a purchase.

The company officials would like to know if there is evidence of an increase in conversion rate at the 5% level of significance.

145. Referring to Scenario 9-8, the parameter the company officials is interested in is: a) the mean number of browsers who buy something in their visit to the company’s website. b) the total number of browsers who buy something in their visit to the company’s website. c) the mean number of company officials who buy something in their visit to the company’s website. d) the proportion of browsers who buy something in their visit to the company’s website.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: proportion, Z test, parameter 146. Referring to Scenario 9-8, state the null hypothesis for this study.

ANSWER: H0:   0.101 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, form of hypothesis 147. Referring to Scenario 9-8, state the alternative hypothesis for this study.

ANSWER: H1:  > 0.101 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, form of hypothesis 148. Referring to Scenario 9-8, what critical value should the company officials use to determine the rejection region?

ANSWER: 1.645 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, critical value

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149. Referring to Scenario 9-8, the null hypothesis will be rejected if the test statistic is a) greater than 1.645 b) less than 1.645 c) greater than -1.645 d) less than -1.645 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, rejection region 150. True or False: Referring to Scenario 9-8, the null hypothesis would be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, decision 151. Referring to Scenario 9-8, the lowest level of significance at which the null hypothesis can be rejected is ______.

ANSWER: 0.1863 using PHStat or 0.1867 using Table E.2 with a Z value of 0.89 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, proportion, Z test, p-value 152. Referring to Scenario 9-8, the largest level of significance at which the null hypothesis will not be rejected is ______.

ANSWER: 0.1863 using PHStat or 0.1867 using Table E.2 with a Z value of 0.89 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, proportion, Z test, p-value 153. True or False: Referring to Scenario 9-8, the company officials can conclude that there is sufficient evidence that the conversion rate at the company’s website has increased using a level of significance of 0.05.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, proportion, Z test, conclusion

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154. True or False: Referring to Scenario 9-8, the value of the probability of committing a Type II error  is 0.95.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, Z test, beta-risk 155. Referring to Scenario 9-8, what will be the p-value if these data were used to perform a two-tail test?

ANSWER: 0.3725 using PHStat or 0.3734 using Table E.2 with a Z value of 0.89 TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, proportion, Z test, p-value SCENARIO 9-9 The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years, but their mean SAT score is lower than previous years. He took a sample of 20 of this year’s entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university’s record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance.

156. Referring to Scenario 9-9, the parameter the president is interested in is: a) the mean number of entering students to his university this year. b) the mean number of entering students to all U.S. universities this year. c) the mean SAT score of the entering students to his university this year. d) the mean SAT score of the entering students to all U.S. universities this year.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, t test, parameter 157. Referring to Scenario 9-9, the population the president is interested in is: a) all entering students to all universities in the U.S this year. b) all entering students to his university this year. c) all SAT test centers in the U.S. this year. d) the mean SAT scores of all students entering his university this year .

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: mean, t test, population Copyright ©2020 Pearson Education, Inc.

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158. Referring to Scenario 9-9, state the null hypothesis for this study.

ANSWER: H 0 :   1520 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, form of hypothesis 159. Referring to Scenario 9-9, state the alternative hypothesis for this study.

ANSWER: H1 :   1520 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, form of hypothesis 160. Referring to Scenario 9-9, what critical value should the president use to determine the rejection region?

ANSWER: -1.7291 TYPE: PR DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, critical value 161. True or False: Referring to Scenario 9-9, the null hypothesis would be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, decision 162. True or False: Referring to Scenario 9-9, the null hypothesis would be rejected if a 10% probability of committing a Type I error is allowed.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, decision 163. True or False: Referring to Scenario 9-9, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, decision

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Fundamentals of Hypothesis Testing: One-Sample Tests

164. Referring to Scenario 9-9, the lowest level of significance at which the null hypothesis can still be rejected is ______.

ANSWER: 0.0627 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, p-value 165. Referring to Scenario 9-9, the highest level of significance at which the null hypothesis cannot be rejected is ______.

ANSWER: 0.0627 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, p-value 166. True or False: Referring to Scenario 9-9, the evidence proves beyond a doubt that the mean SAT score of the entering class this year is lower than previous years.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, conclusion 167. True or False: Referring to Scenario 9-9, the president can conclude that the mean SAT score of the entering class this year is lower than previous years using a level of significance of 0.10.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, conclusion 168. True or False: Referring to Scenario 9-9, the president can conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 5% probability of incorrectly rejecting the true null hypothesis.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, decision

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Fundamentals of Hypothesis Testing: One-Sample Tests

9-43

169. True or False: Referring to Scenario 9-9, the president can conclude that there is sufficient evidence to show that the mean SAT score of the entering class this year is lower than previous years with no more than a 10% probability of incorrectly rejecting the true null hypothesis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-tail test, mean, t test, decision 170. True or False: Referring to Scenario 9-9, if these data were used to perform a two-tail test, the p-value would be 0.1254.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-tail test, mean, t test, p-value 171. Referring to Scenario 9-9, which of the following best describes the Type I error? a) The president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower. b) The president concludes that the mean SAT score of the entering students is higher than previous years when it is indeed not higher. c) The president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower. d) The president concludes that the mean SAT score of the entering students is not higher than previous years when it is indeed higher.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean, t test, Type I error 172. Referring to Scenario 9-9, which of the following best describes the Type II error? a) The president concludes that the mean SAT score of the entering students is lower than previous years when it is indeed not lower. b) The president concludes that the mean SAT score of the entering students is higher than previous years when it is indeed not higher. c) The president concludes that the mean SAT score of the entering students is not lower than previous years when it is indeed lower. d) The president concludes that the mean SAT score of the entering students is not higher than previous years when it is indeed higher.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: mean, t test, Type II error Copyright ©2020 Pearson Education, Inc.

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Fundamentals of Hypothesis Testing: One-Sample Tests

SCENARIO 9-10 A manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. Based on past experience, the population standard deviation is 50 hours and the light bulb life is normally distributed. The operations manager stops the production process if there is evidence that the population mean light bulb life is below 500 hours.

173. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10, the probability of a Type I error is _____ if the population mean bulb life is 510 hours.

ANSWER: 0.10 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, type I error, mean, Z test 174. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.10, the confidence coefficient of the test is _____ if the population mean bulb life is 510 hours.

ANSWER: 0.90 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, confidence coefficient, mean, Z test 175. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05, the probability of the operations manager incorrectly stopping the process when the process is in fact working properly is _____.

ANSWER: 0.05 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, type I error, mean, Z test 176. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.05, the probability of the operations manager not stopping the process when the process is in fact working properly is in fact below 500 hours is _____.

ANSWER: 0.95 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, confidence coefficient, mean, Z test

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Fundamentals of Hypothesis Testing: One-Sample Tests

9-45

177. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01, the probability of the operations manager incorrectly stopping the process if the population mean bulb life is 510 hours is _____.

ANSWER: 0.01 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, type I error, mean, Z test 178. Referring to Scenario 9-10, if you select a sample of 100 light bulbs and are willing to have a level of significance of 0.01, the probability of the operations manager not stopping the process if the population mean bulb life is 510 hours is _____.

ANSWER: 0.99 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-tail test, confidence coefficient, mean, Z test

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Fundamentals of Hypothesis Testing: One-Sample Tests

182. True or False In setting up a hypothesis test, you consider the null hypothesis as stating the status quo claim.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: hypothesis tests 183. Which of the following is true regarding setting up a hypothesis test? a) If you do not reject the null hypothesis, you have proven it to be true. b) The null hypothesis may refer to a sample statistic such as the sample mean c) The alternative hypothesis never includes an equal sign d) The null and alternative hypotheses may or may not be collectively exhaustive statements.

ANSWER: c TYPE: TF DIFFICULTY: Easy KEYWORDS: hypothesis tests 184. In checking normality assumptions for using the t test when σ is not known, which of the following is not true? a) The sample mean is close to the sample median. b) The normal probability plot is approximately a straight line. c) The sample size to be used is not a factor. d) The boxplot of the sample appears approximately symmetrical.

ANSWER: c TYPE: TF DIFFICULTY: Moderate KEYWORDS: hypothesis tests, normality assumptions, normality checks 185. True or False With a test being robust, it does not lose power when the shape of the population distribution departs from a normal distribution.

ANSWER: True TYPE: MC DIFFICULTY: Moderate KEYWORDS: t tests, normality assumptions, robust property

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Two-Sample Tests

10-1

CHAPTER 10: TWO-SAMPLE TESTS 1. True or False: For all two-sample tests, the sample sizes must be equal in the two groups.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sample size 2. True or False: When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pooled-variance t test, sample size 3. The t test for the difference between the means of 2 independent populations assumes that the respective a) sample sizes are equal. b) sample variances are equal. c) populations are approximately normal. d) All the above.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, assumption 4. If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to a) 39. b) 38. c) 19. d) 18.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, degrees of freedom 5. In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are a) n – 1. b) n1 + n2 – 1. c) n1 + n2 – 2. d) n – 2.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, degrees of freedom Copyright ©2020 Pearson Education, Inc.

10-2

Two-Sample Tests

6. In testing for differences between the means of two independent populations, the null hypothesis is: a) H 0 : 1  2 = 2. b) H0 :  1 –  2 = 0. c) H0 :  1 –  2 > 0. d) H0 :  1 –  2 < 2.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, form of hypothesis 7. In testing for the differences between the means of two independent populations, you assume that the 2 populations each follow a _______ distribution.

ANSWER: normal TYPE: FI DIFFICULTY: Easy KEYWORDS: pooled-variance t test, assumption 8.

Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test. s12 = 4 s22 = 6 n1 = 16 n2 = 25 a) df = 41 b) df = 39 c) df = 16 d) df = 25

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, degrees of freedom 9. Given the following information, calculate sp2, the pooled sample variance that should be used in the pooled-variance t test. s12 = 4 s22 = 6 n1 = 16 n2 = 25 a) sp2 = 6.00 b) sp2 = 5.00 c) sp2 = 5.23 d) sp2 = 4.00 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test

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Two-Sample Tests

10-3

10. True or False: The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: pooled-variance t test, sample size 11. True or False: When you test for differences between the means of two independent populations, you can only use a two-tail test.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: pooled-variance t test, rejection region 12. True or False: A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: pooled-variance t test 13. True or False: A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: pooled-variance t test

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10-4

Two-Sample Tests

SCENARIO 10-1 Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

Sample Size Sample Mean SSATL Score Sample Std. Dev.

American 211 65.75 11.07

Japanese 100 79.83 6.41

14. Referring to Scenario 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ? a) Paired t test b) Pooled-variance t test for the difference between two means c) F test for the ratio of two variances d) Z test for the difference between two proportions ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, difference between two means 15. Referring to Scenario 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers. a) H 0 :  A –  J  0 versus H1 :  A –  J  0 b) H 0 :  A –  J  0 versus H 1 :  A –  J  0 c) H 0 :  A –  J  0 versus H 1 :  A –  J  0 d) H0 : X A – X J  0 versus H1 : X A – X J  0 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, mean differences, form of hypothesis 16. Referring to Scenario 10-1, what is the value of the test statistic? a) b) c) d)

-14.08 -11.8092 -1.9677 96.4471

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, mean differences, test statistic

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Two-Sample Tests

10-5

17. Referring to Scenario 10-1, find the p-value if we assume that the alternative hypothesis was a two-tail test. a) Smaller than 0.01 b) Between 0.01 and 0.05 c) Between 0.05 and 0.10 d) Greater than 0.10 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, mean differences, p-value SCENARIO 10-2 A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries.

The result of the pooled-variance t-test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below.

Hypothesized Difference Level of Significance Population 1 Sample Sample Size Sample Mean Sample Standard Deviation Population 2 Sample Sample Size Sample Mean Sample Standard Deviation

0 0.05

12 105820 11741

Difference in Sample Means t Test Statistic

-6610 -1.37631

Lower-Tail Test Lower Critical Value p-Value

-1.70113 0.089816

18 99210 13577

18. Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.

Which of the following is an appropriate alternative hypothesis? a) H1 : females  males b)

H1 : females  males

H1 : females  males d) H1 : females  males c)

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, form of hypothesis Copyright ©2020 Pearson Education, Inc.

10-6

Two-Sample Tests

19. Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.

From the analysis in Scenario 10-2, the correct test statistic is: a) -6610 b) -1.3763 c) -1.7011 d) 0.0898 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, test statistic 20. Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.

The proper conclusion for this test is: a) At the  = 0.10 level, there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates. b) At the  = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates. c) At the  = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates. d) At the  = 0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, conclusion 21. Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates.

What assumptions were necessary to conduct this hypothesis test? a) Both populations of salaries (male and female) must have approximate normal distributions. b) The population variances are approximately equal. c) The samples were randomly and independently selected. d) All of the above assumptions were necessary.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, assumption 22. Referring to Scenario 10-2, what is the 99% confidence interval estimate for the difference between two means?

ANSWER: $ 19,881.07 to $6,661.07 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval Copyright ©2020 Pearson Education, Inc.

Two-Sample Tests

10-7

23. Referring to Scenario 10-2, what is the 95% confidence interval estimate for the difference between two means?

ANSWER: $16,447.85 to $3,227.85 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval 24. Referring to Scenario 10-2, what is the 90% confidence interval estimate for the difference between two means?

ANSWER: $14,779.99 to $1,559.99 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

Gotham: X G = 35 months, SG2 = 900 Metropolis: X M = 50 months, SM2 = 1050 25. Referring to Scenario 10-3, which of the following represents the relevant hypotheses tested by the real estate company? a) H 0 :  G –  M  0 versus H1 :  G –  M  0 b) H 0 :  G –  M  0 versus H 1 :  G –  M  0 c) H 0 :  G –  M  0 versus H1 :  G –  M  0 d) H0 : X G – X M  0 versus H1 : X G – X M  0 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, form of hypothesis 26. Referring to Scenario 10-3, what is the estimated standard error of the difference between the 2sample means? a) 4.06 b) 5.61 c) 8.01 d) 16.00 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, standard error

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10-8

Two-Sample Tests

27. Referring to Scenario 10-3, what is a point estimate for the mean of the sampling distribution of the difference between the 2-sample means? a) – 22 b) – 10 c) – 15 d) 0 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, unbiased, point estimate 28. Referring to Scenario 10-3, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05? a) t  Z = – 1.645 b) t  Z =  1.96 c) t  Z = – 1.96 d) t  Z = – 2.080 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, critical value 29. Referring to Scenario 10-3, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.01? a) t  Z = – 1.96 b) t  Z =  1.96 c) t  Z = – 2.080 d) t  Z = – 2.33 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, critical value 30. Referring to Scenario 10-3, what is the test statistic for the difference between sample means? a) – 8.75 b) – 3.69 c) – 2.33 d) – 1.96 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, test statistic

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Two-Sample Tests

10-9

31. Referring to Scenario 10-3, suppose  = 0.10. Which of the following represents the result of the relevant hypothesis test? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, decision 32. Referring to Scenario 10-3, suppose  = 0.05. Which of the following represents the result of the relevant hypothesis test? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, decision 33. Referring to Scenario 10-3, suppose  = 0.01. Which of the following represents the result of the relevant hypothesis test? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, decision 34. Referring to Scenario 10-3, suppose  = 0.10. Which of the following represents the correct conclusion? a) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. b) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. c) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. d) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, conclusion

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10-10

Two-Sample Tests

35. Referring to Scenario 10-3, suppose  = 0.05. Which of the following represents the correct conclusion? a) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. b) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. c) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. d) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, conclusion 36. Referring to Scenario 10-3, suppose  = 0.01. Which of the following represents the correct conclusion? a) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. b) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is less than families in Metropolis. c) There is not enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis. d) There is enough evidence that the mean amount of time families in Gotham have been living in their current homes is not less than families in Metropolis.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, conclusion 37. Referring to Scenario 10-3, what is the 99% confidence interval estimate for the difference in the two means?

ANSWER: 25.54 to 4.46 months TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval 38. Referring to Scenario 10-3, what is the 95% confidence interval estimate for the difference in the two means?

ANSWER: 23.00 to 7.00 months TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval

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Two-Sample Tests

10-11

SCENARIO 10-4 Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.

39. Referring to Scenario 10-6, the pooled (i.e., combined) variance is _______.

ANSWER: 12.5 TYPE: FI DIFFICULTY: Easy KEYWORDS: pooled-variance t test 40. Referring to Scenario 10-4, the computed t statistic is _______.

ANSWER: 2.50 TYPE: FI DIFFICULTY: Easy KEYWORDS: pooled-variance t test, test statistic 41. Referring to Scenario 10-4, there are _______ degrees of freedom for this test.

ANSWER: 48 TYPE: FI DIFFICULTY: Easy KEYWORDS: pooled-variance t test, degrees of freedom 42. Referring to Scenario 10-4, the critical values for a two-tail test of the null hypothesis of no difference in the population means at the  = 0.05 level of significance are _______.

ANSWER:  2.0106 TYPE: FI DIFFICULTY: Easy KEYWORDS: pooled-variance t test, critical value 43. Referring to Scenario 10-4, a two-tail test of the null hypothesis of no difference would _______ (be rejected/not be rejected) at the  = 0.05 level of significance.

ANSWER: be rejected TYPE: FI DIFFICULTY: Easy KEYWORDS: pooled-variance t test, decision 44. Referring to Scenario 10-4, the p-value for a two-tail test is _______.

ANSWER: 0.016 if using PHStat or between 0.01 and 0.02 if using Table E.3 TYPE: FI DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, p-value

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10-12

Two-Sample Tests

45. Referring to Scenario 10-4, if you were interested in testing against the one-tail alternative that 1   2 at the  = 0.01 level of significance, the null hypothesis would ______ (be rejected/not be rejected).

ANSWER: be rejected TYPE: FI DIFFICULTY: Easy KEYWORDS: pooled-variance t test, decision 46. Referring to Scenario 10-4, the p-value for a one-tail test (in the hypothesized direction) is _______.

ANSWER: 0.0079 if using PHStat or between 0.005 and 0.01 if using Table E.3 TYPE: FI DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, p-value 47. Referring to Scenario 10-4, what is the 99% confidence interval estimate for the difference in the two means?

ANSWER: 0.1822 to 5.1822 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval 48. Referring to Scenario 10-4, what is the 95% confidence interval estimate for the difference in the two means?

ANSWER: 0.4894 to 4.5106 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval 49. Referring to Scenario 10-4, what is the 90% confidence interval estimate for the difference in the two means?

ANSWER: 0.8228 to 4.1772 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval 50. The t test for the mean difference between 2 related populations assumes that the a) population sizes are equal. b) sample variances are equal. c) population of differences is approximately normal, or sample sizes are large enough. d) All of the above.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, assumption Copyright ©2020 Pearson Education, Inc.

Two-Sample Tests

10-13

51. If we are testing for the difference between the means of 2 related populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to a) 39. b) 38. c) 19. d) 18.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, degrees of freedom 52. In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves? a) A test for the equality of variances from 2 independent populations. b) A test for the difference between the means of 2 related populations. c) A test for the difference between the means of 2 independent populations. d) All of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference 53. In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are a) n – 1. b) n1 + n2 – 1. c) n1 + n2 – 2. d) n – 2.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, degrees of freedom 54. In testing for differences between the means of two related populations, the null hypothesis is a) H 0 :  D  2 .

H0 : D  0 . c) H 0 :  D  0 . d) H 0 :  D  0 . b)

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, form of hypothesis

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10-14

Two-Sample Tests

55. In testing for the differences between the means of two related populations, the _______ hypothesis is the hypothesis of "no differences."

ANSWER: null or HO TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, form of hypothesis 56. In testing for the differences between the means of two related populations, you assume that the differences follow a _______ distribution.

ANSWER: normal TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, assumption 57. True or False: When testing for differences between the means of 2 related populations, you can use either a one-tail or two-tail test.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, rejection region 58. True or False: A researcher is curious about the effect of sleep on students’ test performances. He chooses 60 students and gives each two tests: one given after two hours’ sleep and one after eight hours’ sleep. The test the researcher should use would be a related samples test.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: paired t test, mean difference 59. True or False: Repeated measurements from the same individuals is an example of data collected from two related populations.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: paired t test, mean difference 60. True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 11 degrees of freedom.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, degrees of freedom

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Two-Sample Tests

10-15

61. True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t-distribution with 10 degrees of freedom.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, degrees of freedom SCENARIO 10-5 To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 62. Referring to Scenario 10-5, the number of degrees of freedom is a) 14. b) 13. c) 8. d) 7.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, degrees of freedom 63. Referring to Scenario 10-5, the value of the sample mean difference is _______ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course. a) 0 b) 50 c) 68 d) 400 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, test statistic

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10-16

Two-Sample Tests

64. Referring to Scenario 10-5, the value of the standard error of the difference scores is a) 65.027 b) 60.828 c) 22.991 d) 14.696 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, standard error 65. Referring to Scenario 10-5, what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores? a) 2.365 b) 2.145 c) 1.761 d) 1.895 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, critical value 66. Referring to Scenario 10-5, at the 0.05 level of significance, the decision for this hypothesis test would be: a) reject the null hypothesis. b) do not reject the null hypothesis. c) reject the alternative hypothesis. d) It cannot be determined from the information given.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, decision 67. Referring to Scenario 10-5, at the 0.05 level of significance, the conclusion for this hypothesis test is that there is sufficient evidence that: a) the business school preparation course does improve exam score. b) the business school preparation course does not improve exam score. c) the business school preparation course has no impact on exam score. d) no conclusion can be drawn from the information given.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, conclusion

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Two-Sample Tests

10-17

68. True or False: Referring to Scenario 10-5, you must assume that the population of difference scores is normally distributed.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, assumption 69. Referring to Scenario 10-5, the calculated value of the test statistic is ________.

ANSWER: 2.175 TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, test statistic 70. Referring to Scenario 10-5, the p-value of the test statistic is ________.

ANSWER: 0.0331 (using Excel) or ‘between 0.025 and 0.05’ (using Table E.3 with 7 degrees of freedom) TYPE: FI DIFFICULTY: Moderate EXPLANATION: p-value obtained from Excel KEYWORDS: paired t test, mean difference, p-value 71. True or False: Referring to Scenario 10-5, in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, sampling distribution SCENARIO 10-6 To investigate the efficacy of a diet, a random sample of 16 male patients is selected from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t-test for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.

72. Referring to Scenario 10-6, the t test should be _______-tail.

ANSWER: one TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, rejection region

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10-18

Two-Sample Tests

73. Referring to Scenario 10-6, the computed t statistic is _______.

ANSWER: 2.00 TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, test statistic 74. Referring to Scenario 10-6, there are _______ degrees of freedom for this test.

ANSWER: 15 TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, degrees of freedom 75. Referring to Scenario 10-6, the critical value for a one-tail test of the null hypothesis of no difference at the  = 0.05 level of significance is _______.

ANSWER: 1.7531 TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, critical value 76. Referring to Scenario 10-6, a one-tail test of the null hypothesis of no difference would _______ (be rejected/not be rejected) at the  = 0.05 level of significance.

ANSWER: be rejected TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, decision 77. Referring to Scenario 10-6, the p-value for a one-tail test is _______.

ANSWER: 0.032 if using PHStat or 0.025 and 0.05 if using Table E.3 TYPE: FI DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, p-value 78. Referring to Scenario 10-6, if we were interested in testing against the two-tail alternative that  D is not equal to zero at the  = 0.05 level of significance, the null hypothesis would _______ (be rejected/not be rejected).

ANSWER: not be rejected TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, decision 79. Referring to Scenario 10-6, the p-value for a two-tail is _______.

ANSWER: 0.064 if using PHStat or 0.05 and 0.10 if using Table E.3 TYPE: FI DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, p-value Copyright ©2020 Pearson Education, Inc.

Two-Sample Tests

10-19

80. Referring to Scenario 10-6, what is the 95% confidence interval estimate for the mean difference in weight before and after the diet?

ANSWER: 0.2 to 6.2 TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean difference, confidence interval 81. Referring to Scenario 10-6, what is the 99% confidence interval estimate for the mean difference in weight before and after the diet?

ANSWER:  to 7.42 TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean difference, confidence interval 82. Referring to Scenario 10-6, what is the 90% confidence interval estimate for the mean difference in weight before and after the diet?

ANSWER: 0to 5.63 TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean difference, confidence interval SCENARIO 10-7 A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging.

In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier.

The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.

Primary Secondary Material Supplier Supplier Difference 1 $55 $45 $10 2 $48 $47 $1 3 $31 $32 – $1 4 $83 $77 $6 5 $37 $37 $0 6 $55 $54 $1 Sum: $309 $292 $17 Sum of Squares: $17,573 $15,472 $139

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10-20

Two-Sample Tests

83. Referring to Scenario 10-7, the hypotheses that the buyer should test are a null hypothesis that ________ versus an alternative hypothesis that ________.

ANSWER:

H 0 :  D  0, H1 :  D  0

TYPE: FI DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, form of hypothesis 84. Referring to Scenario 10-7, the test to perform is a a) pooled-variance t test for differences between two means. b) separate-variance t test for differences between two means. c) Z test for the difference between two proportions. d) paired t-test for the mean difference.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: paired t test, mean difference 85. Referring to Scenario 10-7, the decision rule is to reject the null hypothesis if ________.

ANSWER: t > 3.3649 TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, decision 86. Referring to Scenario 10-7, the calculated value of the test statistic is ________.

ANSWER: 1.628 TYPE: FI DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, test statistic 87. Referring to Scenario 10-7, the p-value of the test statistic is ________.

ANSWER: 0.082 if using PHStat or 0.05 and 0.10 if using Table E.3 TYPE: FI DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, p-value 88. True or False: Referring to Scenario 10-7, the null hypothesis should be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: paired t test, mean difference, decision

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Two-Sample Tests

10-21

89. Referring to Scenario 10-7, the buyer should decide that the primary supplier is a) overcharging because there is strong evidence that this is the case. b) overcharging because there is insufficient evidence to prove otherwise. c) not overcharging because there is insufficient evidence to prove otherwise. d) not overcharging because there is strong evidence to prove otherwise.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, conclusion 90. Referring to Scenario 10-7, if the buyer had decided to perform a two-tail test, the p-value would have been ________.

ANSWER: 0.16 if using PHStat or 0.01 and 0.2 if using Table E.3 TYPE: FI DIFFICULTY: Moderate KEYWORDS: paired t test, mean difference, p-value 91. Referring to Scenario 10-7, what is the 99% confidence interval estimate for the mean difference in prices?

ANSWER: $4.18 to $9.85 TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean difference, confidence interval 92. Referring to Scenario 10-7, what is the 95% confidence interval estimate for the mean difference in prices?

ANSWER: $1.64 to $7.31 TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean difference, confidence interval 93. Referring to Scenario 10-7, what is the 90% confidence interval estimate for the mean difference in prices?

ANSWER: $0.67 to $6.34 TYPE: PR DIFFICULTY: Moderate KEYWORDS: mean difference, confidence interval

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10-22

Two-Sample Tests

94. When testing H 0 : 1 –  2  0 versus H1 : 1 –  2  0 , the observed value of the Z test statistic was found to be – 2.13. The p-value for this test is a) 0.0166. b) 0.0332. c) 0.9668. d) 0.9834.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in proportions, p-value 95. When testing H 0 : 1   2  0 versus H1 : 1   2  0 , the observed value of the Z test statistic was found to be – 2.13. The p-value for this test is a) 0.0166. b) 0.0332. c) 0.9668. d) 0.9834.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in proportions, p-value 96. When testing H 0 : 1   2  0 versus H1 : 1   2  0 , the observed value of the Z test statistic was found to be – 2.13. The p-value for this test is a) 0.0166. b) 0.0332. c) 0.9668. d) 0.9834.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in proportions, p-value

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Two-Sample Tests

10-23

97. Moving companies are required by the government to publish a Carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose two companies, Econo-Move and On-the-Move, each decide to estimate this figure by sampling their records, and they report the data shown in the following table.

Econo-Move

On-the-Move

Total shipments sampled

900

750

Number of shipments with a claim  $50

162

60

The owner of On-the-Move is hoping to use these data to show that the company is superior to Econo-Move with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment? a) t test for the difference between two means b) F test for the ratio of variances c) Separate variance t test for the difference between two means d) Z test for the difference between two proportions ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in proportions 98. The Wall Street Journal recently published an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” 24% of the men compared to 62% of the women responded “Yes.” Assuming W designates women’s responses and M designates men’s, what hypothesis should The Wall Street Journal test in order to show that its claim is true? a) H0: W   M  0 versus H1: W   M < 0 b) H0: W   M  0 versus H1: W   M > 0 c) H0: W   M = 0 versus H1: W   M  0 d) H0: W   M  0 versus H1: W   M = 0 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for difference in proportions, form of hypothesis

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10-24

Two-Sample Tests

99. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. For a 0.01 level of significance, what is the critical value for the rejection region? a) 7.173 b) 7.106 c) 6.635 d) 2.33 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in proportions, critical value 100. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. What is the value of the test statistic? a) 7.173 b) 7.106 c) 6.635 d) 2.33 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in proportions, test statistic 101. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. Construct a 99% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

ANSWER: 0.25 to 0.51 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval

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Two-Sample Tests

10-25

102. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. Construct a 95% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

ANSWER: 0.28 to 0.48 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 103. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. Construct a 90% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.

ANSWER: 0.30 to 0.46 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 104. The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. What conclusion should be reached? a) Using a 0.01 level of significance, there is sufficient evidence to conclude that women perceive the problem of sexual harassment on the job as much more prevalent than do men. b) There is insufficient evidence to conclude with at least 99% confidence that women perceive the problem of sexual harassment on the job as much more prevalent than do men. c) There is no evidence of a significant difference between the men and women in their perception. d) More information is needed to draw any conclusions from the data set.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in proportions, decision, conclusion

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10-26

Two-Sample Tests

105. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Assuming W designates women’s responses and M designates men’s, which of the following are the appropriate null and alternative hypotheses to test the group’s claim? a) H0:  M   W  0 versus H1:  M   W  0 b) H0:  M   W  0 versus H1:  M   W  0 c) H0:  M   W  0 versus H1:  M   W  0 d) H0:  M   W  0  0 versus H1:  M   W  0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in proportions, form of hypothesis 106. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic. a) Z = – 2.55 b) Z = – 0.85 c) Z = – 1.05 d) Z = – 1.20 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in proportions, test statistic 107. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. If the p-value turns out to be 0.035 (which is not the real value in this data set), then a) at  = 0.05, you should fail to reject H0 b) at  = 0.04, you should reject H0 c) at  = 0.03, you should reject H0 d) None of the above would be correct statements.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for difference in proportions, decision, conclusion

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Two-Sample Tests

10-27

108. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Construct a 99% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.

ANSWER: 0.508 to 0.002 or 0.002 to 0.508 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 109. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Construct a 95% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.

ANSWER: 0.448 to 0.062 or 0.062 to 0.448 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 110. A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Construct a 90% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.

ANSWER: 0.417 to 0.093 or 0.093 to 0.417 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 111. If you wish to determine whether there is evidence that the proportion of items of interest is higher in group 1 than in group 2, the appropriate test to use is a) the Z test for the difference between two proportions. b) the F test for the ratio of variances. c) the pooled-variance t test for the difference between two proportions. d) the F test for the difference between two proportions.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions

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10-28

Two-Sample Tests

112. True or False: In testing the difference between two proportions using the normal distribution, you may use a two-tail Z test.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions 113. If you wish to determine whether there is evidence that the proportion of items of interest is higher in Group 1 than in Group 2, and the test statistic for Z = +2.07 where the difference is defined as Group 1’s proportion minus Group 2’s proportion, the p-value is equal to ______.

ANSWER: 0.0192 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, p-value 114. If we wish to determine whether there is evidence that the proportion of items of interest is higher in Group 1 than in Group 2, and the test statistic for Z = 2.07 where the difference is defined as Group 1’s proportion minus Group 2’s proportion, the p-value is equal to ______.

ANSWER: 0.9808 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, p-value SCENARIO 10-8 A few years ago, Pepsi invited consumers to take the “Pepsi Challenge.” Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people’s taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi.

Males: n = 109, pM = 0.422018 Females: n = 52, pF = 0.25 pM – pF = 0.172018 Z = 2.11825 115. Referring to Scenario 10-8, to determine if a difference exists in the taste preferences of men and women, give the correct alternative hypothesis that Pepsi would test. a) H1: M –  F  0 b) H1: M –  F  0 c) H1:  M   F  0 d) H1:  M   F = 0

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, form of hypothesis

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Two-Sample Tests

10-29

116. Referring to Scenario 10-8, suppose Pepsi wanted to test to determine if the males preferred Pepsi more than the females. Using the test statistic given, compute the appropriate p-value for the test. a) 0.0171 b) 0.0340 c) 0.2119 d) 0.4681 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, p-value 117. Referring to Scenario 10-8, suppose Pepsi wanted to test to determine if the males preferred Pepsi less than the females. Using the test statistic given, compute the appropriate p-value for the test. a) 0.0170 b) 0.0340 c) 0.9660 d) 0.9830 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, p-value 118. Referring to Scenario 10-8, suppose that the two-tail p-value was really 0.0734. State the proper conclusion. a) At  = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. b) At  = 0.10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi. c) At  = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi. d) At  = 0.08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, decision, conclusion 119. Referring to Scenario 10-8, construct a 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

ANSWER: 0.05 to 0.30 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval

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10-30

Two-Sample Tests

120. Referring to Scenario 10-8, construct a 95% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

ANSWER: 0.02 to 0.32 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 121. Referring to Scenario 10-8, construct a 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

ANSWER: 0.03 to 0.37 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval SCENARIO 10-9 The following EXCEL output contains the results of a test to determine whether the proportions of satisfied customers at two resorts are the same or different.

Hypothesized Difference Level of Significance Group 1 Number of Items of Interest Sample Size Group 2 Number of Items of Interest

0 0.05

Sample Size

250

160 200 172

Intermediate Calculations Group 1 Proportion Group 2 Proportion Difference in Two Proportions Average Proportion Z Test Statistic

0.8 0.688 0.112 0.737777778 2.684103363

Two-Tail Test Lower Critical Value Upper Critical Value 2-tailed p-Value

-1.959963985 1.959963985 0.007272462

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Two-Sample Tests

10-31

122. Referring to Scenario 10-9, allowing for 1% probability of committing a Type I error, what are the decision and conclusion on testing whether there is any difference in the proportions of satisfied customers in the two resorts? a) Do not reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. b) Do not reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts. c) Reject the null hypothesis; there is enough evidence to conclude that there is a significant difference in the proportions of satisfied guests at the two resorts. d) Reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, decision, conclusion 123. Referring to Scenario 10-9, if you want to test the claim that "Resort 1 (Group 1) has a higher proportion of satisfied customers compared to Resort 2 (Group 2)", the p-value of the test will be a) 0.007272 b) 0.00727/2 c) 2*(0.00727) d) 1-(0.00727/2) ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, p-value 124. Referring to Scenario 10-9, if you want to test the claim that "Resort 1 (Group 1) has a lower proportion of satisfied customers compared to Resort 2 (Group 2)", you will use a) a t-test for the difference between two proportions. b) a Z-test for the difference between two proportions. c) an F test for the difference between two proportions. d) an F test for the ratio of two variances.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions 125. Referring to Scenario 10-9, construct a 99% confidence interval estimate of the difference in the population proportion of satisfied customers between the two resorts.

ANSWER: 0.0071 to 0.2169 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval

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10-32

Two-Sample Tests

126. Referring to Scenario 10-9, construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

ANSWER: 0.0322 to 0.1918 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 127. Referring to Scenario 10-9, construct a 90% confidence interval estimate of the difference in the population proportion of satisfied customers between the two resorts.

ANSWER: 0.0450 to 0.1790 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval SCENARIO 10-10 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a selfimprovement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let 1 and  2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

128. Referring to Scenario 10-11, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses? a) H0:  1   2 = 0 versus H1:  1   2  0 b) H0:  1   2  0 versus H1:  1   2 = 0 c) H0:  1   2  0 versus H1:  1   2 > 0

d) H0:  1   2  0 versus H1:  1   2 < 0 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, form of hypothesis

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Two-Sample Tests

10-33

129. Referring to Scenario 10-10, if the firm wanted to test whether a greater proportion of workers would currently like to attend a self-improvement course than in the past, which represents the relevant hypotheses? a) H0:  1   2 = 0 versus H1:  1   2  0 b) H0:  1   2  0 versus H1:  1   2 = 0

c) H0:  1   2  0 versus H1:  1   2 > 0

d) H0:  1   2  0 versus H1:  1   2 < 0 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, form of hypothesis 130. Referring to Scenario 10-10, what is the point estimate for the difference between the two population proportions? a) 0.06 b) 0.10 c) 0.15 d) 0.22 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: point estimate, Z test for the difference in proportions 131. Referring to Scenario 10-10, what is/are the critical value(s) when performing a Z test on whether population proportions are different if  = 0.05? a)  1.645 b)  1.96 c) 1.96 d)  2.08 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, critical value 132. Referring to Scenario 10-10, what is/are the critical value(s) when testing whether population proportions are different if  = 0.10? a)  1.645 b)  1.96 c) -1.96 d)  2.08 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, critical value

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10-34

Two-Sample Tests

133. Referring to Scenario 10-10, what is/are the critical value(s) when testing whether the current population proportion is higher than before if  = 0.05? a)  1.645 b) + 1.645 c)  1.96 d) + 1.96 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, critical value 134. Referring to Scenario 10-10, what is the estimated standard error of the difference between the two sample proportions? a) 0.629 b) 0.500 c) 0.055 d) 0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, standard error 135. Referring to Scenario 10-10, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions? a) 4.335 b) 1.96 c) 1.093 d) 0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, test statistic 136. Referring to Scenario 10-10, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is correct? a) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years. b) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years. c) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. d) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, decision, conclusion

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Two-Sample Tests

10-35

137. Referring to Scenario 10-10, construct a 99% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

ANSWER: 0.08 to 0.20 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 138. Referring to Scenario 10-10, construct a 95% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

ANSWER: 0.05 to 0.17 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 139. Referring to Scenario 10-10, construct a 90% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

ANSWER: 0.03 to 0.15 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval SCENARIO 10-11 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as “Group 1” and the economics majors are designated as “Group 2,” perform the appropriate hypothesis test using a level of significance of 0.05.

140. Referring to Scenario 10-12, the hypotheses the dean should use are: a) H0:  1   2 = 0 versus H1:  1   2  0 b) H0:  1   2  0 versus H1:  1   2 = 0 c) H0:  1   2  0 versus H1:  1   2 > 0

d) H0:  1   2  0 versus H1:  1   2 < 0 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, form of hypothesis

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10-36

Two-Sample Tests

141. Referring to Scenario 10-11, the null hypothesis will be rejected if the test statistic is ________.

ANSWER: Z > 1.96 or < -1.96 TYPE: FI DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, critical value 142. Referring to Scenario 10-11, the value of the test statistic is ________.

ANSWER: Z = 1.866 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, test statistic 143. Referring to Scenario 10-11, the p-value of the test is ________.

ANSWER: 0.0621 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, p-value 144. True or False: Referring to Scenario 10-11, the null hypothesis should be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, decision 145. True or False: Referring to Scenario 10-11, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, decision 146. True or False: Referring to Scenario 10-11, the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, decision 147. Referring to Scenario 10-11, construct a 99% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

ANSWER: 0.05 to 0.31 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval Copyright ©2020 Pearson Education, Inc.

Two-Sample Tests

10-37

148. Referring to Scenario 10-11, construct a 95% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

ANSWER: 0.01 to 0.27 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 149. Referring to Scenario 10-11, construct a 90% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.

ANSWER: 0.02 to 0.24 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval SCENARIO 10-12 A quality control engineer is in charge of the manufacture of USB flash drives. Two different processes can be used to manufacture the flash drives. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell flash drives and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as “Group 1” and Russell is designated as “Group 2,” perform the appropriate test at a level of significance of 0.01.

150. Referring to Scenario 10-12, the hypotheses that should be tested are: a) H0:  1   2 = 0 versus H1:  1   2  0 b) H0:  1   2  0 versus H1:  1   2 = 0

c) H0:  1   2  0 versus H1:  1   2 > 0

d) H0:  1   2  0 versus H1:  1   2 < 0 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, form of hypothesis 151. Referring to Scenario 10-12, the null hypothesis will be rejected if the test statistic is ________.

ANSWER: Z > 2.575 TYPE: FI DIFFICULTY: Easy KEYWORDS: Z test for the difference in proportions, critical value, one tailed test

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10-38

Two-Sample Tests

152. Referring to Scenario 10-12, the value of the test statistic is ________.

ANSWER: 2.49 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, test statistic 153. Referring to Scenario 10-12, the p-value of the test is ________.

ANSWER: 0.0064 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, p-value 154. True or False: Referring to Scenario 10-12, the null hypothesis should be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, decision 155. True or False: Referring to Scenario 10-12, the same decision would be made with this test if the level of significance had been 0.05 rather than 0.01.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, decision 156. True or False: Referring to Scenario 10-12, the same decision would be made if this had been a two-tail test at a level of significance of 0.01.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Z test for the difference in proportions, decision 157. Referring to Scenario 10-12, construct a 90% confidence interval estimate of the difference in proportion between the Kohler and Russell flash drives that are defective.

ANSWER: 0.03 to 0.15 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 158. Referring to Scenario 10-12, construct a 95% confidence interval estimate of the difference in proportion between the Kohler and Russell flash drives that are defective.

ANSWER: 0.02 to 0.16 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval Copyright ©2020 Pearson Education, Inc.

Two-Sample Tests

10-39

159. Referring to Scenario 10-12, construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell flash drives that are defective.

ANSWER: -0.01 to 0.19 TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two proportions, confidence interval 160. When testing for the difference between 2 population variances with sample sizes of n1 = 8 and n2 = 10, where n1 has the larger variance, the number of degrees of freedom are a) 8 and 10. b) 7 and 9. c) 18. d) 16.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, degrees of freedom 161. The statistical distribution used for testing the difference between two population variances is the ___ distribution. a) t b) standardized normal c) binomial d) F ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, degrees of freedom 162. The test for the equality of two population variances is based on a) the difference between the 2 sample variances. b) the ratio of the 2 sample variances. c) the difference between the 2 population variances. d) the difference between the sample variances divided by the difference between the sample means.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances 163. True or False: The F test used for testing the difference in two population variances is always a one-tail test.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, rejection region

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10-40

Two-Sample Tests

164. True or False: The test for the equality of two population variances assumes that each of the two populations is normally distributed.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, assumption 165. True or False: The F distribution is symmetric.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F distribution, properties 166. True or False: The F distribution can only have positive values.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F distribution, properties 167. True or False: F tests are one-tail tests.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F distribution, properties SCENARIO 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal. t-Test: Two-Sample Assuming Unequal Variances Hotel 1 Mean 2.214 Variance 2.951657 Observations 20 Hypothesized Mean Difference 0 df 38 t Stat 0.354386 P(T<=t) one-tail 0.362504 t Critical one-tail 1.685953 P(T<=t) two-tail 0.725009 t Critical two-tail 2.024394

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Hotel 2 2.0115 3.57855 20

Two-Sample Tests

10-41

168. Referring to Scenario 10-13, which of the following represents the relevant hypotheses tested? a) H 0 :  I –  II  0 versus H1 :  I –  II  0 b)

H 0 :  I –  II  0 versus H1 :  I –  II  0

H 0 :  I –  II  0 versus H1 :  I –  II  0 d) H 0 :  I –  II  0 versus H 1 :  I –  II  0 c)

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: separate-variance t test, form of hypothesis 169. Referring to Scenario 10-13, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05? a) 1.6860 b)  1.6860 c) 2.0244 d)  2.0244 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: separate-variance t test, critical value 170. Referring to Scenario 10-13, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.10? a) 1.6860 b)  1.6860 c) 2.0244 d)  2.0244 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: separate-variance t test, critical value 171. Referring to Scenario 10-13, what is the standardized value of the estimate of the mean of the sampling distribution for the difference between sample means? a) 0.2025 b) 0.3544 c) 2.0115 d) 2.2140 ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: separate-variance t test, test statistic

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10-42

Two-Sample Tests

172. Referring to Scenario 10-13, what is the value of the test statistic? a) 0.2025 b) 0.3544 c) 2.0115 d) 2.2140 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: separate-variance t test, test statistic 173. Referring to Scenario 10-13, what is the smallest level of significance at which the null hypothesis will still not be rejected? a) 0.05 b) 0.10 c) 0.3625 d) 0.7250 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: separate-variance t test, p-value 174. Referring to Scenario 10-13, suppose  = 0.10. Which of the following represents the result of the relevant hypothesis test? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: separate-variance t test, decision 175. Referring to Scenario 10-13, suppose  = 0.05. Which of the following represents the result of the relevant hypothesis test? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: separate-variance t test, decision

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Two-Sample Tests

10-43

176. Referring to Scenario 10-13, suppose  = 0.10. Which of the following represents the correct conclusion? a) There is not enough evidence of a difference in the mean amounts of time between the two hotels. b) There is enough evidence of a difference in the mean amounts of time between the two hotels. c) There is not enough evidence that the mean amounts of time for the two hotels are the same. d) There is enough evidence that the mean amounts of time for the two hotels are the same.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: separate-variance t test, conclusion 177. Referring to Scenario 10-13, suppose  = 0.05. Which of the following represents the correct conclusion? a) There is not enough evidence of a difference in the mean amounts of time between the two hotels. b) There is enough evidence of a difference in the mean amounts of time between the two hotels. c) There is not enough evidence that the mean amounts of time for the two hotels are the same. d) There is enough evidence that the mean amounts of time for the two hotels are the same.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: separate-variance t test, conclusion 178. Referring to Scenario 10-13, what is the 95% confidence interval estimate for the difference in the two means if the two population variances are assumed to be the same?

ANSWER:

0.9543  1  2  1.3593

TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval 179. Referring to Scenario 10-13, state the null and alternative hypotheses for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels. a) H 0 :  I2 –  II2  0 versus H 1 :  I2 –  II2  0 b)

H 0 :  I2 –  II2  0 versus H 1 :  I2 –  II2  0

c)

H 0 :  I2 –  II2  0 versus H 1 :  I2 –  II2  0

d) H 0 :  I2 –  II2  0 versus H 1 :  I2 –  II2  0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: F test for the ratio of variances, form of hypothesis

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10-44

Two-Sample Tests

180. Referring to Scenario 10-13, what is the value of the test statistic for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels?

ANSWER: 1.2124 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, test statistic 181. Referring to Scenario 10-13, what assumptions are necessary for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels to be valid? a) Both sampled populations are normally distributed. b) Both samples are random and independent. c) Neither (a) nor (b) is necessary. d) Both (a) and (b) are necessary.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, assumption 182. Referring to Scenario 10-13, what is the critical value for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels at the 5% level of significance?

ANSWER: 2.5264 (using Excel) or 2.51 (using Table E.5 with 20 and 19 degrees of freedom) TYPE: PR DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, critical value 183. Referring to Scenario 10-13, what is the largest level of significance at which a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels will not be rejected?

ANSWER: 0.6789 (using Excel) or ‘greater than 0.10’ (using Table E.5 with 20 and 19 degrees of freedom) TYPE: PR DIFFICULTY: Difficult KEYWORDS: F test for the ratio of variances, p-value 184. Referring to Scenario 10-13, suppose  = 0.05. Which of the following represents the result of the test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, decision Copyright ©2020 Pearson Education, Inc.

Two-Sample Tests

10-45

185. Referring to Scenario 10-13, suppose  = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels? a) There is no evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels. b) There is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels. c) There is no evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same. d) There is evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, conclusion SCENARIO 10-14 The use of preservatives by food processors has become a controversial issue. Suppose two preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.

Preservative I Preservative II X I = 106.4 hours X II = 96.54 hours S I = 10.3 hours S II = 13.4 hours 186. Referring to Scenario 10-14, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II. a) H 0 :  I2 –  II2  0 versus H 1 :  I2 –  II2  0 b)

H 0 :  I2 –  II2  0 versus H 1 :  I2 –  II2  0

c)

H 0 :  I2 –  II2  0 versus H 1 :  I2 –  II2  0

d) H 0 :  I2 –  II2  0 versus H 1 :  I2 –  II2  0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: F test for the ratio of variances, form of hypothesis 187. Referring to Scenario 10-14, what is the value of the test statistic for testing if the population variances differ for preservatives I and II? ANSWER: 1.6925 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, test statistic

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10-46

Two-Sample Tests

188. Referring to Scenario 10-14, what assumptions are necessary for testing if the population variances differ for preservatives I and II? a) Both sampled populations are normally distributed. b) Both samples are random and independent. c) Neither (a) nor (b) is necessary. d) Both (a) and (b) are necessary.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, assumption 189. Referring to Scenario 10-14, what is the critical value for testing if the population variances differ for preservatives I and II at the 5% level of significance?

ANSWER: 2.9786 (using Excel) or 2.95 (using Table E.5 with 14 and 14 degrees of freedom) TYPE: PR DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, critical value 190. Referring to Scenario 10-14, what is the largest level of significance at which a test of whether the population variances differ for preservatives I and II will not be rejected?

ANSWER: 0.3362 or ‘greater than 0.10’ (using Table E.5 with 15 and 14 degrees of freedom) TYPE: PR DIFFICULTY: Moderate KEYWORDS: F test for the ratio of variances, p-value 191. Referring to Scenario 10-14, suppose  = 0.05. Which of the following represents the result of the relevant hypothesis test? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, decision

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Two-Sample Tests

10-47

192. Referring to Scenario 10-14, suppose  = 0.05. Which of the following represents the correct conclusion? a) There is no evidence of a difference in the population variances between preservatives I and II. b) There is evidence of a difference in the population variances between preservatives I and II. c) There is no evidence that the population variances between preservatives I and II are the same. d) There is evidence that the population variances between preservatives I and II are the same.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, conclusion SCENARIO 10-15 The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions.

Sample I (public accounting): X 1  60.35 , S1  3.25 , n1  12 Sample II (financial planning): X 2  58.20 , S2  2.48 , n2  14 Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same.

193. Referring to Scenario 10-15, which of the following represents the relevant hypotheses tested? a) H 0 : 1 – 2  0 versus H1 : 1 – 2  0 b)

H 0 : 1 – 2  0 versus H1 : 1 – 2  0

H 0 : 1 – 2  0 versus H1 : 1 – 2  0 d) H 0 : 1 – 2  0 versus H1 : 1 – 2  0 c)

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, form of hypothesis 194. Referring to Scenario 10-15, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05?

ANSWER: +1.7109 TYPE: PR DIFFICULTY: Easy KEYWORDS: pooled-variance t test, critical value

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10-48

Two-Sample Tests

195. Referring to Scenario 10-15, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.10?

ANSWER: 1.3178 TYPE: PR DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, critical value 196. Referring to Scenario 10-15, what is the value of the test statistic?

ANSWER: 1.9117 TYPE: PR DIFFICULTY: Easy KEYWORDS: pooled-variance t test, test statistic 197. Referring to Scenario 10-15, what is the smallest level of significance at which the null hypothesis will still not be rejected?

ANSWER: 0.0340 TYPE: PR DIFFICULTY: Moderate KEYWORDS: pooled-variance t test, p-value 198. Referring to Scenario 10-15, suppose  = 0.10. Which of the following represents the result of the relevant hypothesis test? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, decision 199. Referring to Scenario 10-15, suppose  = 0.01. Which of the following represents the result of the relevant hypothesis test? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, decision

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Two-Sample Tests

10-49

200. Referring to Scenario 10-15, suppose  = 0.10. Which of the following represents the correct conclusion? a) There is not enough evidence that the mean starting annual salaries for individuals entering the public accounting professions is not higher than that of financial planning. b) There is not enough evidence that the mean starting annual salaries for individuals entering the public accounting professions is not higher than that of financial planning. c) There is not enough evidence that the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning. d) There is enough evidence that the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, conclusion 201. Referring to Scenario 10-15, suppose  = 0.01. Which of the following represents the correct conclusion? a) There is not enough evidence that the mean starting annual salaries for individuals entering the public accounting professions is not higher than that of financial planning. b) There is not enough evidence that the mean starting annual salaries for individuals entering the public accounting professions is not higher than that of financial planning. c) There is not enough evidence that the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning. d) There is enough evidence that the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, conclusion. P-value exceeds level of significance 0.01.

202. Referring to Scenario 10-15, what is the 95% confidence interval estimate for the difference in the two means?

ANSWER:

0.1711  1  2  4.4711

TYPE: PR DIFFICULTY: Moderate KEYWORDS: difference between two means, confidence interval, 203. Referring to Scenario 10-15, what additional assumption is needed for the test to be valid? a) The two sample sizes have to be equal. b) The two population sizes have to be equal. c) The two population means have to be the same. d) The population distributions of the two annual salaries have to be normal.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: pooled-variance t test, assumption

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10-50

Two-Sample Tests

204. Referring to Scenario 10-15, state the null and alternative hypotheses for testing whether there is evidence of a difference in the variances of the starting annual salaries. a) H 0 :  12 –  22  0 versus H 1 :  12 –  22  0 b)

H 0 :  12 –  22  0 versus H 1 :  12 –  22  0

c)

H 0 :  12 –  22  0 versus H 1 :  12 –  22  0

d) H 0 :  12 –  22  0 versus H 1 :  12 –  22  0 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: F test for the ratio of variances, form of hypothesis 205. Referring to Scenario 10-15, what is the value of the test statistic for testing whether there is evidence of a difference in the variances?

ANSWER: 1.7174 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, test statistic 206. Referring to Scenario 10-15, what assumptions are necessary for testing whether there is evidence of a difference in the variances to be valid? a) Both sampled populations are normally distributed. b) Both samples are random and independent. c) Neither (a) nor (b) is necessary. d) Both (a) and (b) are necessary.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, assumption 207. Referring to Scenario 10-15, what is the critical value for testing whether there is evidence of a difference in the variances at the 5% level of significance?

ANSWER: 3.1975 (using Excel), F.INV.RT(0.025,11,13) or “between 3.15 and 3.25” (using Table E.5 with 10 or 12 and 13 degrees of freedom) TYPE: PR DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, critical value 208. Referring to Scenario 10-15, what is the highest level of significance at which a test on a difference in the variances will not be rejected?

ANSWER: 0.3514 (using Excel or “greater than 0.10” (using Table E.5 with 10 or 12 and 13 degrees of freedom) TYPE: PR DIFFICULTY: Difficult KEYWORDS: F test for the ratio of variances, p-value

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Two-Sample Tests

10-51

209. Referring to Scenario 10-15, suppose  = 0.05. Which of the following represents the result of the test on a difference in the variances? a) The alternative hypothesis is rejected. b) The null hypothesis is rejected. c) The null hypothesis is not rejected. d) Insufficient information exists on which to decide.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, decision 210. Referring to Scenario 10-15, suppose  = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variances? a) There is no evidence of a difference in the variances. b) There is evidence of a difference in the variances. c) There is no evidence that the variances are the same. d) There is evidence that variances are the same.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the ratio of variances, conclusion 211. True or False: A low p-value indicates a small probability the null hypothesis will not be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: p-value, rejection region 212. The p-value is the probability of obtaining a test statistic more extreme than the sample result given the null hypothesis is true.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: p-value, rejection region

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10-52

Two-Sample Tests

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One Way Analysis of Variance

10-1

CHAPTER 10: ONE WAY ANALYSIS OF VARIANCE 1. In a one-way ANOVA, if the computed F statistic is greater than the critical F value you may a) reject H0 since there is evidence all the means differ. b) reject H0 since there is evidence some of the group means are significantly different. c) not reject H0 since there is no evidence of a difference in the means. d) not reject H0 because a mistake has been made.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, decision 2. Which of the following components in an ANOVA table are not additive? a) Sum of squares. b) Degrees of freedom. c) Mean squares. d) It is not possible to tell.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, sum of squares, properties 3. When would you use the Tukey-Kramer procedure? a) To test for normality. b) To test for homogeneity of variance. c) To test independence of errors. d) To test for differences in pairs of means.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: Tukey-Kramer procedure, randomized block design 4. A completely randomized design a) has only one factor with several treatment groups. b) can have more than one factor, each with several treatment groups. c) has one factor and one block. d) has one factor and one block and multiple values.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: completely randomized design

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One Way Analysis of Variance

10-2

5. The F test statistic in a one-way ANOVA is a) MSW/MSA. b) SSW/SSA. c) MSA/MSW. d) SSA/SSW. ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor 6. The degrees of freedom for the F test in a one-way ANOVA are a) (n – c) and (c – 1). b) (c – 1) and (n – c). c) (c – n) and (n – 1). d) (n – 1) and (c – n).

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, degrees of freedom 7. In a one-way ANOVA, the null hypothesis is always a) there is no difference in the population means. b) there is some treatment effect. c) all the population means are different. d) some of the population means are different.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, form of hypothesis 8. In a one-way ANOVA a) an interaction term is present. b) an interaction effect can be tested. c) there is no interaction term. d) the interaction term has (c – 1)(n – 1) degrees of freedom.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, properties, interaction

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One Way Analysis of Variance

10-3

9. An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps the fewest mean number of passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is given below. How should the data be analyzed?

Package 1: 12, 14, 9, 11, 16 Package 2: 2, 4, 7, 3, 1 Package 3: 10, 9, 6, 10, 12 Package 4: 7, 6, 6, 15, 12 a) b) c) d)

F test for differences in variances.

One-way ANOVA F test. t test for the differences in means. t test for the mean difference.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor 10. True or False: The analysis of variance (ANOVA) tests hypotheses about the population variance.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance 11. True or False: When the F test is used for ANOVA, the rejection region is always in the right tail.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, rejection region 12. True or False: If you are comparing the mean sales among 3 different brands you are dealing with a three-way ANOVA design.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, properties

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One Way Analysis of Variance

10-4

13. True or False: The MSE must always be positive.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, mean squares, properties 14. True or False: In a one-factor ANOVA analysis, the among sum of squares and within sum of squares must add up to the total sum of squares.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, sum of squares, properties SCENARIO 10-1 An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) The number of passengers bumped each week is obtained, which gives rise to the following Excel output: ANOVA Source of Variation Between Groups Within Groups

SS 212.4 136.4

Total

348.8

df

MS 3

F 8.304985

8.525

15. Referring to SCENARIO 10-1, the within groups degrees of freedom is a) 3 b) 4 c) 16 d) 19 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, degrees of freedom

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P-value 0.001474

F crit 3.238867

One Way Analysis of Variance

10-5

16. Referring to SCENARIO 10-1, the total degrees of freedom is a) 3 b) 4 c) 16 d) 19 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, degrees of freedom 17. Referring to SCENARIO 10-1, the among-group (between-group) mean squares is a) 8.525 b) 70.8 c) 212.4 d) 637.2 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, mean squares 18. Referring to SCENARIO 10-1, at a significance level of 1%, a) there is insufficient evidence to conclude that the mean number of customers bumped by the 4 packages are not all the same. b) there is insufficient evidence to conclude that the mean number of customers bumped by the 4 packages are all the same. c) there is sufficient evidence to conclude that the mean number of customers bumped by the 4 packages are not all the same. d) there is sufficient evidence to conclude that the mean number of customers bumped by the 4 packages are all the same.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, decision, conclusion SCENARIO 10-2 A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.

A: 1.2, 1.1, 0.9, 0.4 C: 1.0, 1.5, 1.1, 1.3 B: 2.5, 2.1, 1.9, 1.6 D: 0.8, 1.3, 1.1, 0.7 Interpret the results of the analysis summarized in the following table: Source Neighborhoods Error Total

df

SS 3.1819

MS 1.0606

F 10.76

PR > F 0.001

12 4.3644 Copyright ©2020 Pearson Education, Inc.

One Way Analysis of Variance

10-6

19. Referring to SCENARIO 10-2, the among group degrees of freedom is a) 3 b) 4 c) 12 d) 16 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, degrees of freedom 20. Referring to SCENARIO 10-2, the within group sum of squares is a) 1.0606 b) 1.1825 c) 3.1819 d) 4.3644 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, sum of squares 21. Referring to SCENARIO 10-2, the within group mean square is a) 0.0985 b) 0.2910 c) 1.0606 d) 1.1825 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, mean squares 22. Referring to SCENARIO 10-2, a) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not all the same. b) at the 0.01 level of significance, the mean ratios for the 4 neighborhoods are all the same. c) at the 0.10 level of significance, the mean ratios for the 4 neighborhoods are not significantly different. d) at the 0.05 level of significance, the mean ratios for the 4 neighborhoods are not significantly different from 0.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, decision, conclusion

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One Way Analysis of Variance

10-7

23. Referring to SCENARIO 10-2, the null hypothesis for Levene’s test for homogeneity of variances is a) H 0 :  A  B  C  D b)

H0 : M A  M B  M C  M D

c)

H 0 :  A2   B2   C2   D2

d)

H0 :  A   B   C   D

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene’s test, form of hypothesis 24. Referring to SCENARIO 10-2, the value of the test statistic for Levene’s test for homogeneity of variances is a) 0.25 b) 0.37 c) 4.36 d) 10.76 ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: Levene’s test, test statistic NOTE: This question will be easier for students if Excel or Minitab is available.

25. Referring to SCENARIO 10-2, the numerator and denominator degrees of freedom for Levene’s test for homogeneity of variances at a 5% level of significance are, respectively, a) 3, 12 b) 12, 3 c) 3, 15 d) 15, 3 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Levene’s test, degrees of freedom 26. Referring to SCENARIO 10-2, the critical value of Levene’s test for homogeneity of variances at a 5% level of significance is a) 0.64 b) 2.48 c) 3.29 d) 3.49 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Levene’s test, critical value

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One Way Analysis of Variance

10-8

27. Referring to SCENARIO 10-2, the p-value of the test statistic for Levene’s test for homogeneity of variances is a) 0.25 b) 0.64 c) 0.86 d) 3.49 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: Levene’s test, p-value NOTE: This question requires PHStat/Excel.Minitab 28. Referring to SCENARIO 10-2, what should be the decision for the Levene’s test for homogeneity of variances at a 5% level of significance? a) Reject the null hypothesis because the p-value is smaller than the level of significance. b) Reject the null hypothesis because the p-value is larger than the level of significance. c) Do not reject the null hypothesis because the p-value is smaller than the level of significance. d) Do not reject the null hypothesis because the p-value is larger than the level of significance.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Levene’s test, decision 29. Referring to SCENARIO 10-2, what should be the conclusion for the Levene’s test for homogeneity of variances at a 5% level of significance? a) There is insufficient evidence that the variances are all the same. b) There is sufficient evidence that the variances are all the same. c) There is insufficient evidence that the variances are not all the same. d) There is sufficient evidence that the variances are not all the same.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene’s test, conclusion SCENARIO 10-3 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of 4 brands of bicycles. She took 3 of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Trial Barth Tornado Reiser Shaw 1 43 37 41 43 2 46 38 45 45 3 43 39 42 46

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One Way Analysis of Variance

10-9

30. Referring to SCENARIO 10-3, the sporting goods retailer decided to perform an ANOVA F test.

The amount of total variation or SST is __________.

ANSWER: 102.67 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, sum of squares, interpretation 31. Referring to SCENARIO 10-3, the among group variation or SSA is __________.

ANSWER: 81.33 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, sum of squares 32. Referring to SCENARIO 10-3, the within group variation or SSW is __________.

ANSWER: 21.33 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, sum of squares 33. Referring to SCENARIO 10-3, the value of MSA is __________, while MSW is __________.

ANSWER: 27.11; 2.67 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, mean squares 34. Referring to SCENARIO 10-3, the null hypothesis that the mean downhill coasting speeds of the 4 brands of bicycles are equal will be rejected at a level of significance of 0.05 if the value of the test statistic is greater than __________.

ANSWER: 4.07 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, decision 35. Referring to SCENARIO 10-3, in testing the null hypothesis that the mean downhill coasting speeds of the 4 brands of bicycles are equal, the value of the test statistic is __________.

ANSWER: 10.17 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, F test for factor, test statistic

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One Way Analysis of Variance

10-10

36. Referring to SCENARIO 10-3, construct the ANOVA table from the sample data.

ANSWER: Analysis of Variance Source df SS MS F Bicycle Brands 3 81.33 27.11 10.17 Error 8 21.33 2.67 Total 11 102.67 * or p < 0.005, tabular value TYPE: PR DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, properties

p 0.004*

37. True or False: Referring to SCENARIO 10-3, the null hypothesis should be rejected at a 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, decision 38. True or False: Referring to SCENARIO 10-3, the decision made implies that all 4 means are significantly different.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, conclusion, interpretation 39. True or False: Referring to SCENARIO 10-3, the test is valid only if the population of speeds has the same variance for the 4 brands.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, assumption 40. True or False: Referring to SCENARIO 10-3, the test is less sensitive to the assumption that the population of speeds has the same variance for the 4 brands because the sample sizes of the 4 brands are equal.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, assumption 41. True or False: Referring to SCENARIO 10-3, the test is valid only if the population of speeds is normally distributed.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, assumption Copyright ©2020 Pearson Education, Inc.

One Way Analysis of Variance

10-11

42. True or False: Referring to SCENARIO 10-3, the test is robust to the violation of the assumption that the population of speeds is normally distributed.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, assumption 43. Referring to SCENARIO 10-3, the sporting goods retailer decided to compare the 4 treatment means by using the Tukey-Kramer procedure with an overall level of significance of 0.05. There are ________ pairwise comparisons that can be made.

ANSWER: 6 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure 44. Referring to SCENARIO 10-3, using an overall level of significance of 0.05, the critical value of the Studentized range Q used in calculating the critical range for the Tukey-Kramer procedure is ________.

ANSWER: 4.53 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, critical value 45. Referring to SCENARIO 10-3, using an overall level of significance of 0.05, the critical range for the Tukey-Kramer procedure is ________.

ANSWER: 4.27 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, critical value 46. True or False: Referring to SCENARIO 10-3, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that there is a significant difference between all pairs of mean speeds.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 47. True or False: Referring to SCENARIO 10-3, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that there is no significant difference between any pair of mean speeds.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion

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One Way Analysis of Variance

10-12

48. True or False: Referring to SCENARIO 10-3, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that the mean speed for the Tornado brand is significantly different from each of the mean speeds for other brands.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 49. True or False: Referring to SCENARIO 10-3, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that the 3 means other than the mean for Tornado are not significantly different from each other.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 50. Referring to SCENARIO 10-3, the null hypothesis for Levene’s test for homogeneity of variances is a) H 0 :  A  B  C  D b)

H0 : M A  M B  M C  M D

c)

H 0 :  A2   B2   C2   D2

d)

H0 :  A   B   C   D

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene’s test, form of hypothesis 51. Referring to SCENARIO 10-3, what is the value of the test statistic for Levene’s test for homogeneity of variances?

ANSWER: 0.1333 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Levene’s test, test statistic NOTE: This question will be easier for students if Excel is available.

52. Referring to SCENARIO 10-3, what are the numerator and denominator degrees of freedom for Levene’s test for homogeneity of variances respectively?

ANSWER: 3, 8 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Levene’s test, degrees of freedom

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One Way Analysis of Variance

10-13

53. Referring to SCENARIO 10-3, what is the critical value of Levene’s test for homogeneity of variances at a 5% level of significance?

ANSWER: 4.07 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Levene’s test, critical value 54. Referring to SCENARIO 10-3, what is the p-value of the test statistic for Levene’s test for homogeneity of variances?

ANSWER: 0.94 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Levene’s test, p-value NOTE: The answer is obtained with the help of PHStat/Excel/Minitab 55. Referring to SCENARIO 10-3, what should be the decision for the Levene’s test for homogeneity of variances at a 5% level of significance? a) Reject the null hypothesis because the p-value is smaller than the level of significance. b) Reject the null hypothesis because the p-value is larger than the level of significance. c) Do not reject the null hypothesis because the p-value is smaller than the level of significance. d) Do not reject the null hypothesis because the p-value is larger than the level of significance.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene’s test, decision 56. Referring to SCENARIO 10-3, what should be the conclusion for the Levene’s test for homogeneity of variances at a 5% level of significance? a) There is insufficient evidence that the variances are all the same. b) There is sufficient evidence that the variances are all the same. c) There is insufficient evidence that the variances are not all the same. d) There is sufficient evidence that the variances are not all the same.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene’s test, conclusion

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One Way Analysis of Variance

10-14

SCENARIO 10-4 An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants 15 fields, 5 with each variety. She then measures the crop yield in bushels per acre. Treating this as a completely randomized design, the results are presented in the table that follows.

Trial Smith Walsh Trevor 1 11.1 19.0 14.6 2 13.5 18.0 15.7 3 15.3 19.8 16.8 4 14.6 19.6 16.7 5 9.8 16.6 15.2 57. Referring to SCENARIO 10-4, the agronomist decided to perform an ANOVA F test. The amount of total variation or SST is __________.

ANSWER: 114.82 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, sum of squares 58. Referring to SCENARIO 10-4, the among-group variation or SSA is __________.

ANSWER: 82.39 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, sum of squares 59. Referring to SCENARIO 10-4, the within-group variation or SSW is __________.

ANSWER: 32.43 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, sum of squares 60. Referring to SCENARIO 10-4, the value of MSA is __________, while MSW is __________.

ANSWER: 41.19; 2.70 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, mean squares 61. Referring to SCENARIO 10-4, the null hypothesis will be rejected at a level of significance of 0.01 if the value of the test statistic is greater than __________.

ANSWER: 6.93 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, critical value

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One Way Analysis of Variance

10-15

62. Referring to SCENARIO 10-4, the value of the test statistic is __________.

ANSWER: 15.24 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, F test for factor, test statistic 63. Referring to SCENARIO 10-4, construct the ANOVA table from the sample data.

ANSWER: Analysis of Variance Source df SS MS F p Seed Varieties 2 82.39 41.19 15.24 0.000508* Error 12 32.43 2.70 Total 14 114.82 * or p < 0.005, tabular value TYPE: PR DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, F test for factor, properties 64. Referring to SCENARIO 10-4, state the null hypothesis that can be tested.

ANSWER: H0:  Smith   Walsh   Trevor TYPE: PR DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, form of hypothesis 65. True or False: Referring to SCENARIO 10-4, the null hypothesis should be rejected at 0.005 level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, F test for factor, decision 66. True or False: Referring to SCENARIO 10-4, the decision made at 0.005 level of significance implies that all 3 means are significantly different.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, F test for factor, conclusion 67. True or False: Referring to SCENARIO 10-4, the test is valid only if the population of crop yields has the same variance for the 3 varieties.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, assumption

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One Way Analysis of Variance

10-16

68. True or False: Referring to SCENARIO 10-4, the test is valid only if the population of crop yields is normally distributed for the 3 varieties.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, assumption 69. Referring to SCENARIO 10-4, the agronomist decided to compare the 3 treatment means by using the Tukey-Kramer procedure with an overall level of significance of 0.01. There are ________ pairwise comparisons that can be made.

ANSWER: 3 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, properties 70. Referring to SCENARIO 10-4, using an overall level of significance of 0.01, the critical value of the Studentized range Q used in calculating the critical range for the Tukey-Kramer procedure is ________.

ANSWER: 5.04 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, critical value 71. Referring to SCENARIO 10-4, using an overall level of significance of 0.01, the critical range for the Tukey-Kramer procedure is ________.

ANSWER: 3.71 TYPE: FI DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, critical value 72. True or False: Referring to SCENARIO 10-4, based on the Tukey-Kramer procedure with an overall level of significance of 0.01, the agronomist would decide that there is a significant difference between the crop yield of Smith and Walsh seeds.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 73. True or False: Referring to SCENARIO 10-4, based on the Tukey-Kramer procedure with an overall level of significance of 0.01, the agronomist would decide that there is a significant difference between the crop yield of Smith and Trevor seeds.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion

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One Way Analysis of Variance

10-17

74. True or False: Referring to SCENARIO 10-4, based on the Tukey-Kramer procedure with an overall level of significance of 0.01, the agronomist would decide that there is a significant difference between the crop yield of Walsh and Trevor seeds.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion SCENARIO 10-5 A hotel chain has identically small sized resorts in 5 locations in different small islands. The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the 5 locations.

ROW Location A Location B Location C Location D Location E 1 28 40 21 37 22 2 33 35 21 47 19 3 41 33 27 45 25 Analysis of Variance Source df SS Location 4 963.6 Error 10 210.0 Total

MS

F 11.47

p 0.001

75. True or False: Referring to SCENARIO 10-5, if a level of significance of 0.05 is chosen, the null hypothesis should be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, decision 76. True or False: Referring to SCENARIO 10-5, if a level of significance of 0.05 is chosen, the decision made indicates that all 5 locations have different mean occupancy rates.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, conclusion 77. True or False: Referring to SCENARIO 10-5, if a level of significance of 0.05 is chosen, the decision made indicates that at least 2 of the 5 locations have different mean occupancy rates.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, F test for factor, conclusion

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One Way Analysis of Variance

10-18

78. Referring to SCENARIO 10-5, the among-group variation or SSA is _________.

ANSWER: 963.6 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, sum of squares 79. Referring to SCENARIO 10-5, the within-group variation or SSW is _________.

ANSWER: 210.0 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, sum of squares 80. Referring to SCENARIO 10-5, the total variation or SST is ________.

ANSWER: 1,173.6 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, sum of squares 81. Referring to SCENARIO 10-5, the value of MSA is ______ while MSW is _______.

ANSWER: 240.9; 21.0 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, mean squares 82. Referring to SCENARIO 10-5, the numerator and denominator degrees of freedom of the test ratio are ________ and ________, respectively.

ANSWER: 4 and 10 TYPE: FI DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, degrees of freedom 83. True or False: Referring to SCENARIO 10-5, the total mean squares is 261.90.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: one-way analysis of variance, sum of squares

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One Way Analysis of Variance

10-19

84. Referring to SCENARIO 10-5, the null hypothesis for Levene’s test for homogeneity of variances is a) H 0 :  A  B  C  D b)

H0 : M A  M B  M C  M D

c)

H 0 :  A2   B2   C2   D2

d)

H0 :  A   B   C   D

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene’s test, form of hypothesis 85. Referring to SCENARIO 10-5, what is the value of the test statistic for Levene’s test for homogeneity of variances?

ANSWER: 0.28 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Levene’s test, test statistic NOTE: This question will be easier for students if Excel or PHStat is available.

86. Referring to SCENARIO 10-5, what are the numerator and denominator degrees of freedom for Levene’s test for homogeneity of variances respectively?

ANSWER: 4, 10 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Levene’s test, degrees of freedom 87. Referring to SCENARIO 10-5, what is the critical value of Levene’s test for homogeneity of variances at a 5% level of significance?

ANSWER: 3.48 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Levene’s test, critical value 88. Referring to SCENARIO 10-5, what is the p-value of the test statistic for Levene’s test for homogeneity of variances?

ANSWER: 0.88 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Levene’s test, p-value NOTE: The answer is obtained with the help of PHStat or Excel.

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One Way Analysis of Variance

10-20

89. Referring to SCENARIO 10-5, what should be the decision for the Levene’s test for homogeneity of variances at a 5% level of significance? a) Reject the null hypothesis because the p-value is smaller than the level of significance. b) Reject the null hypothesis because the p-value is larger than the level of significance. c) Do not reject the null hypothesis because the p-value is smaller than the level of significance. d) Do not reject the null hypothesis because the p-value is larger than the level of significance.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene’s test, decision 90. Referring to SCENARIO 10-5, what should be the conclusion for the Levene’s test for homogeneity of variances at a 5% level of significance? a) There is insufficient evidence that the variances are all the same. b) There is sufficient evidence that the variances are all the same. c) There is insufficient evidence that the variances are not all the same. d) There is sufficient evidence that the variances are not all the same.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Levene’s test, conclusion 91. True or False: The F test in a completely randomized model is just an expansion of the t test for independent samples.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: completely randomized design, F test for factor 92. True or False: A completely randomized design with 4 groups would have 6 possible pairwise comparisons.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: completely randomized design, properties

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Chi-Square Tests

11-1

CHAPTER 11: CHI-SQUARE TESTS 1. If we use the  method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to: a) 3 b) 4 c) 5 d) 1 2

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in proportions, degrees of freedom 2. If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate test to use is a) the Z test.

2 b) the  test. c) Both a) and b). d) Neither of a) nor b).

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in proportions 3. In testing a hypothesis using the  test, the theoretical frequencies are based on the a) null hypothesis. b) alternative hypothesis. c) normal distribution. d) None of the above.

2

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in proportions, Chi-square test of independence, properties

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Chi-Square Tests 11-2 SCENARIO 12-1 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a selfimprovement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let  1 and  2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

4. Referring to Scenario 12-1, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses? a) H0:  1   2 = 0 versus H1:  1   2  0 b) H0:  1   2  0 versus H1:  1   2 = 0 c) H0:  1   2  0 versus H1:  1   2 > 0 d) H0:  1   2  0 versus H1:  1   2 < 0 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions 5. Referring to Scenario 12-1, what is the critical value when performing a chi-square test on whether the population proportions are different if  = 0.05? a)  1.645 b)  1.96 c) 3.841 d) 2.706 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, critical value 6. Referring to Scenario 12-1, what is the critical value when testing whether the population proportions are different if  = 0.10? a)  1.645 b)  1.96 c) 3.842 d) 2.706 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, critical value

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Chi-Square Tests

11-3

7. Referring to Scenario 12-1, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions using  = 0.10? a) 4.335 b) 2.706 c) 1.194 d) 0.274 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, test statistic 8. Referring to Scenario 12-1, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is most correct? a) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years. b) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years. c) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years. d) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, decision, conclusion 9. True or False: In testing the difference between two proportions using the normal distribution, we may use either a one-tail Chi-square test or two-tail Z test.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Z test for difference in two proportions, Chi-square test for difference in two proportions 10. True or False: The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, properties

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Chi-Square Tests 11-4 11. True or False: A test for the difference between two proportions can be performed using the chisquare distribution.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions 12. True or False: A test for whether one proportion is higher than the other can be performed using the chi-square distribution.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions SCENARIO 12-2 The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as “Group 1” and the economics majors are designated as “Group 2,” perform the appropriate hypothesis test using a level of significance of 0.05.

13. Referring to Scenario 12-2, the hypotheses the dean should use are: a) H0:  1   2 = 0 versus H1:  1   2  0 b) H0:  1   2  0 versus H1:  1   2 = 0 c) H0:  1   2  0 versus H1:  1   2 > 0 d) H0:  1   2  0 versus H1:  1   2 < 0 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, form of hypothesis 14. Referring to Scenario 12-2, the null hypothesis will be rejected if the test statistic is ________.

ANSWER:  2 > 3.841 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, critical value 15. Referring to Scenario 12-2, the value of the test statistic is ________.

ANSWER:  2 = 3.4806 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, test statistic Copyright ©2020 Pearson Education, Inc.

Chi-Square Tests

11-5

16. Referring to Scenario 12-2, the p-value of the test is ________.

ANSWER: 0.0621 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, p-value 17. True or False: Referring to Scenario 12-2, the null hypothesis should be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, decision 18. True or False: Referring to Scenario 12-2, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, decision 19. True or False: Referring to Scenario 12-2, the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, decision SCENARIO 12-3 The director of transportation of a large company is interested in the usage of her van pool. She considers her routes to be divided into local and non-local. She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes. She takes a sample of a day's riders and finds the following:

Local Non-Local Total

Male 27 33 60

Female 44 25 69

Total 71 58 129

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

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Chi-Square Tests 11-6 20. Referring to Scenario 12-3, the test will involve _________ degree(s) of freedom.

ANSWER: 1 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, degrees of freedom 21. Referring to Scenario 12-3, the overall or mean proportion of local riders is __________.

ANSWER: 0.5504 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, properties 22. Referring to Scenario 12-3, the expected cell frequency in the Male/Local cell is __________.

ANSWER: 33.02 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, contingency table, properties 23. Referring to Scenario 12-3, the expected cell frequency in the Female/Non-Local cell is __________.

ANSWER: 31.02 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, contingency table, properties 24. Referring to Scenario 12-3, the critical value of the test is _________.

ANSWER: 3.841 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in two proportions, critical value 25. Referring to Scenario 12-3, the value of the test statistic is _________.

ANSWER: 4.568 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, test statistic 26. True or False: Referring to Scenario 12-3, the null hypothesis will be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, decision

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Chi-Square Tests

11-7

27. True or False: Referring to Scenario 12-3, the decision made suggests that there is a difference between the proportion of males and females who ride local versus non-local routes.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in two proportions, conclusion SCENARIO 12-4 A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day’s transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

Memory Location:

1

2

3

4

5

Number of Transactions:

82

100

74

92

102

Number of Reported Errors

11

12

6

9

10

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

28. Referring to Scenario 12-4, which test would be used to properly analyze the data in this experiment?

2 a)  test of independence 2 b)  test for difference among more than two proportions c) Wilcoxon rank sum test d) Kruskal-Wallis rank Test ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions 29. Referring to Scenario 12-4, the degrees of freedom of the test statistic is a) 4 b) 8 c) 10 d) 448 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, degrees of freedom

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Chi-Square Tests 11-8 30. Referring to Scenario 12-4, the critical value of the test statistic at 1% level of significance is a) 7.7794 b) 13.2767 c) 20.0902 d) 23.2093 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, critical value 31. Referring to Scenario 12-4, the calculated value of the test statistic is a) -0.1777 b) -0.0185 c) 1.2068 d) 1.5190 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, test statistic 32. Referring to Scenario 12-4, at 1% level of significance a) there is sufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different. b) there is insufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different. c) there is sufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same. d) there is insufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, decision, conclusion SCENARIO 12-5 Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the 4 procedures, and collects the following numbers of patients from their own records:

Clear Return Total

A 27 11 38

Procedure B C 41 21 15 9 56 30

D 7 11 18

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Total 96 46 142

Chi-Square Tests

11-9

They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.

33. Referring to Scenario 12-5, the test will involve _________ degrees of freedom.

ANSWER: 3 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, degrees of freedom 34. Referring to Scenario 12-5, the overall or mean proportion of clear operations is __________.

ANSWER: 0.676 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, properties 35. Referring to Scenario 12-5, the expected cell frequency for the Procedure A/Clear cell is __________.

ANSWER: 25.69 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, contingency table, properties 36. Referring to Scenario 12-5, the expected cell frequency for the Procedure D/Return cell is __________.

ANSWER: 5.83 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, contingency table, properties 37. Referring to Scenario 12-5, the critical value of the test is ________.

ANSWER: 7.815 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, critical value 38. Referring to Scenario 12-5, the value of the test statistic is _________.

ANSWER: 7.86759 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, test statistic

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Chi-Square Tests 11-10 39. True or False: Referring to Scenario 12-5, the null hypothesis will be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, decision 40. True or False: Referring to Scenario 12-5, the decision made suggests that the 4 procedures all have different proportions of clear operations.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, conclusion 41. True or False: Referring to Scenario 12-5, the decision made suggests that the 4 procedures do not all have the same proportion of clear operations.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, conclusion 42. Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure B using a 0.05 level of significance?

ANSWER: 0.26 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 43. True or False: Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure A and procedure B are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion 44. Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure C using a 0.05 level of significance?

ANSWER: 0.31 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value Copyright ©2020 Pearson Education, Inc.

Chi-Square Tests

11-11

45. True or False: Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure A and procedure C are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion 46. Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure D using a 0.05 level of significance?

ANSWER: 0.38 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 47. True or False: Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure A and procedure D are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion 48. Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure B and procedure C using a 0.05 level of significance?

ANSWER: 0.28 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 49. True or False: Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure B and procedure C are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion

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Chi-Square Tests 11-12 50. Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure B and procedure D using a 0.05 level of significance?

ANSWER: 0.36 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 51. True or False: Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure B and procedure D are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in proportions, Marascuilo procedure, decision, conclusion 52. Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure C and procedure D using a 0.05 level of significance?

ANSWER: 0.40 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 53. True or False: Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure C and procedure D are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion SCENARIO 12-6 According to an article in Marketing News, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Check Written Yes No

Year 1 225 275

Year Year 2 175 325

Year 3 125 375

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Chi-Square Tests

11-13

54. Referring to Scenario 12-6, what is the expected number of shoppers who pay by check in year 1 if there is no difference in the proportion of shoppers who pay by check among the three years?

ANSWER: 175 TYPE: PR DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, properties 55. Referring to Scenario 12-6, what is the expected number of shoppers who do not pay by check in year 3 if there is no difference in the proportion of shoppers who pay by check among the three years?

ANSWER: 325 TYPE: PR DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, properties 56. Referring to Scenario 12-6, what is the form of the null hypothesis? a) H0 : 1   2   3

H 0 : 1   2   3 c) H0 : 1   2   3 d) H0 : 1   2   3 b)

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, forms of hypothesis 57. Referring to Scenario 12-6, what is the form of the alternative hypothesis? a) H1 : 1   2   3 b)

H1 : 1   2   3

H1 : 1   2   3 d) H1 : not all  j are the same c)

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, forms of hypothesis 58. True or False: Referring to Scenario 12-6, the assumptions needed to perform the test are satisfied.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, assumption

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Chi-Square Tests 11-14 59. Referring to Scenario 12-6, what are the degrees of freedom of the test statistic?

ANSWER: 2 TYPE: PR DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, degrees of freedom 60. Referring to Scenario 12-6, what is the value of the test statistic?

ANSWER: 43.96 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, test statistic 61. Referring to Scenario 12-6, what is the critical value?

ANSWER: 5.991 TYPE: PR DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in proportions, critical value 62. Referring to Scenario 12-6, what is the p-value of the test statistic?

ANSWER: 2.9E-10 or smaller than 0.005 TYPE: PR DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, p-value 63. True or False: Referring to Scenario 12-6, the null hypothesis cannot be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, decision 64. Referring to Scenario 12-6, what is the correct conclusion? a) There is enough evidence that the proportions are all different in the 3 years. b) There is not enough evidence that the proportions are all different in the 3 years. c) There is enough evidence that at least two of the proportions are not equal. d) There is not enough evidence that at least two of the proportions are not equal.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, conclusion

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Chi-Square Tests

11-15

65. Referring to Scenario 12-6, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 2 using a 0.05 level of significance?

ANSWER: 0.0754 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 66. Referring to Scenario 12-6, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 3 using a 0.05 level of significance?

ANSWER: 0.0722 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical range 67. Referring to Scenario 12-6, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 2 and year 3 using a 0.05 level of significance?

ANSWER: 0.0705 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 68. True or False: Referring to Scenario 12-6, there is sufficient evidence to conclude that the proportions between year 1 and year 2 are different at a 0.05 level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion 69. True or False: Referring to Scenario 12-6, there is insufficient evidence to conclude that the proportions between year 1 and year 3 are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion

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Chi-Square Tests 11-16 70. True or False: Referring to Scenario 12-6, there is sufficient evidence to conclude that the proportions between year 2 and year 3 are different at a 0.05 level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision conclusion SCENARIO 12-7 Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.

Yes No

Hong Kong 86% 14%

New York 76% 24%

Paris 78% 22%

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.

71. Referring to Scenario 12-7, the test will involve _________ degrees of freedom.

ANSWER: 2 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, degrees of freedom 72. Referring to Scenario 12-7, the expected cell frequency for the Hong Kong/Yes cell is __________.

ANSWER: 160 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, contingency table, properties 73. Referring to Scenario 12-7, the expected cell frequency for the Paris/No cell is __________.

ANSWER: 40 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, contingency table, properties

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Chi-Square Tests

11-17

74. Referring to Scenario 12-7, the critical value of the test is ________.

ANSWER: 5.9915 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test for difference in more than two proportions, critical value 75. Referring to Scenario 12-7, the value of the test statistic is _________.

ANSWER: 7.00 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, test statistic 76. True or False: Referring to Scenario 12-7, the null hypothesis will be rejected.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, decision 77. True or False: Referring to Scenario 12-7, the decision made suggests that the 3 cities all have different proportions of hotels that correctly post minibar charges.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, conclusion 78. True or False: Referring to Scenario 12-7, the decision made suggests that the 3 cities do not all have the same proportion of hotels that correctly post minibar charges.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, conclusion 79. Referring to Scenario 12-7, what are the values of the absolute difference and the critical range for the Marascuilo procedure to test for the difference in proportions between Hong Kong and New York using a 0.05 level of significance?

ANSWER: 0.1 and 0.0952 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value

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Chi-Square Tests 11-18 80. True or False: Referring to Scenario 12-7, there is sufficient evidence to conclude that the proportions between Hong Kong and New York are different at a 0.05 level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion 81. Referring to Scenario 12-7, what are the values of the absolute difference and the critical range for the Marascuilo procedure to test for the difference in proportions between Hong Kong and Paris using a 0.05 level of significance?

ANSWER: 0.08 and 0.0935 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 82. True or False: Referring to Scenario 12-7, there is sufficient evidence to conclude that the proportions between Hong Kong and Paris are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion 83. Referring to Scenario 12-7, what are the values of the absolute difference and the critical range for the Marascuilo procedure to test for the difference in proportions between New York and Paris using a 0.05 level of significance?

ANSWER: 0.02 and 0.1030 TYPE: PR DIFFICULTY: Difficult KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, critical value 84. True or False: Referring to Scenario 12-7, there is sufficient evidence to conclude that the proportions between New York and Paris are different at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test for difference in more than two proportions, Marascuilo procedure, decision, conclusion

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Chi-Square Tests

11-19

85. True or False: When using the  tests for independence, you should be aware that expected frequencies that are too small will lead to a large Type I error.

2

ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: Chi-square test of independence, properties, assumption 86. True or False: If we use the chi-square method of analysis to test for the difference between proportions, we must assume that there are at least 5 observed frequencies in each cell of the contingency table.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, properties, assumption 87. When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom. a) 5 b) 6 c) 7 d) 12 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, degrees of freedom SCENARIO 12-8 A study was conducted to determine whether the use of seat belts in motor vehicles depends on the educational status of the parents. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) parents’ educational status (College Degree or Non-College Degree) and (2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.

Seat belts not worn Seat belts worn

Non-College Degree 31 283

College Degree 148 330

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Chi-Square Tests 11-20 88. Referring to Scenario 12-8, which test would be used to properly analyze the data in this experiment?

2 a)  test for independence 2 b)  test for differences among more than two proportions c) Wilcoxon rank sum test for independent populations d) Kruskal-Wallis rank test ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence 89. Referring to Scenario 12-8, the calculated test statistic is a) -0.9991 b) -0.1368 c) 48.1849 d) 72.8063 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, test statistic 90. Referring to Scenario 12-8, at 5% level of significance, the critical value of the test statistic is a) 3.8415 b) 5.9914 c) 9.4877 d) 13.2767 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, critical value 91. Referring to Scenario 12-8, at 5% level of significance, there is sufficient evidence to conclude that a) use of seat belts in motor vehicles is related to the educational status of the parents. b) use of seat belts in motor vehicles depends on the educational status of the parents. c) use of seat belts in motor vehicles is associated with the educational status of the parents. d) All of the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, decision, conclusion

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Chi-Square Tests

11-21

SCENARIO 12-9 Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Identified product Could not identify

Male Celebrity 41 109

Female Celebrity 61 89

92. Referring to Scenario 12-9, which test would be used to properly analyze the data in this experiment?

2 a)  test for independence 2 b)  test for differences among more than two proportions c) Wilcoxon rank sum test for independent populations d) Kruskal-Wallis rank test ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence 93. Referring to Scenario 12-9, the calculated test statistic is a) -0.1006 b) 0.00 c) 5.9418 d) 6.1194 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, test statistic 94. Referring to Scenario 12-9, at 5% level of significance, the critical value of the test statistic is a) 3.8415 b) 5.9914 c) 9.4877 d) 13.2767 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, critical value

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Chi-Square Tests 11-22 95. Referring to Scenario 12-9, the degrees of freedom of the test statistic are a) 1 b) 2 c) 4 d) 299 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, degrees of freedom 96. Referring to Scenario 12-9, at 5% level of significance, the conclusion is that a) brand awareness of female TV viewers and the gender of the spokesperson are independent. b) brand awareness of female TV viewers and the gender of the spokesperson are not independent. c) brand awareness of female TV viewers and the gender of the spokesperson are related. d) Both (b) and (c).

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, decision, conclusion SCENARIO 12-10 One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.

Years Since Training Period < 1 Year 1 – 4 Years 5 – 9 Years High 6 9 9 Defect Rate: Average 9 19 23 Low 7 8 10

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Chi-Square Tests

11-23

97. Referring to Scenario 12-10, which test would be used to properly analyze the data in this experiment to determine whether there is a relationship between defect rate and years of experience?

2 a)  test for independence 2 b)  test for differences among more than two proportions c) Wilcoxon rank sum test for independent populations d) Kruskal-Wallis rank test ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence 98. Referring to Scenario 12-10, find the rejection region necessary for testing at the 0.05 level of significance whether there is a relationship between defect rate and years of experience.

2 a) Reject H0 if  > 16.919 2 b) Reject H0 if  > 15.507 2 c) Reject H0 if  > 11.143 2 d) Reject H0 if  > 9.488 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, critical value 99. Referring to Scenario 12-10, what is the expected number of employees with less than 1 year of training time and a high defect rate? a) 4.17 b) 4.60 c) 5.28 d) 9.17 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, contingency table, properties 100. Referring to Scenario 12-10, what is the expected number of employees with 1 to 4 years of training time and a high defect rate? a) 12.00 b) 8.64 c) 6.67 d) 6.00 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, contingency table, properties

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Chi-Square Tests 11-24 101. Referring to Scenario 12-10, for the cell with 1 to 4 years of training time and a high defect 2 rate, what is the contribution to the overall  statistic for the independence test? a) 0.36 b) 0.1296 c) 0.015 d) 0.0144 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, contingency table, properties 102. Referring to Scenario 12-10, a test was conducted to determine if a relationship exists between defect rate and years of experience. Which of the following p-values would indicate that defect rate and years of experience are dependent? Assume you are testing at  = 0.05. a) 0.045 b) 0.055 c) 0.074 d) 0.080 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, p-value, decision SCENARIO 12-11 The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is independent of the type of community in which an applicant resides. He takes a sample of recent admissions decisions and forms the following table:

Urban Rural Suburban Total

Admitted 45 33 34 112

Wait List 21 13 12 46

Denied 17 24 39 80

Total 83 70 85 238

He will use this table to do a chi-square test of independence with a level of significance of 0.01.

103. Referring to Scenario 12-11, the test will involve _________ degrees of freedom.

ANSWER: 4 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, degrees of freedom

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Chi-Square Tests

11-25

104. Referring to Scenario 12-11, the critical value of the test is _________.

ANSWER: 13.277 TYPE: FI DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, critical value 105. Referring to Scenario 12-11, the expected cell frequency for the Admitted/Urban cell is _________.

ANSWER: 39.06 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, contingency table, properties 106. Referring to Scenario 12-11, the value of the test statistic is _________.

ANSWER: 12.624 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, test statistic 107. True or False: Referring to Scenario 12-11, the null hypothesis will be rejected.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, decision 108. True or False: Referring to Scenario 12-11, the p-value of this test is greater than 0.01.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, p-value 109. True or False: Referring to Scenario 12-11, the decision made suggests that admissions status at the college is independent of the type of community in which an applicant resides.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, conclusion 110. True or False: Referring to Scenario 12-11, the same decision would be made with this test if the level of significance had been 0.005.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, decision Copyright ©2020 Pearson Education, Inc.

Chi-Square Tests 11-26 111. True or False: Referring to Scenario 12-11, the same decision would be made with this test if the level of significance had been 0.05.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, decision 112. True or False: Referring to Scenario 12-11, the null hypothesis claims that "there is no association between admission status at the college and the type of community in which an applicant resides."

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, form of hypothesis, conclusion 113. True or False: Referring to Scenario 12-11, the alternative hypothesis claims that "there is some connection between admission status at the college and the type of community in which an applicant resides."

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, form of hypothesis, conclusion 114. True or False: The chi-square test of independence requires that the expected frequency in each cell to be at least 5.

ANSWERS: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, assumption 115. True or False: The chi-square test of independence requires that the expected frequency in each cell to be at least 1.

ANSWERS: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, assumption

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Chi-Square Tests

11-27

SCENARIO 12-12 Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks

Average time spent watching TV Less than 2 hours More than 2 hours

Average time spent reading story books Less than 1 hour Between 1and 2 hours

More than 2 hours

90 655

130 8

85 32

116. Referring to Scenario 12-12, how many children in the survey spent less than 2 hours watching TV and more than 2 hours reading story books on average? a) 8 b) 130 c) 175 d) 687 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, properties 117. Referring to Scenario 12-12, how many children in the survey spent less than 2 hours watching TV and no more than 2 hours reading storybooks on average? a) 8 b) 130 c) 175 d) 687 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: contingency table, properties 118. Referring to Scenario 12-12, if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true, how many children watching less than 2 hours of TV and reading no more than 2 hours of story books on average can we expect? a) 35.69 b) 227.23 c) 262.91 d) 969.75 ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: Chi-square test of independence, contingency table, properties

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Chi-Square Tests 11-28 119. Referring to Scenario 12-12, if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true, how many children watching less than 2 hours of TV and reading more than 2 hours of story books on average can we expect? a) 42.09 b) 155.25 c) 262.92 d) 987.75 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, contingency table, properties 120. Referring to Scenario 12-12, to test whether there is any relationship between average time spent watching TV and average time spent reading story books, the value of the measured test statistic is a) -12.59 b) 1.61 c) 481.49 d) 1,368.06 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, test statistic 121. Referring to Scenario 12-12, suppose we want to constrain the probability of committing a Type I error to 5% when testing whether there is any relationship between average time spent watching TV and average time spent reading story books, the critical value will be a) 5.991 b) 7.378 c) 12.592 d) 14.449 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, critical value

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Chi-Square Tests

11-29

122. Referring to Scenario 12-12, we want to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks. Suppose the value of the test statistic was 164 (which is not the correct answer) and the critical value was 19.00 (which is not the correct answer), then we could conclude that a) There is a connection between time spent reading storybooks and time spent watching TV. b) There is no connection between time spent reading storybooks and time spent watching TV. c) More time spent reading storybooks leads to less time spent watching TV. d) More time spent watching TV leads to less time spent reading storybooks.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, decision, conclusion SCENARIO 12-13 Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-yearolds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the mean number of hours spent watching TV and weights are independent at 1% level of significance.

Weights More than 10 lbs. overweight Within 10 lbs. of normal weight More than 10 lbs. underweight Total

0-3 1 20 10 31

TV Hours 3-6 9 15 5 29

6+ 20 15 5 40

Total 30 50 20 100

123. Referring to Scenario 12-13, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to be spending 3-6 hours on average watching TV and are more than 10 lbs. underweight? a) 5 b) 5.8 c) 6.2 d) 8 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, contingency table, properties

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Chi-Square Tests 11-30 124. Referring to Scenario 12-13, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to be spending no more than 6 hours on average watching TV and are more than 10 lbs. underweight? a) 5.8 b) 6.2 c) 8 d) 12 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, contingency table, properties 125. Referring to Scenario 12-13, how many children in the survey spend more than 6 hours watching TV and are more than 10 lbs. overweight? a) 1 b) 9 c) 20 d) 40 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, contingency table, properties 126. Referring to Scenario 12-13, how many children in the survey spend no more than 6 hours watching TV and are more than 10 lbs. underweight? a) 5 b) 10 c) 15 d) 20 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, contingency table, properties 127. Referring to Scenario 12-13, the value of the test statistic is a) 8.532 b) 15.483 c) 18.889 d) 69.744 ANSWER: c TYPE: MC DIFFICULTY: moderate KEYWORDS: Chi-square test of independence, test statistic

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Chi-Square Tests

11-31

128. Referring to Scenario 12-13, the critical value of the test will be a) 6.635 b) 13.277 c) 14.860 d) 21.666 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, critical value 129. Referring to Scenario 12-13, suppose the value of the test statistic was 30.00 (which is not the correct value) and the critical value at 1% level of significance was 10.00 (which is not the correct value), which of the following conclusions would be correct? a) We will not reject the null and conclude that mean number of hours spent watching TV and weights are independent. b) We will reject the null and conclude that mean number of hours spent watching TV and weights are independent. c) We will not reject the null and conclude that mean number of hours spent watching TV and weights are not independent. d) We will reject the null and conclude that mean number of hours spent watching TV and weights are not independent.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Chi-square test of independence, decision, conclusion 130. Referring to Scenario 12-13, which of the following statements is correct? a) We cannot reject the null for any level of significance greater than 0.005 b) We can reject the null for any level of significance greater than 0.005. c) We cannot reject the null for any level of significance smaller than 0.005 d) We can reject the null for any level of significance smaller than 0.005.

ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: Chi-square test of independence, decision 131. Referring to Scenario 12-13, the degrees of freedom of the test statistic are a) 1 b) 2 c) 4 d) 9 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, degrees of freedom

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Chi-Square Tests 11-32 132. True or False: Referring to Scenario 12-13, the test is always a one-tail test.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Chi-square test of independence, properties

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Simple Linear Regression

CHAPTER 12: SIMPLE LINEAR REGRESSION 1. The Y-intercept (b0) represents the a) predicted value of Y when X = 0. b) change in estimated Y per unit change in X. c) predicted value of Y. d) variation around the sample regression line.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: intercept, interpretation 2. The slope (b1) represents a) predicted value of Y when X = 0. b) the estimated average change in Y per unit change in X. c) the predicted value of Y. d) variation around the line of regression.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, interpretation 3. The least squares method minimizes which of the following? a) SSR b) SSE c) SST d) All of the above ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: least squares, properties

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12-1

12-2

Simple Linear Regression

SCENARIO 12-1 A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank’s charges (Y) -- measured in dollars per month -- for services rendered to local companies. One independent variable used to predict service charges to a company is the company’s sales revenue (X) -- measured in millions of dollars. Data for 21 companies who use the bank’s services were used to fit the model:

Yi  0  1 X i   i

The results of the simple linear regression are provided below.

Y  2, 700  20 X , SYX  65, two-tail p value  0.034 (for testing  ) 4. Referring to Scenario 12-1, interpret the estimate of  0 , the Y-intercept of the line. a) All companies will be charged at least $2,700 by the bank. b) There is no practical interpretation since a sales revenue of $0 is a nonsensical value. c) About 95% of the observed service charges fall within $2,700 of the least squares line. d) For every $1 million increase in sales revenue, we expect a service charge to decrease $2,700.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: intercept, interpretation 5. Referring to Scenario 12-1, interpret the estimate of  , the standard deviation of the random error term (standard error of the estimate) in the model. a) About 95% of the observed service charges fall within $65 of the least squares line. b) About 95% of the observed service charges equal their corresponding predicted values. c) About 95% of the observed service charges fall within $130 of the least squares line. d) For every $1 million increase in sales revenue, we expect a service charge to increase $65.

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: standard error of the estimate, interpretation 6. Referring to Scenario 12-1, interpret the p-value for testing whether 1 exceeds 0. a) There is sufficient evidence (at the  = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y). b) There is insufficient evidence (at the  = 0.10) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y). c) Sales revenue (X) is a poor predictor of service charge (Y). d) For every $1 million increase in sales revenue, you expect a service charge to increase $0.034.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: p-value, interpretation

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Simple Linear Regression

12-3

7. Referring to Scenario 12-1, a 95% confidence interval for 1 is (15, 30). Interpret the interval. a) You are 95% confident that the mean service charge will fall between $15 and $30 per month. b) You are 95% confident that the sales revenue (X) will increase between $15 and $30 million for every $1 increase in service charge (Y). c) You are 95% confident that mean service charge (Y) will increase between $15 and $30 for every $1 million increase in sales revenue (X). d) At the  = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X).

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, interpretation SCENARIO 12-2 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below: City Price ($) Sales River Falls 1.30 100 Hudson 1.60 90 Ellsworth 1.80 90 Prescott 2.00 40 Rock Elm 2.40 38 Stillwater 2.90 32 8. Referring to Scenario 12-2, what is the estimated slope for the candy bar price and sales data? a) 161.386 b) 0.784 c) – 3.810 d) – 48.193 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, estimation 9. Referring to Scenario 12-2, what is the estimated mean change in the sales of the candy bar if price goes up by $1.00? a) 161.386 b) 0.784 c) – 3.810 d) – 48.193 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, interpretation Copyright ©2020 Pearson Education, Inc.

12-4

Simple Linear Regression

10. Referring to Scenario 12-2, what is the coefficient of correlation for these data? a) – 0.8854 b) – 0.7839 c) 0.7839 d) 0.8854 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of correlation, estimation 11. Referring to Scenario 12-2, what is the percentage of the total variation in candy bar sales explained by the regression model? a) 100% b) 88.54% c) 78.39% d) 48.19% ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of determination, interpretation 12. Referring to Scenario 12-2, what percentage of the total variation in candy bar sales is explained by prices? a) 100% b) 88.54% c) 78.39% d) 48.19% ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of determination, interpretation 13. Referring to Scenario 12-2, what is the standard error of the estimate, SYX, for the data? a) 0.784 b) 0.885 c) 12.650 d) 16.299 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error of the estimate, estimation

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Simple Linear Regression

12-5

14. Referring to Scenario 12-2, what is the standard error of the regression slope estimate, S b1 ? a) b) c) d)

0.784 0.885 12.650 16.299

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: standard error, slope 15. Referring to Scenario 12-2, what is ( X – X )2 for these data? a) 0 b) 1.66 c) 2.54 d) 25.66 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sum of squares 16. Referring to Scenario 12-2, to test that the regression coefficient, 1, is not equal to 0, what would be the critical values? Use  = 0.05. a)  2.5706 b)  2.7764 c)  3.1634 d)  3.4954 ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: t test on slope, critical value 17. Referring to Scenario 12-2, to test whether a change in price will have any impact on sales, what would be the critical values? Use  = 0.05. a)  2.5706 b)  2.7765 c)  3.1634 d)  3.4954 ANSWER: b TYPE: MC DIFFICULTY: Difficult EXPLANATION: This is a test for 1 is not equal to 0.

KEYWORDS: t test on slope, critical value

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12-6

Simple Linear Regression

18. Referring to Scenario 12-2, if the price of the candy bar is set at $2, the estimated mean sales will be a) 30 b) 65 c) 90 d) 100 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values 19. Referring to Scenario 12-2, if the price of the candy bar is set at $2, the predicted sales will be a) 30 b) 65 c) 90 d) 100 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values 20. True or False: The Chancellor of a university has commissioned a team to collect data on students’ GPAs and the amount of time they spend bar hopping every week (measured in minutes). He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students' GPAs. His team should use a t test on the slope of the population regression.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: t test on slope 21. The residual represents the discrepancy between the observed dependent variable and its _____ value.

ANSWER: predicted or estimated mean TYPE: FI DIFFICULTY: Moderate KEYWORDS: estimation of mean values, prediction of individual values

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Simple Linear Regression

12-7

SCENARIO 12-3 The director of cooperative education at a state college wants to examine the effect of cooperative education job experience on marketability in the work place. She takes a random sample of 4 students. For these 4, she finds out how many times each had a cooperative education job and how many job offers they received upon graduation. These data are presented in the table below.

Student 1 2 3 4

Coop Jobs 1 2 1 0

Job Offer 4 6 3 1

22. Referring to Scenario 12-3, set up a scatter plot.

ANSWER: Scatter Diagram 6 5 4 3 2 1 0 0

1

2

Coop Jobs

TYPE: PR DIFFICULTY: Moderate KEYWORDS: scatter plot 23. Referring to Scenario 12-3, the least squares estimate of the slope is __________.

ANSWER: 2.50 TYPE: FI DIFFICULTY: 2 Moderate KEYWORDS: slope, estimation, least squares 24. Referring to Scenario 12-3, the least squares estimate of the Y-intercept is __________.

ANSWER: 1.00 TYPE: FI DIFFICULTY: Moderate KEYWORDS: intercept, estimation, least squares Copyright ©2020 Pearson Education, Inc.

12-8

Simple Linear Regression

25. Referring to Scenario 12-3, the prediction for the number of job offers for a person with 2 coop jobs is _________.

ANSWER: 6 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values 26. Referring to Scenario 12-3, the total sum of squares (SST) is __________.

ANSWER: 13.0 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sum of squares 27. Referring to Scenario 12-3, the regression sum of squares (SSR) is __________.

ANSWER: 12.5 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sum of squares 28. Referring to Scenario 12-3, the error or residual sum of squares (SSE) is __________.

ANSWER: 0.50 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sum of squares 29. Referring to Scenario 12-3, the coefficient of determination is __________.

ANSWER: 0.962 TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of determination 30. Referring to Scenario 12-3, the standard error of estimate is __________.

ANSWER: 0.50 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standard error of estimate 31. Referring to Scenario 12-3, the coefficient of correlation is __________.

ANSWER: 0.981 TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of correlation

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Simple Linear Regression

12-9

32. Referring to Scenario 12-3, suppose the director of cooperative education wants to construct a 95% confidence-interval estimate for the mean number of job offers received by students who have had exactly one cooperative education job. The t critical value she would use is ________.

ANSWER: 4.3027 TYPE: FI DIFFICULTY: Easy KEYWORDS: confidence interval, estimation of mean values, critical value 33. Referring to Scenario 12-3, suppose the director of cooperative education wants to construct a 95% confidence interval estimate for the mean number of job offers received by students who have had exactly one cooperative education job. The confidence interval is from ________ to ________.

ANSWER: 2.424 to 4.576 TYPE: FI DIFFICULTY: Moderate KEYWORDS: confidence interval, estimation of mean values, critical value 34. Referring to Scenario 12-3, suppose the director of cooperative education wants to construct a 95% prediction interval estimate for the number of job offers received by students who have had exactly one cooperative education job. The prediction interval is from ________ to ________.

ANSWER: 1.0947 to 5.9053 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction interval, prediction of individual values 35. True or False: Referring to Scenario 12-3, suppose the director of cooperative education wants to construct two 95% confidence interval estimates. One is for the mean number of job offers received by students who have had exactly one cooperative education job and one for students who have had two. The confidence interval for students who have had one cooperative education job would be the wider of the two intervals.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, estimation of mean values 36. Referring to Scenario 12-3, suppose the director of cooperative education wants to construct a 95% prediction interval for the number of job offers received by a student who has had exactly two cooperative education jobs. The t critical value she would use is ________.

ANSWER: 4.3027 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction interval, prediction of individual values, critical value

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12-10

Simple Linear Regression

37. Referring to Scenario 12-3, suppose the director of cooperative education wants to construct a 95% prediction interval for the number of job offers received by a student who has had exactly two cooperative education jobs. The prediction interval is from ________ to ________.

ANSWER: 3.154 to 8.846 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction interval, prediction of individual values 38. True or False: Referring to Scenario 12-3, suppose the director of cooperative education wants to construct both a 95% confidence interval estimate and a 95% prediction interval for X = 2. The confidence interval estimate would be the wider of the two intervals.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, prediction interval, estimation of mean values, prediction of individual values, properties 39. Referring to Scenario 12-3, the director of cooperative education wanted to test the hypothesis that the population slope was equal to 0. The denominator of the test statistic is s b1 . The value of s b1 in this sample is ________.

ANSWER: 0.3536 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, standard error, slope 40. Referring to Scenario 12-3, the director of cooperative education wanted to test the hypothesis that the population slope was equal to 0. The value of the test statistic is ________.

ANSWER: 7.07 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, test statistic, slope 41. Referring to Scenario 12-3, the director of cooperative education wanted to test the hypothesis that the population slope was equal to 3.0. The value of the test statistic is ________.

ANSWER: -1.4142 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, test statistic, slope

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Simple Linear Regression

12-11

42. Referring to Scenario 12-3, the director of cooperative education wanted to test the hypothesis that the population slope was equal to 0. For a test with a level of significance of 0.05, the null hypothesis should be rejected if the value of the test statistic is ________.

ANSWER: > 4.3027 or < -4.3027 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, critical value, slope, decision 43. Referring to Scenario 12-3, the director of cooperative education wanted to test the hypothesis that the population slope was equal to 3.0. For a test with a level of significance of 0.05, the null hypothesis should be rejected if the value of the test statistic is ________.

ANSWER: > 4.3027 or < -4.3027 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, critical value, slope, decision 44. Referring to Scenario 12-3, the director of cooperative education wanted to test the hypothesis that the population slope was equal to 0. The p-value of the test is between ________ and ________.

ANSWER: 0.01 and 0.02 using the Table, or 0.0194 using Excel or Minitab TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, p-value, slope 45. Referring to Scenario 12-3, the director of cooperative education wanted to test the hypothesis that the population slope was equal to 3.0. The p-value of the test is between ________ and ________.

ANSWER: 0.2 and 0.5 using the Table, or 0.2929 using Excel or Minitab TYPE: FI DIFFICULTY: Difficult EXPLANATION: The t-test statistic is t 

 b1  1    2.5  3  1.4142 Sb1

0.3536

KEYWORDS: t test on slope, p-value, slope

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12-12

Simple Linear Regression

SCENARIO 12-4 The managers of a brokerage firm are interested in finding out if the number of new clients a broker brings into the firm affects the sales generated by the broker. They sample 12 brokers and determine the number of new clients they have enrolled in the last year and their sales amounts in thousands of dollars. These data are presented in the table that follows.

Broker Clients Sales 1 27 52 2 11 37 3 42 64 4 33 55 5 15 29 6 15 34 7 25 58 8 36 59 9 28 44 10 30 48 11 17 31 12 22 38 46. Referring to Scenario 12-4, set up a scatter plot.

ANSWER:

Scatter Diagram 70 60 50 40 30 20 10 0 0

5

10

15

20

25

30

Clients TYPE: PR DIFFICULTY: Moderate KEYWORDS: scatter plot

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35

40

45

Simple Linear Regression

12-13

47. Referring to Scenario 12-4, the least squares estimate of the slope is __________.

ANSWER: 1.12 TYPE: FI DIFFICULTY: Moderate KEYWORDS: slope, estimation, least squares 48. Referring to Scenario 12-4, the least squares estimate of the Y-intercept is __________.

ANSWER: 17.7 TYPE: FI DIFFICULTY: Moderate KEYWORDS: intercept, estimation, least squares 49. Referring to Scenario 12-4, the prediction for the amount of sales (in $1,000s) for a person who brings 25 new clients into the firm is ________.

ANSWER: 45.66 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values 50. Referring to Scenario 12-4, the total sum of squares (SST) is __________.

ANSWER: 1,564.2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sum of squares 51. Referring to Scenario 12-4, the regression sum of squares (SSR) is __________.

ANSWER: 1,227.4 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sum of squares 52. Referring to Scenario 12-4, the error or residual sum of squares (SSE) is __________.

ANSWER: 336.9 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sum of squares 53. Referring to Scenario 12-4, the coefficient of determination is __________.

ANSWER: 0.785 TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of determination

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12-14

Simple Linear Regression

54. Referring to Scenario 12-4, ______% of the total variation in sales generated can be explained by the number of new clients brought in.

ANSWER: 78.5 TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of determination, interpretation 55. Referring to Scenario 12-4, the standard error of the estimated slope coefficient is __________.

ANSWER: 0.185 TYPE: FI DIFFICULTY: Moderate KEYWORDS: slope, standard error 56. Referring to Scenario 12-4, the standard error of estimate is __________.

ANSWER: 5.804 TYPE: FI DIFFICULTY: Moderate KEYWORDS: standard error of estimate 57. Referring to Scenario 12-4, the coefficient of correlation is __________.

ANSWER: 0.886 TYPE: FI DIFFICULTY: Moderate KEYWORDS: coefficient of correlation 58. Referring to Scenario 12-4, suppose the managers of the brokerage firm want to construct a 99% confidence interval estimate for the mean sales made by brokers who have brought into the firm 24 new clients. The t critical value they would use is ________.

ANSWER: 3.1693 TYPE: FI DIFFICULTY: Easy KEYWORDS: estimation of mean values, confidence interval, critical value 59. Referring to Scenario 12-4, suppose the managers of the brokerage firm want to construct a 99% confidence interval estimate for the mean sales made by brokers who have brought into the firm 24 new clients. The confidence interval is from ________ to ________.

ANSWER: 39.19 to 49.89 TYPE: FI DIFFICULTY: Moderate KEYWORDS: estimation of mean values, confidence interval

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Simple Linear Regression

12-15

60. Referring to Scenario 12-4, suppose the managers of the brokerage firm want to construct n a 99% prediction interval for the sales made by a broker who has brought into the firm 18 new clients. The t critical value they would use is ________.

ANSWER: 3.1693 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values, prediction interval, critical value 61. Referring to Scenario 12-4, suppose the managers of the brokerage firm want to construct a 99% prediction interval for the sales made by a broker who has brought into the firm 18 new clients.

The prediction interval is from ________ to ________.

ANSWER: 18.23 to 57.42 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values, prediction interval 62. Referring to Scenario 12-4, suppose the managers of the brokerage firm want to construct both a 99% confidence interval estimate and a 99% prediction interval for X = 24. The confidence interval estimate would be the __________ (wider or narrower) of the two intervals.

ANSWER: narrower TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values, prediction interval, estimation of mean values, confidence interval, properties 63. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. The denominator of the test statistic is s b1 . The value of s b1 in this sample is ________.

ANSWER: 0.1853 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, standard error 64. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. The value of the test statistic is _______.

ANSWER: 6.04 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, test statistic

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12-16

Simple Linear Regression

65. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in did not affect the amount of sales generated. The value of the test statistic is _______.

ANSWER: 6.04 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, test statistic 66. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. For a test with a level of significance of 0.01, the null hypothesis should be rejected if the value of the test statistic is ________.

ANSWER: > 3.1693 or < -3.1693 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, critical value, decision 67. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. The p-value of the test is ________.

ANSWER: < 0.01 using the Table, or 0.000126 using Excel or Minitab TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, p-value 68. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. At a level of significance of 0.01, the null hypothesis should be _______ (rejected or not rejected).

ANSWER: rejected TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, decision 69. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the population slope was equal to 0. At a level of significance of 0.01, the decision that should be made implies that _____ (there is a or there is no) linear dependent relationship between the independent and dependent variables.

ANSWER: there is a TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, conclusion

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Simple Linear Regression

12-17

70. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in had a positive impact on the amount of sales generated. The value of the test statistic is _______.

ANSWER: 6.04 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, test statistic 71. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in had a positive impact on the amount of sales generated. For a test with a level of significance of 0.01, the null hypothesis should be rejected if the value of the test statistic is ________.

ANSWER: > 2.7638 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, critical value, decision 72. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in had a positive impact on the amount of sales generated. The p-value of the test is ________.

ANSWER: < 0.005 using the Table, or 0.000126/2 using Excel or Minitab TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, p-value 73. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in had a positive impact on the amount of sales generated. At a level of significance of 0.01, the null hypothesis should be _______ (rejected or not rejected).

ANSWER: rejected TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, decision 74. Referring to Scenario 12-4, the managers of the brokerage firm wanted to test the hypothesis that the number of new clients brought in had a positive impact on the amount of sales generated. At a level of significance of 0.01, the decision that should be made implies that the number of new clients brought in _____ (had or did not have) a positive impact on the amount of sales generated.

ANSWER: had TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, conclusion

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12-18

Simple Linear Regression

SCENARIO 12-5 The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel to analyze the last 4 years of quarterly data (i.e., n = 16) with the following results: Regression Statistics Multiple R 0.802 R Square 0.643 Adjusted R Square 0.618 Standard Error SYX 0.9224 Observations 16 ANOVA df Regression 1 Error 14 Total 15 Predictor Coef Intercept 3.962 Industry 0.040451

SS 21.497 11.912 33.409

MS 21.497 0.851

StdError 1.440 0.008048

F 25.27

t Stat 2.75 5.03

Durbin-Watson Statistic

Sig.F 0.000

P-value 0.016 0.000 1.59

75. Referring to Scenario 12-5, the value of the quantity that the least squares regression line minimizes is ________.

ANSWER: 11.912 TYPE: FI DIFFICULTY: Moderate KEYWORDS: least squares, properties, sum of squares 76. Referring to Scenario 12-5, the estimates of the Y-intercept and slope are ________ and ________, respectively.

ANSWER: 3.962 and 0.040451na TYPE: FI DIFFICULTY: Easy KEYWORDS: intercept, slope, estimation 77. Referring to Scenario 12-5, the prediction for a quarter in which X = 120 is Y = ________.

ANSWER: 8.816 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values

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Simple Linear Regression

12-19

78. Referring to Scenario 12-5, the standard error of the estimate is ________.

ANSWER: 0.9224 TYPE: FI DIFFICULTY: Easy KEYWORDS: standard error of estimate 79. Referring to Scenario 12-5, the coefficient of determination is ________.

ANSWER: 0.643 TYPE: FI DIFFICULTY: Easy KEYWORDS: coefficient of determination 80. Referring to Scenario 12-5, the standard error of the estimated slope coefficient is ________.

ANSWER: 0.008 TYPE: FI DIFFICULTY: Easy KEYWORDS: slope, standard error 81. Referring to Scenario 12-5, the correlation coefficient is ________.

ANSWER: 0.802 TYPE: FI DIFFICULTY: Easy KEYWORDS: coefficient of correlation 82. Referring to Scenario 12-5, the partner wants to test for autocorrelation using the Durbin-Watson statistic. Using a level of significance of 0.05, the critical values of the test are dL = ________, and dU = ________.

ANSWER: 1.10; 1.37 TYPE: FI DIFFICULTY: Easy KEYWORDS: Durbin-Watson statistic, critical value, autocorrelation 83. Referring to Scenario 12-5, the partner wants to test for autocorrelation using the Durbin-Watson statistic. Using a level of significance of 0.05, the decision he should make is: a) there is evidence of autocorrelation. b) the test is unable to make a definite conclusion. c) there is no evidence of autocorrelation. d) there is not enough information to perform the test.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Durbin-Watson statistic, decision, autocorrelation

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12-20

Simple Linear Regression

84. If the Durbin-Watson statistic has a value close to 0, which assumption is violated? a) Normality of the errors. b) Independence of errors. c) Homoscedasticity. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Durbin-Watson statistic, autocorrelation, assumption 85. If the Durbin-Watson statistic has a value close to 4, which assumption is violated? a) Normality of the errors. b) Independence of errors. c) Homoscedasticity. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Durbin-Watson statistic, assumption, autocorrelation 86. The standard error of the estimate is a measure of a) total variation of the Y variable. b) the variation around the sample regression line. c) explained variation. d) the variation of the X variable.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: standard error of estimate, interpretation 87. The coefficient of determination (r2) tells you a) that the coefficient of correlation (r) is larger than 1. b) whether r has any significance. c) that you should not partition the total variation. d) the proportion of total variation that is explained.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of determination, interpretation

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Simple Linear Regression

12-21

SCENARIO 12-6 The following Excel tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course.

Regression Statistics Multiple R 0.142620229 R Square 0.02034053 Standard Error 20.25979924 Observations 22

Intercept Attendance

Coefficients Standard Error 39.39027309 37.24347659 0.340583573 0.52852452

T Stat 1.057642216 0.644404489

P-value 0.302826622 0.526635689

88. Referring to Scenario 12-6, which of the following statements is true? a) 14.26% of the total variability in score received can be explained by percentage attendance. b) 14.2% of the total variability in percentage attendance can be explained by score received. c) 2% of the total variability in score received can be explained by percentage attendance. d) 2% of the total variability in percentage attendance can be explained by score received.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of determination, interpretation 89. Referring to Scenario 12-6, which of the following statements is true? a) If attendance increases by 0.341%, the estimated mean score received will increase by 1 percentage point. b) If attendance increases by 1%, the estimated mean score received will increase by 39.39 percentage points. c) If attendance increases by 1%, the estimated mean score received will increase by 0.341 percentage points. d) If the score received increases by 39.39%, the estimated mean attendance will go up by 1%.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, interpretation

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12-22

Simple Linear Regression

90. True or False: The Regression Sum of Squares (SSR) can never be greater than the Total Sum of Squares (SST).

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: sum of squares, properties 91. True or False: The coefficient of determination represents the ratio of SSR to SST. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of determination, properties 92. True or False: Regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two numerical variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of correlation, slope, interpretation 93. True or False: The value of r is always positive.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of correlation, properties 94. In performing a regression analysis involving two numerical variables, you are assuming a) the variances of X and Y are equal. b) the variation around the line of regression is the same for each X value. c) that X and Y are independent. d) All of the above.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: assumption 95. Which of the following assumptions concerning the probability distribution of the random error term is stated incorrectly? a) The distribution is normal. b) The mean of the distribution is 0. c) The variance of the distribution increases as X increases. d) The errors are independent.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: assumption Copyright ©2020 Pearson Education, Inc.

Simple Linear Regression

12-23

96. Based on the residual plot below, you will conclude that there might be a violation of which of the following assumptions.

Footage Residual Plot 6000

Residuals

4000 2000 0 -2000

0

1,000 2,000 3,000 4,000 5,000 6,000

-4000 Footage

a) b) c) d)

Linearity of the relationship Normality of errors Homoscedasticity Independence of errors

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: assumption, homoscedasticity 97. True or False: Data that exhibit an autocorrelation effect violate the regression assumption of independence.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: assumption, autocorrelation 98. True or False: The Durbin-Watson D statistic is used to check the assumption of normality.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Durbin-Watson statistic, assumption, autocorrelation 99. If the residuals in a regression analysis of time-ordered data are not correlated, the value of the Durbin-Watson D statistic should be near __________.

ANSWER: 2 TYPE: FI DIFFICULTY: Moderate KEYWORDS: Durbin-Watson statistic, autocorrelation, properties Copyright ©2020 Pearson Education, Inc.

12-24

Simple Linear Regression

100. The residuals represent a) the difference between the actual Y values and the mean of Y. b) the difference between the actual Y values and the predicted Y values. c) the square root of the slope. d) the predicted value of Y for the average X value.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: residual, properties 101. If the plot of the residuals is fan shaped, which assumption is violated? a) Normality. b) Homoscedasticity. c) Independence of errors. d) No assumptions are violated, the graph should resemble a fan.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: residual plot, homoscedasticity 102. What do we mean when we say that a simple linear regression model is “statistically” useful? a) All the statistics computed from the sample make sense. b) The model is an excellent predictor of Y. c) The model is “practically” useful for predicting Y. d) The model is a better predictor of Y than the sample mean, Y .

ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: slope, interpretation 103. If the correlation coefficient (r) = 1.00, then a) the Y-intercept (b0) must equal 0. b) the explained variation equals the unexplained variation. c) there is no unexplained variation. d) there is no explained variation.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of correlation, properties, interpretation

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Simple Linear Regression

12-25

104. If the correlation coefficient (r) = 1.00, then a) all the data points must fall exactly on a straight line with a slope that equals 1.00. b) all the data points must fall exactly on a straight line with a negative slope. c) all the data points must fall exactly on a straight line with a positive slope. d) all the data points must fall exactly on a horizontal straight line with a zero slope.

ANSWER: c TYPE: MC DIFFICULTY: - Moderate KEYWORDS: coefficient of correlation, properties 105. Assuming a linear relationship between X and Y, if the coefficient of correlation (r) equals – 0.30, a) there is no correlation. b) the slope (b1) is negative. c) variable X is larger than variable Y. d) the variance of X is negative.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of correlation, properties, interpretation 106. Testing for the existence of correlation is equivalent to a) testing for the existence of the slope (   ).

b) testing for the existence of the Y-intercept (  ). c) the confidence interval estimate for predicting Y. d) None of the above.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of correlation, t test for correlation coefficient, t test on slope 107. The strength of the linear relationship between two numerical variables may be measured by the a) scatter plot. b) coefficient of correlation. c) slope. d) Y-intercept.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation

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12-26

Simple Linear Regression

108. In a simple linear regression problem, r and b1 a) may have opposite signs. b) must have the same sign. c) must have opposite signs. d) are equal.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, slope, properties 109. The sample correlation coefficient between X and Y is 0.375. It has been found out that the pvalue is 0.256 when testing H0 :   0 against the two-sided alternative H 1 :   0 . To test

H0 :   0 against the one-sided alternative H1 :   0 at a significance level of 0.1, the p-value is a) 0.256/2 b) (0.256)(2) c) 1-0.256 d) 1-0.256/2 ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: coefficient of correlation, t test for correlation coefficient, p-value 110. The sample correlation coefficient between X and Y is 0.375. It has been found out that the pvalue is 0.256 when testing H0 :   0 against the two-sided alternative H 1 :   0 . To test

H0 :   0 against the one-sided alternative H1 :   0 at a significance level of 0.1, the p-value is a) 0.256/ 2 b)  0.256  2 c) 1  0.256 d) 1  0.256/ 2 ANSWER: a TYPE: MC DIFFICULTY: Difficult KEYWORDS: coefficient of correlation, t test for correlation coefficient, p-value

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Simple Linear Regression

12-27

111. The sample correlation coefficient between X and Y is 0.375. It has been found out that the pvalue is 0.256 when testing H0 :   0 against the one-sided alternative H 1 :   0 . To test

H0 :   0 against the two-sided alternative H1 :   0 at a significance level of 0.1, the p-value is a) 0.256/ 2 b) 0.256 2 

c) 1  0.256 d) 1  0.256/ 2

ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: coefficient of correlation, t test for correlation coefficient, p-value 112. The sample correlation coefficient between X and Y is 0.375. It has been found out that the pvalue is 0.744 when testing H0 :   0 against the one-sided alternative H 1 :   0 . To test

H0 :   0 against the two-sided alternative H1 :   0 at a significance level of 0.1, the p-value is a) 0.744/ 2 b) 0.744 2 

c) 1  0.744 d) 1  0.744 2 

ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: coefficient of correlation, t test for correlation coefficient, p-value 113. If you wanted to find out if alcohol consumption (measured in fluid oz.) and grade point average on a 4-point scale are linearly related, you would perform a 2 a.  test for the difference in two proportions. b.  test for independence. c. a Z test for the difference in two proportions. d. a t test for a correlation coefficient.

2

ANSWER: d TYPE: MC DIFFICULTY: Difficult KEYWORDS: coefficient of correlation, t test for correlation coefficient 114. True or False: When r = – 1, it indicates a perfect relationship between X and Y. ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of correlation, properties

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12-28

Simple Linear Regression

SCENARIO 12-7 An investment specialist claims that if one holds a portfolio that moves in the opposite direction to the market index like the S&P 500, then it is possible to reduce the variability of the portfolio's return. In other words, one can create a portfolio with positive returns but less exposure to risk.

A sample of 26 years of S&P 500 index and a portfolio consisting of stocks of private prisons, which are believed to be negatively related to the S&P 500 index, is collected. A regression analysis was performed by regressing the returns of the prison stocks portfolio (Y) on the returns of S&P 500 index (X) to prove that the prison stocks portfolio is negatively related to the S&P 500 index at a 5% level of significance. The results are given in the following EXCEL output.

Intercept S&P

Coefficients Standard Error 4.8660 0.3574 -0.5025 0.0716

T Stat 13.6136 -7.0186

P-value 0.0000 0.0000

115. Referring to Scenario 12-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the appropriate null and alternative hypotheses are, respectively, a) H0 :   0 vs. H1 :   0 b)

H0 :   0 vs. H1 :   0

c)

H0 : r  0 vs. H1 : r  0

d)

H0 : r  0 vs. H1 : r  0

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, t test for correlation coefficient, form of hypothesis 116. Referring to Scenario 12-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the measured value of the test statistic is a) -7.019 b) -0.503 c) 0.072 d) 0.357 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, t test for correlation coefficient, test statistic 117. Referring to Scenario 12-7, to test whether the prison stocks portfolio is negatively related to the S&P 500 index, the p-value of the associated test statistic is ______ ANSWER: 0.0000 TYPE: FI DIFFICULTY: Easy KEYWORDS: coefficient of correlation, t test for correlation coefficient, p-value

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Simple Linear Regression

12-29

118. Referring to Scenario 12-7, which of the following will be a correct conclusion? a) You cannot reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prisons stock portfolio and S&P 500 index are negatively related. b) You can reject the null hypothesis and, therefore, conclude that there is sufficient evidence to show that the prisons stock portfolio and S&P 500 index are negatively related. c) You cannot reject the null hypothesis and, therefore, conclude that there is insufficient evidence to show that the prisons stock portfolio and S&P 500 index are negatively related. d) You can reject the null hypothesis and conclude that there is insufficient evidence to show that the prisons stock portfolio and S&P 500 index are negatively related.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, t test for correlation coefficient, decision, conclusion SCENARIO 12-8 It is believed that GPA (grade point average, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the Excel output for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a Big-Ten university.

Regressing GPA on ACT Regression Statistics Multiple R 0.7598 R Square 0.5774 Adjusted R Square 0.5069 Standard Error 0.2691 Observations 8 ANOVA df Regression Residual Total

Intercept ACT

SS 1 6 7

0.5940 0.4347 1.0287

Coefficients Standard Error 0.5681 0.9284 0.1021 0.0356

MS 0.5940 0.0724

F Significance F 8.1986 0.0286

t Stat P-value 0.6119 0.5630 2.8633 0.0286

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Lower 95% Upper 95% -1.7036 2.8398 0.0148 0.1895

12-30

Simple Linear Regression

119. Referring to Scenario 12-8, the interpretation of the coefficient of determination in this regression is a) 57.74% of the total variation of ACT scores can be explained by GPA. b) ACT scores account for 57.74% of the total fluctuation in GPA. c) GPA accounts for 57.74% of the variability of ACT scores. d) None of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of determination, interpretation 120. Referring to Scenario 12-8, the value of the measured test statistic to test whether there is any linear relationship between GPA and ACT is a) 0.0356 b) 0.1021 c) 0.7598 d) 2.8633 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, t test for correlation coefficient, test statistic 121. Referring to Scenario 12-8, what is the predicted value of GPA when ACT = 20? a. 2.61 b. 2.66 c. 2.80 d. 3.12 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: prediction of individual values 122. Referring to Scenario 12-8, what are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores? a) Do not reject the null hypothesis; hence there is insufficient evidence to show that ACT scores and GPA are linearly related. b) Reject the null hypothesis; hence there is insufficient evidence to show that ACT scores and GPA are linearly related. c) Do not reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related. d) Reject the null hypothesis; hence there is sufficient evidence to show that ACT scores and GPA are linearly related.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of correlation, t test for correlation coefficient, decision, conclusion

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Simple Linear Regression

12-31

123. Referring to Scenario 12-8, the value of the measured (observed) test statistic of the F-test for

H0 :   0 vs. H1 :   0 a) b) c) d)

may be negative. is always positive. is always negative. has the same sign as the corresponding t test statistic.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on slope, test statistic SCENARIO 12-9 It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown.

Regression Statistics Multiple R 0.8857 R Square 0.7845 Adjusted R Square 0.7801 Standard Error 1.3704 Observations 51 ANOVA df Regression Residual Total

Intercept Hours

1

SS 335.0472

50

427.0798

Coefficients -1.8940 0.9795

Standard Error 0.4018 0.0733

MS 335.0473 1.8782

F Significance F 178.3859

t Stat -4.7134 13.3561

P-value 0.0000 0.0000

Note: 2.051E  05  2.051*10 05 and 5.944 E  18  5.944 *10 18 .

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Lower 95% Upper 95% -2.7015 -1.0865 0.8321 1.1269

12-32

Simple Linear Regression

124.

Referring to Scenario 12-9, the estimated change in mean salary (in thousands of dollars) as a result of spending an extra hour per day studying is a. -1.8940 b. 0.7845 c. 0.9795 d. 335.0473 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, interpretation 125. Referring to Scenario 12-9, the value of the measured t-test statistic to test whether mean SALARY depends linearly on HOURS is a) -4.7134 b) -1.8940 c) 0.9795 d) 13.3561 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, test statistic 126. Referring to Scenario 12-9, the p-value of the measured F-test statistic to test whether HOURS affects SALARY is _____.

ANSWER: 0.0000 TYPE: FI DIFFICULTY: Difficult KEYWORDS: F test on slope, slope, test statistic EXPLANATION: The p-value of the measured F-test statistic is the same as the p-value of the individual t-test statistic on the slope coefficient.

127. Referring to Scenario 12-9, the degrees of freedom for the F test on whether HOURS affects SALARY are a) 1, 49 b) 1, 50 c) 49, 1 d) 50, 1 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: F test on slope, slope, degrees of freedom

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Simple Linear Regression

12-33

128. Referring to Scenario 12-9, the error sum of squares (SSE) of the above regression is a) 1.878215 b) 92.0325465 c) 335.047257 d) 427.079804 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sum of squares 129. Referring to Scenario 12-9, the 90% confidence interval for the average change in SALARY (in thousands of dollars) as a result of spending an extra hour per day studying is a) wider than [-2.70159, -1.08654]. b) narrower than [-2.70159, -1.08654]. c) wider than [0.8321927, 1.12697]. d) narrower than [0.8321927, 1.12697].

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, interpretation, confidence interval 130. Referring to Scenario 12-9, to test the claim that SALARY depends positively on HOURS against the null hypothesis that SALARY does not depend linearly on HOURS, the p-value of the test statistic is _____.

ANSWER: 0.0000 TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, slope, p-value 131. True or False: A zero population correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of correlation, interpretation 132. True or False: You give a pre-employment examination to your applicants. The test is scored from 1 to 100. You have data on their sales at the end of one year measured in dollars. You want to know if there is any linear relationship between pre-employment examination score and sales.

An appropriate test to use is the t test of the population correlation coefficient.

ANSWER: True TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of correlation, t test for correlation coefficient

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12-34

Simple Linear Regression

133. The width of the prediction interval for the predicted value of Y is dependent on a) the standard error of the estimate. b) the value of X for which the prediction is being made. c) the sample size. d) All of the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values, prediction interval, properties 134. True or False: The confidence interval for the mean of Y is always narrower than the prediction interval for an individual response Y given the same data set, X value, and confidence level.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: estimation of mean values, confidence interval, prediction of individual values, prediction interval, properties SCENARIO 12-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousands of dollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the following results:

Customers Sales (Thousands of Dollars) 907 11.20 926 11.05 713 8.21 741 9.21 780 9.42 898 10.08 510 6.73 529 7.02 460 6.12 872 9.52 650 7.53 603 7.25

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Simple Linear Regression 135. Referring to Scenario 12-10, generate the scatter plot.

ANSWER: Scatter Diagram

Salses (Thousands of Dollars)

12 10 8 6 4 2 0 0

200

400

600

800

1000

Customers

TYPE: PR DIFFICULTY: Moderate KEYWORDS: scatter plot 136. Referring to Scenario 12-10, what are the values of the estimated intercept and slope?

ANSWER: 1.4464, 0.0100 TYPE: PR DIFFICULTY: Moderate KEYWORDS: intercept, slope, estimation 137. Referring to Scenario 12-10, what is the value of the coefficient of determination?

ANSWER: 0.9453 TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of determination 138. Referring to Scenario 12-10, what is the value of the coefficient of correlation?

ANSWER: 0.9723 TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of correlation 139. Referring to Scenario 12-10, what is the value of the standard error of the estimate?

ANSWER: 0.4191 TYPE: PR DIFFICULTY: Moderate KEYWORDS: standard error of estimate

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12-35

12-36

Simple Linear Regression

140. Referring to Scenario 12-10, which is the correct null hypothesis for testing whether the number of customers who make a purchase affects weekly sales? a)

H0 : 0  0

b)

H0 : 1  0

c)

H0 :   0

d)

H0 :   0

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, slope, form of hypothesis 141. Referring to Scenario 12-10, what is the value of the t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

ANSWER: 13.1464 TYPE: PR DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, test statistic 142. Referring to Scenario 12-10, what are the degrees of freedom of the t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

ANSWER: 10 TYPE: PR DIFFICULTY: Easy KEYWORDS: t test on slope, slope, degrees of freedom 143. Referring to Scenario 12-10, what is the p-value of the t test statistic when testing whether the number of customers who make a purchase affects weekly sales?

ANSWER: 1.23323E-07 or smaller than 0.01 TYPE: PR DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, p-value 144. True or False: Referring to Scenario 12-10, the null hypothesis for testing whether the number of customers who make a purchase affects weekly sales cannot be rejected if a 1% probability of committing a type I error is desired.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, decision

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Simple Linear Regression

12-37

145. True or False: Referring to Scenario 12-10, the mean weekly sales will increase by an estimated $0.01 for each additional purchasing customer.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, interpretation 146. True or False: Referring to Scenario 12-10, the mean weekly sales will increase by an estimated $10 for each additional purchasing customer.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, interpretation 147. True or False: Referring to Scenario 12-10, 93.98% of the total variation in weekly sales can be explained by the variation in the number of customers who make purchases.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: coefficient of determination, interpretation 148. Referring to Scenario 12-10, what are the degrees of freedom of the F test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales?

ANSWER: 1 in the numerator and 10 in the denominator TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on slope, slope, test statistic 149. Referring to Scenario 12-10, what is the value of the F test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales?

ANSWER: 172.8265 TYPE: PR DIFFICULTY: Moderate KEYWORDS: F test on slope, slope, test statistic 150. Referring to Scenario 12-10, what is the p-value of the F test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales?

ANSWER: 1.23323E-07 or smaller than 0.005 TYPE: PR DIFFICULTY: Moderate KEYWORDS: F test on slope, slope, p-value

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12-38

Simple Linear Regression

151. True or False: Referring to Scenario 12-10, the p-value of the t test and F test should be the same when testing whether the number of customers who make purchases is a good predictor for weekly sales.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: t test on slope, F test on slope, p-value 152. True or False: Referring to Scenario 12-10, the value of the t test statistic and F test statistic should be the same when testing whether the number of customers who make purchases is a good predictor for weekly sales.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: t test on slope, F test on slope, test statistic 153. True or False: Referring to Scenario 12-10, the value of the F test statistic equals the square of the t test statistic when testing whether the number of customers who make purchases is a good predictor for weekly sales.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: t test on slope, F test on slope, test statistic 154. Referring to Scenario 12-10, generate the residual plot.

ANSWER: Customers Residual Plot 0.8 0.6

Residuals

0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 0

200

400

600

800

1000

Customers

TYPE: PR DIFFICULTY: Moderate KEYWORDS: residual plot

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Simple Linear Regression

12-39

155. Referring to Scenario 12-10, the residual plot indicates possible violation of which assumptions? a) Linearity of the relationship b) Homoscedasticity c) Autocorrelation d) Normality ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: homoscedasticity, residual plot, assumption 156. True or False: Referring to Scenario 12-10, it is inappropriate to compute the Durbin-Watson statistic and test for autocorrelation in this case.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Durbin-Watson statistic, autocorrelation 157. Referring to Scenario 12-10, construct a 95% confidence interval for the change in mean weekly sales when the number of customers who make purchases increases by one.

ANSWER: 0.0083 thousands of dollars to 0.0117 thousands of dollars TYPE: PR DIFFICULTY: Difficult KEYWORDS: slope, confidence interval, interpretation 158. Referring to Scenario 12-10, construct a 95% confidence interval for the mean weekly sales when the number of customers who make purchases is 600.

ANSWER: 7.1194 to 7.7864 thousands of dollars TYPE: PR DIFFICULTY: Difficult KEYWORDS: estimate of mean values, confidence interval 159. Referring to Scenario 12-10, construct a 95% prediction interval for the weekly sales of a store that has 600 purchasing customers.

ANSWER: 6.4614 to 8.4444 thousands of dollars TYPE: PR DIFFICULTY: Difficult KEYWORDS: prediction of individual values, prediction interval

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12-40

Simple Linear Regression

SCENARIO 12-11 A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed: Regression Statistics Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 Standard Error 44.4765 Observations 30.0000 ANOVA Regression Residual Total

df 1 28 29

SS 171062.9193 55388.4309 226451.3503

MS 171062.9193 1978.1582

Intercept Download

Coefficients Standard Error -95.0614 26.9183 3.7297 0.4011

t Stat -3.5315 9.2992

F Significance F 86.4759 0.0000

P-value 0.0015 0.0000

Copyright ©2020 Pearson Education, Inc.

Lower 95% -150.2009 2.9082

Upper 95% -39.9218 4.5513

Simple Linear Regression

12-41

160. Referring to Scenario 12-11, which of the following is the correct interpretation for the slope coefficient? a) For each decrease of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands. b) For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $ 3.7297 thousands. c) For each decrease of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands. d) For each increase of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, interpretation 161. Referring to Scenario 12-11, predict the revenue when the number of downloads is 30 thousand.

ANSWER: $ 16.8296 thousands TYPE: PR DIFFICULTY: Easy KEYWORDS: prediction of individual values

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12-42

Simple Linear Regression

162. Referring to Scenario 12-11, which of the following is the correct interpretation for the coefficient of determination? a) 74.67% of the variation in revenue can be explained by the variation in the number of downloads. b) 75.54% of the variation in revenue can be explained by the variation in the number of downloads. c) 74.67% of the variation in the number of downloads can be explained by the variation in revenue. d) 75.54% of the variation in the number of downloads can be explained by the variation in revenue.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, coefficient of determination EXPLANATION: Even though (a) is the correct interpretation for the adjusted r-square but only (b) is the correct interpretation of r-square.

163. Referring to Scenario 12-11, what is the standard error of estimate?

ANSWER: $44.4765 thousands TYPE: PR DIFFICULTY: Moderate KEYWORDS: standard error of estimate 164. Referring to Scenario 12-11, what is the standard deviation around the regression line?

ANSWER: $44.4765 thousands TYPE: PR DIFFICULTY: Difficult KEYWORDS: interpretation, standard error of estimate 165. Referring to Scenario 12-11, which of the following assumptions appears to have been violated? a) Normality of error b) Homoscedasticity c) Independence of errors d) None of the above ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, assumption, residual plot, homoscedasticity 166. True or False: Referring to Scenario 12-11, the normality of error assumption appears to have been violated.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interpretation, assumption

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Simple Linear Regression

12-43

167. True or False: Referring to Scenario 12-11, the homoscedasticity of error assumption appears to have been violated.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: interpretation, assumption, homoscedasticity 168. True or False: Referring to Scenario 12-11, there appears to be autocorrelation in the residuals.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: interpretation, autocorrelation 169. True or False: Referring to Scenario 12-11, the Durbin-Watson statistic is inappropriate for this data set.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Durbin-Watson statistic, assumption 170. True or False: Referring to Scenario 12-11, the null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads is “There is no linear relationship between revenue and the number of downloads”.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: slope, t test for slope, form of hypothesis 171. Referring to Scenario 12-11, which of the following is the correct null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads? a)

H0 : b1  0

b)

H0 : b1  0

c)

H0 : 1  0

d)

H0 : 1  0

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, t test for slope, form of hypothesis

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12-44

Simple Linear Regression

172. Referring to Scenario 12-11, which of the following is the correct alternative hypothesis for testing whether there is a linear relationship between revenue and the number of downloads? a) b) c) d)

H1 : b1  0 H1 : b1  0 H1 : 1  0 H1 : 1  0

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, t test for slope, form of hypothesis 173. Referring to Scenario 12-11, what is the value of the test statistic for testing whether there is a linear relationship between revenue and the number of downloads?

ANSWER: 9.2992 TYPE: PR DIFFICULTY: Easy KEYWORDS: test statistic, slope, t test for slope 174. Referring to Scenario 12-11, what is the critical value for testing whether there is a linear relationship between revenue and the number of downloads at a 5% level of significance?

ANSWER: 2.0484 TYPE: PR DIFFICULTY: Easy KEYWORDS: critical value, slope, t test for slope 175. Referring to Scenario 12-11, what is the p-value for testing whether there is a linear relationship between revenue and the number of downloads at a 5% level of significance?

ANSWER: virtually zero or 0.0000 TYPE: PR DIFFICULTY: Easy KEYWORDS: p-value , slope, t test for slope 176. True or False: Referring to Scenario 12-11, the null hypothesis that there is no linear relationship between revenue and the number of downloads should be rejected at a 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: decision, slope, t test for slope

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Simple Linear Regression

12-45

177. True or False: Referring to Scenario 12-11, there is sufficient evidence that revenue and the number of downloads are linearly related at a 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: conclusion, slope, t test for slope 178. Referring to Scenario 12-11, what do the lower and upper limits of the 95% confidence interval estimate for population slope?

ANSWER: 2.9082 and 4.5513 thousand dollars TYPE: PR DIFFICULTY: Easy KEYWORDS: slope, confidence interval 179. Referring to Scenario 12-11, what do the lower and upper limits of the 95% confidence interval estimate for the mean change in revenue as a result of a one thousand increase in the number of downloads?

ANSWER: 2.9082 and 4.5513 thousand dollars TYPE: PR DIFFICULTY: Difficult KEYWORDS: slope, confidence interval SCENARIO 12-12 The manager of the purchasing department of a large saving and loan organization would like to develop a model to predict the amount of time (measured in hours) it takes to record a loan application. Data are collected from a sample of 30 days, and the number of applications recorded and completion time in hours is recorded. Below is the regression output: Regression Statistics Multiple R 0.9447 R Square 0.8924 Adjusted R 0.8886 Square Standard 0.3342 Error Observations 30 ANOVA df Regression Residual Total

Intercept Applications Recorded

1 28 29

SS 25.9438 3.1282 29.072

MS 25.9438 0.1117

F 232.2200

Significance F 4.3946E-15

Coefficients 0.4024 0.0126

Standard Error 0.1236 0.0008

t Stat 3.2559 15.2388

P-value 0.0030 0.0000

Lower 95% 0.1492 0.0109

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Upper 95% 0.6555 0.0143

12-46

Simple Linear Regression

Applications Recorded Residual Plot 0.8 0.6 0.4

Residuals

0.2 0 -0.2 -0.4 -0.6 -0.8 0

50

100

150

200

250

Loan Applications Recorded

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300

350

Simple Linear Regression

12-47

180. Referring to Scenario 12-12, the estimated mean amount of time it takes to record one additional loan application is a) 0.4024 fewer hours b) 0.4024 more hours c) 0.0126 fewer hours d) 0.0126 more hours ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, interpretation 181. Referring to Scenario 12-12, the value of the measured t-test statistic to test whether the amount of time depends linearly on the number of loan applications recorded is a) 0.8924 b) 3.2559 c) 15.2388 d) 232.2200 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, slope, test statistic 182. Referring to Scenario 12-12, the p-value of the measured F-test statistic to test whether the number of loan applications recorded affects the amount of time is _____.

ANSWER: 0.0000 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on slope, slope, test statistic 183. Referring to Scenario 12-12, the p-value of the measured t-test statistic to test whether the number of loan applications recorded affects the amount of time is _____.

ANSWER: 0.0000 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, slope, test statistic 184. Referring to Scenario 12-12, the degrees of freedom for the F test on whether the number of load applications recorded affects the amount of time are a) 1, 28 b) 1, 29 c) 28, 1 d) 29, 1 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: F test on slope, slope, degrees of freedom

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12-48

Simple Linear Regression

185. Referring to Scenario 12-12, the degrees of freedom for the t test on whether the number of loan applications recorded affects the amount of time are a) 1 b) 28 c) 29 d) 30 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, degrees of freedom 186. Referring to Scenario 12-12, the error sum of squares (SSE) of the above regression is a) 0.1117 b) 3.1282 c) 25.9438 d) 29.0720 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sum of squares 187. Referring to Scenario 12-12, the 90% confidence interval for the mean change in the amount of time needed as a result of recording one additional loan application is a) wider than [0.1492, 0.6555]. b) narrower than [0.1492, 0.6555]. c) wider than [0.0109, 0.0143]. d) narrower than [0.0109, 0.0143].

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, interpretation, confidence interval 188. True or False: Referring to Scenario 12-12, you can be 95% confident that the mean amount of time needed to record one additional loan application is somewhere between 0.0109 and 0.0143 hours.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, slope, interpretation 189. True or False: Referring to Scenario 12-12, there is a 95% probability that the mean amount of time needed to record one additional loan application is somewhere between 0.0109 and 0.0143 hours.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, slope, interpretation Copyright ©2020 Pearson Education, Inc.

Simple Linear Regression

12-49

190. True or False: Referring to Scenario 12-12, there is sufficient evidence that the amount of time needed linearly depends on the number of loan applications at a 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: conclusion, slope, t test for slope 191. True or False: Referring to Scenario 12-12, there is sufficient evidence that the amount of time needed linearly depends on the number of loan applications at a 1% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: conclusion, slope, t test for slope 192. Referring to Scenario 12-12, to test the claim that the mean amount of time depends positively on the number of loan applications recorded against the null hypothesis that the mean amount of time does not depend linearly on the number of invoices processed, the p-value of the test statistic is ____.

ANSWER: 0.0000 TYPE: FI DIFFICULTY: Moderate KEYWORDS: t test on slope, slope, p-value 193. Referring to Scenario 12-12, predict the amount of time it would take to process 150 invoices.

ANSWER: 2.2924 hours TYPE: PR DIFFICULTY: Easy KEYWORDS: prediction of individual values 194. Referring to Scenario 12-12, what percentage of the variation in the amount of time needed can be explained by the variation in the number of invoices processed?

ANSWER: 89.24% TYPE: PR DIFFICULTY: Moderate KEYWORDS: coefficient of determination, interpretation 195. True or False: Referring to Scenario 12-12, the model appears to be adequate based on the residual analyses.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: residual plot, homoscedasticity, autocorrelation

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12-50

Simple Linear Regression

196. Referring to Scenario 12-12, what are the critical values of the Durbin-Watson test statistic using the 5% level of significance to test for evidence of positive autocorrelation?

ANSWER: 1.35 and 1.49 TYPE: PR DIFFICULTY: Easy KEYWORDS: autocorrelation, Durbin-Watson statistic, critical value 197. True or False: Referring to Scenario 12-12, there is no evidence of positive autocorrelation if the Durbin-Watson test statistic is found to be 1.78.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: autocorrelation, Durbin-Watson statistic, decision SCENARIO 12-13 In this era of tough economic conditions, voters increasingly ask the question: “Is the educational achievement level of students dependent on the amount of money the state in which they reside spends on education?” The partial computer output below is the result of using spending per student ($) as the independent variable and composite score which is the sum of the math, science and reading scores as the dependent variable on 35 states that participated in a study. The table includes only partial results.

Regression Statistics Multiple R 0.3122 R Square 0.0975 Adjusted R 0.0701 Square Standard 26.9122 Error Observations 35 ANOVA df Regression Residual Total

1

MS

F

724.2674 34 Coefficients

Intercept Spending per Student ($)

SS 2581.5759 26482.4000 Standard Error

595.540251

22.115176

0.007996

0.004235

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t Stat

P-value

Simple Linear Regression

12-51

198. Referring to Scenario 12-13, if the state decides to spend 1,000 dollar more per student, the estimated change in mean composite score is _________.

ANSWER: 8.0 TYPE: FI DIFFICULTY: Moderate KEYWORDS: slope, interpretation 199. Referring to Scenario 12-13, the value of the measured t-test statistic to test whether composite score depends linearly on spending per student is ________.

ANSWER: 1.888 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, slope, test statistic 200. Referring to Scenario 12-13, the p-value of the measured t-test statistic to test whether composite score depends linearly on spending per student is ________.

ANSWER: 0.0679 using Excel or “between 0.05 and 0.10” using Table E.3.

TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, slope, p-value 201. Referring to Scenario 12-13, the decision on the test of whether composite score depends linearly on spending per student using a 10% level of significance is to ________ (reject or not reject) H0 .

ANSWER: reject TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, slope, decision 202. Referring to Scenario 12-13, the conclusion on the test of whether composite score depends linearly on spending per student using a 10% level of significance is _________ a) There is not enough evidence that composite score does not depend linearly on spending per student. b) There is enough evidence that composite score does not depend linearly on spending per student. c) There is not enough evidence that composite score depends linearly on spending per student. d) There is enough evidence that composite score depends linearly on spending per student.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, slope, conclusion

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12-52

Simple Linear Regression

203. Referring to Scenario 12-13, the p-value of the measured F-test statistic to test whether spending per student affects composite score is ________.

ANSWER: 0.0679 using Excel TYPE: FI DIFFICULTY: Moderate KEYWORDS: F test on slope, slope, p-value 204. Referring to Scenario 12-13, the degrees of freedom for the F test on whether spending per student affects composite score are _________.

ANSWER: 1 numerator and 33 denominator degrees of freedom TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on slope, slope, degrees of freedom 205. Referring to Scenario 12-13, the value of the F test on whether spending per student affects composite score is _________.

ANSWER: 3.5644 TYPE: FI DIFFICULTY: Moderate KEYWORDS: F test on slope, slope, test statistic 206. Referring to Scenario 12-13, the critical value at 5% level of significance of the F test on whether spending per student affects composite score is _________.

ANSWER: 4.1393 using Excel or 4.17 using Table E.5 with df = 1, 33 TYPE: FI DIFFICULTY: Moderate KEYWORDS: F test on slope, slope, critical value 207. Referring to Scenario 12-13, the decision on the test of whether spending per student affects composite score using a 5% level of significance is to ________ (reject or not reject) H0 .

ANSWER: not reject TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on slope, slope, decision 208. Referring to Scenario 12-13, the conclusion on the test of whether spending per student affects composite score using a 5% level of significance is a) There is not enough evidence that spending per student affects composite score. b) There is enough evidence that spending per student affects composite score. c) There is not enough evidence that spending per student does not affect composite score. d) There is enough evidence that spending per student does not affect composite score.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on slope, slope, conclusion Copyright ©2020 Pearson Education, Inc.

Simple Linear Regression

12-53

209. Referring to Scenario 12-13, the error sum of squares (SSE) of the above regression is _____.

ANSWER: 23,900.8241 TYPE: FI DIFFICULTY: Moderate KEYWORDS: sum of squares 210. Referring to Scenario 12-13, the regression mean square (MSR) of the above regression is _____.

ANSWER: 2,581.5759 TYPE: FI DIFFICULTY: Easy KEYWORDS: mean square 211. Referring to Scenario 12-13, what percentage of the variation in composite score can be explained by the variation in spending per student?

ANSWER: 9.75% TYPE: PR DIFFICULTY: Easy KEYWORDS: coefficient of determination, interpretation 212. Referring to Scenario 12-13, what is the standard deviation of the composite score around the regression line?

ANSWER: 26.9122 TYPE: PR DIFFICULTY: Easy KEYWORDS: standard error of estimate, interpretation 214. True or False: Rejection of the null hypothesis in a simple linear regression analysis can be interpreted as stating a cause and effect relationship between x and y.

ANSWER False TF DIFFICULTY: Moderate KEYWORDS: simple linear regression, correlation EXPLANATION Linear regression can be used to find the best fitting linear model via least squares implying a relation or correlation between x and y, but not necessarily causality.

215. Which of the following statements is not true regarding the standard error of the estimate? a. b. c. d.

It measures the variability of the observed y values from the predicted ones.

It uses the same units as the dependent y values.

It is not analogous to the standard deviation of the sample mean.

It measures variability around the predicted line.

ANSWER c.

MC DIFFICULTY: Moderate KEYWORDS: standard error of the estimate, standard deviation of the sample mean Copyright ©2020 Pearson Education, Inc.

12-54

Simple Linear Regression

216. True or False: In a simple linear regression the best fitting linear model always passes through point (x̅, y̅).

ANSWER True TF DIFFICULTY: Moderate KEYWORDS: scatter diagram, best fit linear model

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Multiple Regression 13-1

CHAPTER 13: MULTIPLE REGRESSION 1. In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means that a) the relationship between X1 and Y is significant. b) the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant. c) the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2. d) the estimated mean of Y is 2 when X1 equals zero.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, interpretation 2. The coefficient of multiple determination r2Y1.2 a) measures the variation around the predicted regression equation. b) measures the proportion of variation in Y that is explained by X1 and X2. c) measures the proportion of variation in Y that is explained by X1 holding X2 constant. d) will have the same sign as b1.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, interpretation 3. In a multiple regression model, the value of the coefficient of multiple determination a) has to fall between -1 and +1. b) has to fall between 0 and +1. c) has to fall between -1 and 0. d) can fall between any pair of real numbers.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, properties 4. In a multiple regression model, which of the following is correct regarding the value of the adjusted r 2 ? a) It can be negative. b) It has to be positive. c) It has to be larger than the coefficient of multiple determination. d) It can be larger than 1.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: adjusted r-square, properties

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13-2

Multiple Regression

SCENARIO 13-1 A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following: Employee Y X1 X2 1 100 10 7 2 90 3 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 1 4 8 30 1 1 5. Referring to SCENARIO 13-1, for these data, what is the value for the regression constant, b0? a) 0.998 b) 3.103 c) 4.698 d) 21.293 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: intercept, estimation 6. Referring to SCENARIO 13-1, for these data, what is the estimated coefficient for the variable representing years an employee has been with the company, b1? a) 0.998 b) 3.103 c) 4.698 d) 21.293 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, estimation 7. Referring to SCENARIO 13-1, for these data, what is the estimated coefficient for the variable representing scores on the aptitude test, b2? a) 0.998 b) 3.103 c) 4.698 d) 21.293 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, estimation

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Multiple Regression 13-3 8. Referring to SCENARIO 13-1, if an employee who had been with the company 5 years scored a 9 on the aptitude test, what would his estimated expected sales be? a) 79.09 b) 60.88 c) 55.62 d) 17.98 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values SCENARIO 13-2 A professor of industrial relations believes that an individual’s wage rate at a factory (Y) depends on his performance rating (X1) and the number of economics courses the employee successfully completed in college (X2). The professor randomly selects 6 workers and collects the following information: Employee Y ($) X1 X2 1 10 3 0 2 12 1 5 3 15 8 1 4 17 5 8 5 20 7 12 6 25 10 9 9. Referring to SCENARIO 13-2, for these data, what is the value for the regression constant, b0? a) 0.616 b) 1.054 c) 6.932 d) 9.103 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: intercept, estimation 10. Referring to SCENARIO 13-2, for these data, what is the estimated coefficient for performance rating, b1? a) 0.616 b) 1.054 c) 6.932 d) 9.103 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, estimation

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13-4

Multiple Regression

11. Referring to SCENARIO 13-2, for these data, what is the estimated coefficient for the number of economics courses taken, b2? a) 0.616 b) 1.054 c) 6.932 d) 9.103 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, estimation 12. Referring to SCENARIO 13-2, suppose an employee had never taken an economics course and managed to score a 5 on his performance rating. What is his estimated expected wage rate? a) 10.90 b) 12.20 c) 17.23 d) 25.11 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values 13. Referring to SCENARIO 13-2, an employee who took 12 economics courses scores 10 on the performance rating. What is her estimated expected wage rate? a) 10.90 b) 12.20 c) 24.87 d) 25.70 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values 14. The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by a) regression sum of squares. b) error sum of squares. c) total sum of squares. d) regression mean squares.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: sum of squares

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Multiple Regression 13-5 SCENARIO 13-3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.

SUMMARY OUTPUT Regression Statistics Multiple R 0.991 R Square 0.982 Adjusted R Square 0.976 Standard Error 0.299 Observations 10 ANOVA Regression Residual Total Intercept GDP Price

df 2 7 9 Coeff – 0.0861 0.7654 – 0.0006

SS 33.4163 0.6277 34.0440

MS 16.7082 0.0897

StdError 0.5674 0.0574 0.0028

t Stat – 0.152 13.340 – 0.219

F 186.325

Signif F 0.0001

P-value 0.8837 0.0001 0.8330

15. Referring to SCENARIO 13-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an r2 value of 0.971. What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression? a) 98.2 b) 11.1 c) 2.8 d) 1.1 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of multiple determination 16. Referring to SCENARIO 13-3, the p-value for GDP is a) 0.05 b) 0.01 c) 0.001 d) None of the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value

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13-6

Multiple Regression

17. Referring to SCENARIO 13-3, the p-value for the aggregated price index is a) 0.05 b) 0.01 c) 0.001 d) None of the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 18. Referring to SCENARIO 13-3, the p-value for the regression model as a whole is a) 0.05 b) 0.01 c) 0.001 d) None of the above.

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: F test for the entire regression, p-value 19. Referring to SCENARIO 13-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150? a) $1.39 billion b) $2.89 billion c) $4.75 billion d) $9.45 billion ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values 20. Referring to SCENARIO 13-3, what is the estimated mean consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150? a) $1.39 billion b) $2.89 billion c) $4.75 billion d) $9.45 billion ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values

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Multiple Regression 13-7 21. Referring to SCENARIO 13-3, what is the estimated mean consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90? a) $1.39 billion b) $2.89 billion c) $4.75 billion d) $9.45 billion ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: estimation of mean values 22. Referring to SCENARIO 13-3, one economy in the sample had an aggregate consumption level of $3 billion, a GDP of $3.5 billion, and an aggregate price level of 125. What is the residual for this data point? a) $2.52 billion b) $0.48 billion c) – $1.33 billion d) – $2.52 billion ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: residual 23. Referring to SCENARIO 13-3, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point? a) $4.39 billion b) $0.39 billion c) – $0.39 billion d) – $1.33 billion ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: residual 24. Referring to SCENARIO 13-3, to test for the significance of the coefficient on aggregate price, the value of the relevant t-statistic is a) 2.365 b) 0.143 c) – 0.219 d) – 1.960 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic

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13-8

Multiple Regression

25. Referring to SCENARIO 13-3, to test for the significance of the coefficient on aggregate price index, the p-value is a) 0.0001 b) 0.8330 c) 0.8837 d) 0.9999 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 26. Referring to SCENARIO 13-3, to test for the significance of the coefficient on gross domestic product, the p-value is a) 0.0001 b) 0.8330 c) 0.8837 d) 0.9999 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 27. Referring to SCENARIO 13-3, to test whether aggregate price index has a negative impact on consumption, the p-value is _______? a) 0.0001 b) 0.4165 c) 0.8330 d) 0.8837 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on slope, p-value 28. Referring to SCENARIO 13-3, to test whether aggregate price index has a positive impact on consumption, the p-value is a) 0.0001 b) 0.4165 c) 0.5835 d) 0.8330 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on slope, p-value

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Multiple Regression 13-9 29. Referring to SCENARIO 13-3, to test whether gross domestic product has a positive impact on consumption, the p-value is a) 0.00005 b) 0.0001 c) 0.9999 d) 0.99995 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value SCENARIO 13-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income) and family size (Size). House size is measured in hundreds of square feet and income is measured in thousands of dollars. The builder randomly selected 50 families and ran the multiple regression. Partial Microsoft Excel output is provided below: Regression Statistics Multiple R 0.8479 R Square 0.7189 Adjusted R Square 0.7069 Standard Error 17.5571 Observations 50 ANOVA df Regression Residual Total

Intercept Income Size

MS 18521.6618 308.2503

F

49

SS 37043.3236 14487.7627 51531.0863

Coefficients -5.5146 0.4262 5.5437

Standard Error 7.2273 0.0392 1.6949

t Stat -0.7630 10.8668 3.2708

P-value 0.4493 0.0000 0.0020

Also SSR  X 1 | X 2   36400.6326 and SSR  X 2 | X 1   3297.7917

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Significance F 0.0000

13-10

Multiple Regression

30. Referring to SCENARIO 13-4, what fraction of the variability in house size is explained by income and size of family? a) 17.56% b) 70.69% c) 71.89% d) 84.79% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, interpretation 31. Referring to SCENARIO 13-4, which of the independent variables in the model are significant at the 5% level? a) Income only b) Size only c) Income and Size d) None ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, critical value, p-value, decision, conclusion 32. Referring to SCENARIO 13-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and family size (Size) as the independent variable, he obtained an r2 value of 1.25%. What additional percentage of the total variation in house size has been explained by including income in the multiple regression? a) 15.00% b) 70.64% c) 71.50% d) 73.62% ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of multiple determination 33. Referring to SCENARIO 13-4, which of the following values for the level of significance is the smallest for which each explanatory variable is significant individually? a) 0.001 b) 0.010 c) 0.025 d) 0.050 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: p-value, interpretation

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Multiple Regression 13-11 34. Referring to SCENARIO 13-4, which of the following values for the level of significance is the smallest for which at least one explanatory variable is significant individually? a) 0.005 b) 0.010 c) 0.025 d) 0.050 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: p-value, interpretation 35. Referring to SCENARIO 13-4, which of the following values for the level of significance is the smallest for which at most one explanatory variable is significant individually? a) 0.001 b) 0.010 c) 0.025 d) 0.050 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: p-value, interpretation 36. Referring to SCENARIO 13-4, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant? a) 0.0005 b) 0.001 c) 0.01 d) 0.05 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: p-value, interpretation 37. Referring to SCENARIO 13-4, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000 and having a family size of 4?

ANSWER: 33.71 TYPE: PR DIFFICULTY: Moderate KEYWORDS: prediction of individual values 38. Referring to SCENARIO 13-4, what annual income (in thousands of dollars) would an individual with a family size of 4 need to attain a predicted 10,000 square foot home (House = 100)?

ANSWER: 195.52 TYPE: PR DIFFICULTY: Difficult KEYWORDS: prediction of individual values

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13-12

Multiple Regression

39. Referring to SCENARIO 13-4, what annual income (in thousands of dollars) would an individual with a family size of 9 need to attain a predicted 5,000 square foot home (House = 50)?

ANSWER: 13.19 TYPE: PR DIFFICULTY: Moderate KEYWORDS: prediction of individual values 40. Referring to SCENARIO 13-4, one individual in the sample had an annual income of $100,000 and a family size of 10. This individual owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet) for this data point?

ANSWER: -22.55 TYPE: PR DIFFICULTY: Moderate KEYWORDS: residual 41. Referring to SCENARIO 13-4, one individual in the sample had an annual income of $40,000 and a family size of 1. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (in hundreds of square feet) for this data point?

ANSWER: -7.08 TYPE: PR DIFFICULTY: Moderate KEYWORDS: residual 42. Referring to SCENARIO 13-4, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant t-statistic? a) -0.7630 b) 3.2708 c) 10.8668 d) 60.0864 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic

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Multiple Regression 13-13 43. Referring to SCENARIO 13-4, at the 0.01 level of significance, what conclusion should the builder reach regarding the inclusion of Income in the regression model? a) Income is significant in explaining house size and should be included in the model because its p-value is less than 0.01. b) Income is significant in explaining house size and should be included in the model because its p-value is more than 0.01. c) Income is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01. d) Income is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on slope, decision, conclusion 44. Referring to SCENARIO 13-4, suppose the builder wants to test whether the coefficient on Size is significantly different from 0. What is the value of the relevant t-statistic? a) -0.7630 b) 3.2708 c) 10.8668 d) 60.0864 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic 45. Referring to SCENARIO 13-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of Size in the regression model? a) Size is significant in explaining house size and should be included in the model because its p-value is less than 0.01. b) Size is significant in explaining house size and should be included in the model because its p-value is more than 0.01. c) Size is not significant in explaining house size and should not be included in the model because its p-value is less than 0.01. d) Size is not significant in explaining house size and should not be included in the model because its p-value is more than 0.01.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on slope, critical value, p-value, decision, conclusion 46. Referring to SCENARIO 13-4, what is the value of the calculated F test statistic that is missing from the output for testing whether the whole regression model is significant?

ANSWER: 60.09 TYPE: PR DIFFICULTY: Moderate KEYWORDS: F test on the entire regression, test statistic

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13-14

Multiple Regression

47. Referring to SCENARIO 13-4, the observed value of the F-statistic is missing from the printout.

What are the degrees of freedom for this F-statistic? a) 2 for the numerator, 47 for the denominator b) 2 for the numerator, 49 for the denominator c) 49 for the numerator, 47 for the denominator d) 47 for the numerator, 49 for the denominator ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on the entire regression, degrees of freedom 48. Referring to SCENARIO 13-4, what are the regression degrees of freedom that are missing from the output? a) 2 b) 47 c) 49 d) 50 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: degrees of freedom 49. Referring to SCENARIO 13-4, what are the residual degrees of freedom that are missing from the output? a) 2 b) 47 c) 49 d) 50 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: degrees of freedom 50. Referring to SCENARIO 13-4 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test H 0 : 1   2  0 vs. H1 : At least one  j  0, j  1, 2 ? a) Do not reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on house size. b) Do not reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on house size. c) Reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on house size. d) Reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on house size.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on the entire regression, critical value, p-value, decision, conclusion Copyright ©2020 Pearson Education, Inc.

Multiple Regression 13-15 51. Referring to SCENARIO 13-4, the value of the partial F test statistic is ____ for H0: Variable X1 does not significantly improve the model after variable X2 has been included H1: Variable X1 significantly improves the model after variable X2 has been included ANSWER: 118.0879 TYPE: FI DIFFICULTY: Difficult KEYWORDS: partial F test, test statistic 52. Referring to SCENARIO 13-4, the partial F test for H0: Variable X1 does not significantly improve the model after variable X2 has been included H1: Variable X1 significantly improves the model after variable X2 has been included has ____ and ____ degrees of freedom.

ANSWER: 1 and 47 TYPE: FI DIFFICULTY: Moderate KEYWORDS: partial F test, degrees of freedom 53. Referring to SCENARIO 13-4, the value of the partial F test statistic is ____ for H0: Variable X2 does not significantly improve the model after variable X1 has been included H1: Variable X2 significantly improves the model after variable X1 has been included ANSWER: 10.6984 TYPE: FI DIFFICULTY: Difficult KEYWORDS: partial F test, test statistic 54. Referring to SCENARIO 13-4, the partial F test for H0: Variable X2 does not significantly improve the model after variable X1 has been included H1: Variable X2 significantly improves the model after variable X1 has been included has ____ and ____ degrees of freedom.

ANSWER: 1 and 47 TYPE: FI DIFFICULTY: Moderate KEYWORDS: partial F test, degrees of freedom 55. Referring to SCENARIO 13-4, the coefficient of partial determination rY212 is ____.

ANSWER: 0.7153 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination 56. Referring to SCENARIO 13-4, the coefficient of partial determination rY221 is ____.

ANSWER: 0.1854 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination Copyright ©2020 Pearson Education, Inc.

13-16

Multiple Regression

57. Referring to SCENARIO 13-4, ____% of the variation in the house size can be explained by the variation in the family income while holding the family size constant.

ANSWER: 71.53 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination 58. Referring to SCENARIO 13-4, ____% of the variation in the house size can be explained by the variation in the family size while holding the family income constant.

ANSWER: 18.54 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination SCENARIO 13-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The Microsoft Excel output below shows results of this multiple regression.

SUMMARY OUTPUT Regression Statistics Multiple R 0.830 R Square 0.689 Adjusted R Square 0.662 Standard Error 17501.643 Observations 26 ANOVA Regression Residual Total

df 2 23 25

SS 15579777040 7045072780 22624849820

Intercept Capital Wages

Coeff 15800.0000 0.1245 7.0762

StdError 6038.2999 0.2045 1.4729

MS 7789888520 306307512 t Stat 2.617 0.609 4.804

F 25.432

P-value 0.0154 0.5485 0.0001

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Signif F 0.0001

Multiple Regression 13-17 59. Referring to SCENARIO 13-5, what fraction of the variability in sales is explained by spending on capital and wages? a) 27.0% b) 50.9% c) 68.9% d) 83.0% ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, interpretation 60. Referring to SCENARIO 13-5, which of the independent variables in the model are significant at the 5% level? a) Capital, Wages b) Capital c) Wages d) None of the above ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, critical value, p-value, decision, conclusion 61. Referring to SCENARIO 13-5, when the microeconomist used a simple linear regression model with sales as the dependent variable and wages as the independent variable, she obtained an r2 value of 0.601. What additional percentage of the total variation of sales has been explained by including capital spending in the multiple regression? a) 60.1% b) 31.1% c) 22.9% d) 8.8% ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of multiple determination 62. Referring to SCENARIO 13-5, what is the p-value for Wages? a) 0.01 b) 0.05 c) 0.0001 d) None of the above ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value

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13-18

Multiple Regression

63. Referring to SCENARIO 13-5, what is the p-value for testing whether Wages have a positive impact on corporate sales? a) 0.01 b) 0.05 c) 0.0001 d) 0.00005 ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 64. Referring to SCENARIO 13-5, what is the p-value for testing whether Wages have a negative impact on corporate sales? a) 0.05 b) 0.0001 c) 0.00005 d) 0.99995 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on slope, p-value 65. Referring to SCENARIO 13-5, what is the p-value for Capital? a) 0.01 b) 0.025 c) 0.05 d) None of the above ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 66. Referring to SCENARIO 13-5, what is the p-value for testing whether Capital has a positive influence on corporate sales? a) 0.025 b) 0.05 c) 0.2743 d) 0.5485 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, p-value

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Multiple Regression 13-19 67. Referring to SCENARIO 13-5, what is the p-value for testing whether Capital has a negative influence on corporate sales? a) 0.05 b) 0.2743 c) 0.5485 d) 0.7258 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on slope, p-value 68. Referring to SCENARIO 13-5, which of the following values for  is the smallest for which the regression model as a whole is significant? a) 0.00005 b) 0.001 c) 0.01 d) 0.05 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: F test on the entire regression, p-value, interpretation 69. Referring to SCENARIO 13-5, what are the predicted sales (in millions of dollars) for a company spending $100 million on capital and $100 million on wages? a) 15,800.00 b) 16,520.07 c) 17,277.49 d) 20,455.98 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values 70. Referring to SCENARIO 13-5, what are the predicted sales (in millions of dollars) for a company spending $500 million on capital and $200 million on wages? a) 15,800.00 b) 16,520.07 c) 17,277.49 d) 20,455.98 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values

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13-20

Multiple Regression

71. Referring to SCENARIO 13-5, one company in the sample had sales of $20 billion (Sales = 20,000). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars) for this data point? a) 874.55 b) 622.87 c) –790.69 d) –983.56 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: residual 72. Referring to SCENARIO 13-5, one company in the sample had sales of $21.439 billion (Sales = 21,439). This company spent $300 million on capital and $700 million on wages. What is the residual (in millions of dollars) for this data point? a) 790.69 b) 648.31 c) –648.31 d) –790.69 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: residual 73. Referring to SCENARIO 13-5, suppose the microeconomist wants to test whether the coefficient on Capital is significantly different from 0. What is the value of the relevant t-statistic? a) 0.609 b) 2.617 c) 4.804 d) 25.432 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic

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Multiple Regression 13-21 74. Referring to SCENARIO 13-5, at the 0.01 level of significance, what conclusion should the microeconomist reach regarding the inclusion of Capital in the regression model? a) Capital is significant in explaining corporate sales and should be included in the model because its p-value is less than 0.01. b) Capital is significant in explaining corporate sales and should be included in the model because its p-value is more than 0.01. c) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is less than 0.01. d) Capital is not significant in explaining corporate sales and should not be included in the model because its p-value is more than 0.01.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: t test on the slope, critical value, p-value, decision, conclusion 75. Referring to SCENARIO 13-5, the observed value of the F-statistic is given on the printout as 25.432. What are the degrees of freedom for this F-statistic? a) 25 for the numerator, 2 for the denominator b) 2 for the numerator, 23 for the denominator c) 23 for the numerator, 25 for the denominator d) 2 for the numerator, 25 for the denominator ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on the entire regression, degrees of freedom SCENARIO 13-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y). To provide its customers with information on that matter, a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit ( X 1 ) and the amount of insulation in inches ( X 2 ). Given below is EXCEL output of the regression model.

Regression Statistics Multiple R

0.5270

R Square

0.2778

Adjusted R Square

0.1928

Standard Error

40.9107

Observations

20

ANOVA df

SS

MS

F 3.2691

Regression

2

10943.0190

5471.5095

Residual

17

28452.6027

1673.6825

Total

19

39395.6218

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Significance F 0.0629

13-22

Multiple Regression Coefficients

Intercept

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

448.2925

90.7853

4.9379

0.0001

256.7522

639.8328

Temperature

-2.7621

1.2371

-2.2327

0.0393

-5.3721

-0.1520

Insulation

-15.9408

10.0638

-1.5840

0.1316

-37.1736

5.2919

Also SSR  X 1 | X 2   8343.3572 and SSR  X 2 | X 1   4199.2672 76. Referring to SCENARIO 13-6, the estimated value of the regression parameter 1 in means that a) holding the effect of the amount of insulation constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 2.76 degrees. b) holding the effect of the amount of insulation constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $2.76. c) holding the effect of the amount of insulation constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $2.76. d) holding the effect of the amount of insulation constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 2.76%.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: slope, interpretation 77. Referring to SCENARIO 13-6, what can we say about the regression model? a) The model explains 17.12% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 27.78% of the sample variability of heating costs. b) The model explains 19.28% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 27.78% of the sample variability of heating costs. c) The model explains 27.78% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 19.28% of the sample variability of heating costs. d) The model explains 19.28% of the variability of heating costs; after correcting for the degrees of freedom, the model explains 17.12% of the sample variability of heating costs.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: adjusted r-square

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Multiple Regression 13-23 78. Referring to SCENARIO 13-6, what is your decision and conclusion for the test H 0 : 2  0 vs. H1 : 2  0 at the  = 0.01 level of significance? a) Do not reject H0 and conclude that the amount of insulation has a linear effect on heating costs. b) Reject H0 and conclude that the amount of insulation does not have a linear effect on heating costs. c) Reject H0 and conclude that the amount of insulation has a linear effect on heating costs. d) Do not reject H0 and conclude that the amount of insulation does not have a linear effect on heating costs.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, critical value, p-value, decision, conclusion 79. Referring to SCENARIO 13-6, what is the 95% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature? a) [256.7522, 639.8328] b) [204.7854, 497.1733] c) [5.3721, 0.1520] d) [37.1736, 5.2919] ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: confidence interval, slope, interpretation 80. Referring to SCENARIO 13-6 and allowing for a 1% probability of committing a type I error, what is the decision and conclusion for the test H 0 : 1   2  0 vs. H1 : At least one  j  0, j  1, 2 ? a) Do not reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on heating costs. b) Do not reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on heating costs. c) Reject H0 and conclude that the 2 independent variables taken as a group have significant linear effects on heating costs. d) Reject H0 and conclude that the 2 independent variables taken as a group do not have significant linear effects on heating costs.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on the entire regression, critical value, p-value, decision, conclusion

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13-24

Multiple Regression

81. Referring to SCENARIO 13-6, the value of the partial F test statistic is ____ for H0: Variable X1 does not significantly improve the model after variable X2 has been included H1: Variable X1 significantly improves the model after variable X2 has been included ANSWER: 4.99 TYPE: FI DIFFICULTY: Difficult KEYWORDS: partial F test, test statistic 82. Referring to SCENARIO 13-6, the partial F test for H0: Variable X1 does not significantly improve the model after variable X2 has been included H1: Variable X1 significantly improves the model after variable X2 has been included has ____ and ____ degrees of freedom.

ANSWER: 1 and 17 TYPE: FI DIFFICULTY: Moderate KEYWORDS: partial F test, degrees of freedom 83. Referring to SCENARIO 13-6, the value of the partial F test statistic is ____ for H0: Variable X2 does not significantly improve the model after variable X1 has been included H1: Variable X2 significantly improves the model after variable X1 has been included ANSWER: 2.51 TYPE: FI DIFFICULTY: Difficult KEYWORDS: partial F test, test statistic 84. Referring to SCENARIO 13-6, the partial F test for H0: Variable X2 does not significantly improve the model after variable X1 has been included H1: Variable X2 significantly improves the model after variable X1 has been included has ____ and ____ degrees of freedom.

ANSWER: 1 and 17 TYPE: FI DIFFICULTY: Moderate KEYWORDS: partial F test, degrees of freedom 85. Referring to SCENARIO 13-6, the coefficient of partial determination rY212 is ____.

ANSWER: 0.2267 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination 86. Referring to SCENARIO 13-6, the coefficient of partial determination rY221 is ____.

ANSWER: 0.1286 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination Copyright ©2020 Pearson Education, Inc.

Multiple Regression 13-25 87. Referring to SCENARIO 13-6, ____% of the variation in heating cost can be explained by the variation in minimum outside temperature while holding the amount of insulation constant.

ANSWER: 22.67 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination 88. Referring to SCENARIO 13-6, ____% of the variation in heating cost can be explained by the variation in the amount of insulation while holding the minimum outside temperature constant.

ANSWER: 12.86 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination 89. True or False: The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: slope, interpretation 90. True or False: The coefficient of multiple determination r2Y.12 measures the proportion of variation in Y that is explained by X1 and X2.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination 91. True or False: When an additional explanatory variable is introduced into a multiple regression model, the coefficient of multiple determination will never decrease.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: coefficient of multiple determination, properties 92. True or False: When an additional explanatory variable is introduced into a multiple regression model, the adjusted r 2 can never decrease.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: adjusted r-square, properties

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13-26

Multiple Regression

93. True or False: When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: coefficient of multiple determination, properties 94. True or False: When an explanatory variable is dropped from a multiple regression model, the adjusted r 2 can increase.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: adjusted r-square, properties 95. True or False: The slopes in a multiple regression model are called net regression coefficients.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: slope 96. True or False: In calculating the standard error of the estimate, SYX  MSE , there are n – k – 1 degrees of freedom, where n is the sample size and k represents the number of independent variables in the model.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: standard error of estimate 97. True or False: The total sum of squares (SST) in a regression model will never be greater than the regression sum of squares (SSR).

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sum of squares, properties 98. True or False: The coefficient of multiple determination measures the proportion of the total variation in the dependent variable that is explained by the set of independent variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, interpretation

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Multiple Regression 13-27 99. True or False: The coefficient of multiple determination is calculated by taking the ratio of the regression sum of squares over the total sum of squares (SSR/SST) and subtracting that value from 1.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, properties 100. True or False: In a particular model, the sum of the squared residuals was 847. If the model had 5 independent variables, and the data set contained 40 points, the value of the standard error of the estimate is 24.912.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: sum of squares, standard error of estimate, properties EXPLANATION Degrees of freedom=40-5-1=34. Standard error of the estimate= SYX  = (

)

=

MSE .

= 4.9912

101. True or False: A multiple regression is called “multiple” because it has several data points.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: properties, interpretation 102. True or False: A multiple regression is called “multiple” because it has several explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: properties, interpretation 103. True or False: If you have considered all relevant explanatory factors, the residuals from a multiple regression model should be random.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: residual, properties 104. True or False: Multiple regression is the process of using several independent variables to predict a number of dependent variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: properties Copyright ©2020 Pearson Education, Inc.

13-28

Multiple Regression

105. True or False: You have just computed a regression model in which the value of coefficient of multiple determination is 0.57. To determine if this indicates that the independent variables explain a significant portion of the variation in the dependent variable, you would perform an Ftest.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression 106. True or False: From the coefficient of multiple determination, you cannot detect the strength of the relationship between Y and any individual independent variable.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: coefficient of multiple determination, interpretation 107. True or False: Consider a regression in which b2 = – 1.5 and the standard error of this coefficient equals 0.3. To determine whether X2 is a significant explanatory variable, you would compute an observed t-value of – 5.0.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic 108. True or False: A regression had the following results: SST = 82.55, SSE = 29.85. It can be said that 73.4% of the variation in the dependent variable is explained by the independent variables in the regression.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient multiple determination, sum of squares, properties 109. True or False: A regression had the following results: SST = 82.55, SSE = 29.85. It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient multiple determination, sum of squares, properties

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Multiple Regression 13-29 110. True or False: A regression had the following results: SST = 102.55, SSE = 82.04. It can be said that 90.0% of the variation in the dependent variable is explained by the independent variables in the regression.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient multiple determination, sum of squares, properties 111. True or False: A regression had the following results: SST = 102.55, SSE = 82.04. It can be said that 20.0% of the variation in the dependent variable is explained by the independent variables in the regression.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: coefficient multiple determination, sum of squares, properties SCENARIO 13-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units and total SAT scores of each. She takes a sample of 6 students and generates the following Microsoft Excel output: SUMMARY OUTPUT Regression Statistics Multiple R 0.916 R Square 0.839 Adjusted R Square 0.732 Standard Error 0.24685 Observations 6 ANOVA Regression Residual Total

df 2 3 5

Coeff Intercept 4.593897 Units – 0.247270 Total SAT 0.001443

SS 0.95219 0.18281 1.13500 StdError 1.13374542 0. 06268485 0.00101241

MS 0.47610 0.06094 t Stat 4.052 – 3.945 1.425

F 7.813

P-value 0.0271 0.0290 0.2494

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Signif F 0.0646

13-30

Multiple Regression

112. Referring to SCENARIO 13-7, the estimate of the unit change in the mean of Y per unit change in X1, holding X2 constant, is ________.

ANSWER: -0.247 TYPE: FI DIFFICULTY: Easy KEYWORDS: slope, interpretation 113. Referring to SCENARIO 13-7, the net regression coefficient of X2 is ________.

ANSWER: 0.001443 TYPE: FI DIFFICULTY: Easy KEYWORDS: slope, interpretation 114. Referring to SCENARIO 13-7, the predicted GPA for a student carrying 15 course units and who has a total SAT of 1,100 is ________.

ANSWER: 2.472 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values 115. Referring to SCENARIO 13-7, the value of the coefficient of multiple determination, r2Y.12, is ________.

ANSWER: 0.839 TYPE: FI DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination 116. Referring to SCENARIO 13-7, the value of the adjusted coefficient of multiple determination, r2adj, is ________.

ANSWER: 0.732 TYPE: FI DIFFICULTY: Easy KEYWORDS: adjusted r-square 117. Referring to SCENARIO 13-7, the department head wants to test H0:  1   2  0 . The appropriate alternative hypothesis is ________.

ANSWER: at least one  i  0 .

TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, form of hypothesis

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Multiple Regression 13-31 118. Referring to SCENARIO 13-7, the department head wants to test H0:  1   2  0 . The critical value of the F test for a level of significance of 0.05 is ________.

ANSWER: 9.55 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, critical value 119. Referring to SCENARIO 13-7, the department head wants to test H0:  1   2  0 . The value of the F-test statistic is ________.

ANSWER: 7.813 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, test statistic 120. Referring to SCENARIO 13-7, the department head wants to test H0:  1   2  0 . The p-value of the test is ________.

ANSWER: 0.0646 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, p-value 121. True or False: Referring to SCENARIO 13-7, the department head wants to test H0: 1  2  0 . At a level of significance of 0.05, the null hypothesis is rejected.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, decision 122. Referring to SCENARIO 13-7, the department head wants to use a t test to test for the significance of the coefficient of X1. For a level of significance of 0.05, the critical values of the test are ________.

ANSWER:  3.1824 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, critical value 123. Referring to SCENARIO 13-7, the department head wants to use a t test to test for the significance of the coefficient of X1. The value of the test statistic is ________.

ANSWER: -3.945 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic

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13-32

Multiple Regression 124. Referring to SCENARIO 13-7, the department head wants to use a t test to test for the significance of the coefficient of X1. The p-value of the test is ________.

ANSWER: 0.0290 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 125. True or False: Referring to SCENARIO 13-7, the department head wants to use a t test to test for the significance of the coefficient of X1. At a level of significance of 0.05, the department head would decide that  1  0 .

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: t test on slope, decision, conclusion 126. Referring to SCENARIO 13-7, the department head decided to construct a 95% confidence interval for 1 . The confidence interval is from ________ to ________.

ANSWER: -0.4468 to -0.0478 TYPE: FI DIFFICULTY: Moderate KEYWORDS: slope, confidence interval SCENARIO 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and 2 variables: age (X1 = Age) and experience in the field (X2 = Exper). He took a sample of 20 employees and obtained the following Microsoft Excel output: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.8535 0.7284 0.6964 10.5630 20

ANOVA df Regression Residual Total

Intercept Age Exper

SS 2 17 19

5086.5764 1896.8050 6983.3814

Coefficients

Standard Error

1.5740 1.3045 -0.1478

9.2723 0.1956 0.1944

MS

F

2543.2882 111.5768

22.7941

0.0000

t Stat

P-value

Lower 95%

Upper 95%

0.8672 0.0000 0.4574

-17.9888 0.8917 -0.5580

21.1368 1.7173 0.2624

0.1698 6.6678 -0.7604

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Significance F

Multiple Regression 13-33 Also, the sum of squares due to the regression for the model that includes only Age is 5022.0654 while the sum of squares due to the regression for the model that includes only Exper is 125.9848.

127. Referring to SCENARIO 13-8, the estimate of the unit change in the mean of Y per unit change in X1, considering the effects of the other variable, is ________.

ANSWER: 1.3045 TYPE: FI DIFFICULTY: Easy KEYWORDS: slope, interpretation 128. Referring to SCENARIO 13-8, the estimated change in the mean salary (in $1,000) when an employee is a year older holding experience constant is ________.

ANSWER: 1.3045 TYPE: FI DIFFICULTY: Easy KEYWORDS: slope, interpretation 129. Referring to SCENARIO 13-8, the estimated change in the mean salary (in $1,000) for an employee who has one additional year of experience holding age constant is ________.

ANSWER: -0.1478 TYPE: FI DIFFICULTY: Easy KEYWORDS: slope, interpretation 130. Referring to SCENARIO 13-8, the predicted salary (in $1,000) for a 35-year-old person with 10 years of experience is ________.

ANSWER: 45.7536 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values 131. Referring to SCENARIO 13-8, the value of the coefficient of multiple determination is ________.

ANSWER: 0.7284 TYPE: FI DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination 132. Referring to SCENARIO 13-8, the value of the adjusted coefficient of multiple determination is ________.

ANSWER: 0.6964 TYPE: FI DIFFICULTY: Easy KEYWORDS: adjusted r-square

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13-34

Multiple Regression

133. Referring to SCENARIO 13-8, the analyst wants to use an F-test to test H 0 : 1  2  0 . The appropriate alternative hypothesis is ________.

ANSWER: at least one  j  0 for j = 1,2 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, form of hypothesis 134. Referring to SCENARIO 13-8, the critical value of an F test on the entire regression for a level of significance of 0.01 is ________.

ANSWER: 6.1121 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, critical value 135. Referring to SCENARIO 13-8, the value of the F-statistic for testing the significance of the entire regression is ________.

ANSWER: 22.7941 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, test statistic 136. Referring to SCENARIO 13-8, the p-value of the F test for the significance of the entire regression is ________.

ANSWER: 0.0000 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, p-value 137. True or False: Referring to SCENARIO 13-8, the F test for the significance of the entire regression performed at a level of significance of 0.01 leads to a rejection of the null hypothesis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, decision 138. Referring to SCENARIO 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X2. For a level of significance of 0.01, the critical values of the test are ________.

ANSWER:  2.8982 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on the slope, critical value

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Multiple Regression 13-35 139. Referring to SCENARIO 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X2. The value of the test statistic is ________.

ANSWER: -0.7604 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on the slope, test statistic 140. Referring to SCENARIO 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X2. The p-value of the test is ________.

ANSWER: 0.4574 TYPE: FI DIFFICULTY: Easy KEYWORDS: t test on the slope, p-value 141. True or False: Referring to SCENARIO 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X2. At a level of significance of 0.01, the department head would decide that 2  0 .

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: t test on the slope, decision, conclusion 142. Referring to SCENARIO 13-8, the analyst decided to construct a 95% confidence interval for 2 . The confidence interval is from ________ to ________.

ANSWER: -0.5580 to 0.2624 TYPE: FI DIFFICULTY: Moderate KEYWORDS: slope, confidence interval 143. Referring to SCENARIO 13-8, the value of the partial F test statistic is ____ for H0: Variable X1 does not significantly improve the model after variable X2 has been included H1: Variable X1 significantly improves the model after variable X2 has been included ANSWER: 45.0099 TYPE: FI DIFFICULTY: Difficult KEYWORDS: partial F test, test statistic 144. Referring to SCENARIO 13-8, the partial F test for H0: Variable X1 does not significantly improve the model after variable X2 has been included H1: Variable X1 significantly improves the model after variable X2 has been included has ____ and ____ degrees of freedom.

ANSWER: 1 and 17 TYPE: FI DIFFICULTY: Moderate KEYWORDS: partial F test, degrees of freedom Copyright ©2020 Pearson Education, Inc.

13-36

Multiple Regression

145. Referring to SCENARIO 13-8, the value of the partial F test statistic is ____ for H0: Variable X2 does not significantly improve the model after variable X1 has been included H1: Variable X2 significantly improves the model after variable X1 has been included ANSWER: 1.1291 TYPE: FI DIFFICULTY: Difficult KEYWORDS: partial F test, test statistic 146. Referring to SCENARIO 13-8, the partial F test for H0: Variable X2 does not significantly improve the model after variable X1 has been included H1: Variable X2 significantly improves the model after variable X1 has been included has ____ and ____ degrees of freedom.

ANSWER: 1 and 17 TYPE: FI DIFFICULTY: Moderate KEYWORDS: partial F test, degrees of freedom 147. Referring to SCENARIO 13-8, the coefficient of partial determination rY212 is ____.

ANSWER: 0.7258 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination 148. Referring to SCENARIO 13-8, the coefficient of partial determination rY221 is ____.

ANSWER: 0.06228 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination 149. Referring to SCENARIO 13-8, ____% of the variation in salary can be explained by the variation in age while holding experience constant.

ANSWER: 72.58 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination 150. Referring to SCENARIO 13-8, ____% of the variation in salary can be explained by the variation in experience while holding age constant.

ANSWER: 6.23 TYPE: FI DIFFICULTY: Difficult KEYWORDS: coefficient of partial determination

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Multiple Regression 13-37 SCENARIO 13-9 You decide to predict gasoline prices in different cities and towns in the United States for your term project. Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income and the number of firms that manufacture automobile parts in and around the city.

You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821. Your computed value of standard error of the estimate is 1.9549.

151. Referring to SCENARIO 13-9, what is the value of the coefficient of multiple determination?

ANSWER: 0.6843 TYPE: PR DIFFICULTY: Difficult KEYWORDS: coefficient of multiple determination

SSE 2 , SSE  SYX  n  k  1  1.9549  32  2  1  56.6921 , n  k 1 SSR 122.8821 = 0.6843 r2   SST (122.8821  56.6921)

EXPLANATION: SYX 

152. Referring to SCENARIO 13-9, the value of adjusted r 2 is ANSWER: 0.6625 TYPE: MC DIFFICULTY: Moderate KEYWORDS: adjusted r-square 153. Referring to SCENARIO 13-9, if the variable that measures the number of firms that manufacture automobile parts in and around the city is removed from the multiple regression model, which of the following would be true? a) The adjusted r 2 will definitely increase. b) The adjusted r 2 cannot increase. c) The coefficient of multiple determination will not increase. d) The coefficient of multiple determination will definitely increase.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: coefficient of multiple determination, adjusted r-square, properties

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13-38

Multiple Regression

SCENARIO 13-10 You worked as an intern at We Always Win Car Insurance Company last summer. You notice that individual car insurance premiums depend very much on the age of the individual and the number of traffic tickets received by the individual. You performed a regression analysis in EXCEL and obtained the following partial information: Regression Statistics Multiple R 0.8546 R Square 0.7303 Adjusted R Square 0.6853 Standard Error 226.7502 Observations 15 ANOVA df Regression Residual Total

Intercept Age Tickets

SS 2 12

MS F Significance F 835284.6500 16.2457 0.0004

616987.8200 2287557.1200

Coefficients Standard Error 821.2617 161.9391 -1.4061 2.5988 243.4401 43.2470

t Stat P-value 5.0714 0.0003 -0.5411 0.5984 5.6291 0.0001

Lower 99% Upper 99% 326.6124 1315.9111 -9.3444 6.5321 111.3406 375.5396

154. Referring to SCENARIO 13-10, the proportion of the total variability in insurance premiums that can be explained by AGE and TICKETS is _________.

ANSWER: 0.7303 TYPE: FI DIFFICULTY: Easy KEYWORDS: coefficient of multiple determination, interpretation 155. Referring to SCENARIO 13-10, the proportion of the total variability in insurance premiums that can be explained by AGE and TICKETS after adjusting for the number of observations and the number independent variables is _________.

ANSWER: 0.6853 TYPE: FI DIFFICULTY: Easy KEYWORDS: adjusted r-square 156. Referring to SCENARIO 13-10, the standard error of the estimate is _________.

ANSWER: 226.7502 TYPE: FI DIFFICULTY: Easy KEYWORDS: standard error of estimate Copyright ©2020 Pearson Education, Inc.

Multiple Regression 13-39 157. Referring to SCENARIO 13-10, the estimated mean change in insurance premiums for every 2 additional tickets received is _____.

ANSWER: (243.4401)*2 = 486.8802 TYPE: FI DIFFICULTY: Difficult KEYWORDS: slope, interpretation 158.

Referring to SCENARIO 13-10, the 99% confidence interval for the change in mean insurance premiums of a person who has become 1 year older (i.e., the slope coefficient for AGE) -1.4061  _______.

ANSWER: 7.9382 TYPE: FI DIFFICULTY: Moderate KEYWORDS: slope, interpretation, confidence interval 159. Referring to SCENARIO 13-10, the total degrees of freedom that are missing in the ANOVA table should be ______.

ANSWER: 14 TYPE: FI DIFFICULTY: Easy KEYWORDS: degrees of freedom 160. Referring to SCENARIO 13-10, the regression sum of squares that is missing in the ANOVA table should be ______.

ANSWER: 1,670,569.3000 TYPE: FI DIFFICULTY: Easy KEYWORDS: sum of squares 161. Referring to SCENARIO 13-10, the residual mean squares (MSE) that are missing in the ANOVA table should be _____.

ANSWER: 51,415.6517 TYPE: FI DIFFICULTY: Easy KEYWORDS: mean squares

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13-40

Multiple Regression

162. Referring to SCENARIO 13-10, to test the significance of the multiple regression model, what is the form of the null hypothesis? a) H0 : 1  0 b)

H 0 : 2  0

c)

H 0 : 1  2  0

d)

H 0 : 0  1  2  0

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on the entire regression, form of hypothesis 163. Referring to SCENARIO 13-10, to test the significance of the multiple regression model, the value of the test statistic is ______.

ANSWER: 16.2457 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, test statistic 164. Referring to SCENARIO 13-10, to test the significance of the multiple regression model, the pvalue of the test statistic in the sample is ______.

ANSWER: 0.0004 TYPE: FI DIFFICULTY: Easy KEYWORDS: F test on the entire regression, p-value 165. Referring to SCENARIO 13-10, to test the significance of the multiple regression model, what are the degrees of freedom?

ANSWER: 2 for the numerator, 12 for the denominator TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on the entire regression, degrees of freedom 166. True or False: Referring to SCENARIO 13-10, to test the significance of the multiple regression model, the null hypothesis should be rejected while allowing for 1% probability of committing a type I error.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, decision

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Multiple Regression 13-41 167. True or False: Referring to SCENARIO 13-10, the multiple regression model is significant at a 10% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, decision, conclusion 168. If a categorical independent variable contains 2 categories, then _________ dummy variable(s) will be needed to uniquely represent these categories. a) 1 b) 2 c) 3 d) 4 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: dummy variable, properties 169. If a categorical independent variable contains 4 categories, then _________ dummy variable(s) will be needed to uniquely represent these categories. a) 1 b) 2 c) 3 d) 4 ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: dummy variable, properties 170. A dummy variable is used as an independent variable in a regression model when a) the variable involved is numerical. b) the variable involved is categorical. c) a curvilinear relationship is suspected. d) when 2 independent variables interact.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: dummy variable, properties

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13-42

Multiple Regression

171. An interaction term in a multiple regression model may be used when a) the coefficient of determination is small. b) there is a curvilinear relationship between the dependent and independent variables. c) neither one of 2 independent variables contribute significantly to the regression model. d) the relationship between X1 and Y changes for differing values of X2.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: interaction, properties 172. To explain personal consumption (CONS) measured in dollars, data is collected for INC: CRDTLIM: APR: ADVT: SEX:

personal income in dollars $1 plus the credit limit in dollars available to the individual mean annualized percentage interest rate for borrowing for the individual per person advertising expenditure in dollars by manufacturers in the city where the individual lives gender of the individual; 1 if female, 0 if male

A regression analysis was performed with CONS as the dependent variable and CRDTLIM, APR, ADVT, and SEX as the independent variables. The estimated model was Y  2.28 - 0.29 CRDTLIM  5.77 APR  2.35 ADVT  0.39 SEX

What is the correct interpretation for the estimated coefficient for SEX? a) Holding the effect of the other independent variables constant, mean personal consumption for females is estimated to be $0.39 higher than males. b) Holding the effect of the other independent variables constant, mean personal consumption for males is estimated to be $0.39 higher than females. c) Holding the effect of the other independent variables constant, mean personal consumption for females is estimated to be 0.39% higher than males. d) Holding the effect of the other independent variables constant, mean personal consumption for males is estimated to be 0.39% higher than females.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: dummy variable, slope, interpretation

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Multiple Regression 13-43 SCENARIO 13-11 A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client (measured in pounds). Two variables thought to affect weight loss are client’s length of time on the weight-loss program and time of session. These variables are described below: Y = Weight loss (in pounds) X1 = Length of time in weight-loss program (in months) X2 = 1 if morning session, 0 if not Data for 25 clients on a weight-loss program at the clinic were collected and used to fit the interaction Y  0  1 X1  2 X 2  3 X1 X 2   model: Output from Microsoft Excel follows: Regression Statistics Multiple R 0.7308 R Square 0.5341 Adjusted R Square 0.4675 Standard Error 43.3275 Observations 25 ANOVA df Regression Residual Total

Intercept Length Morn Length x Morn

SS 3 21 24

45194.0661 39422.6542 84616.7203

Coefficients

Standard Error

-20.7298 7.2472 90.1981 -5.1024

22.3710 1.4992 40.2336 3.3511

MS

F

15064.6887 1877.2692

8.0248

t Stat

P-value

-0.9266 4.8340 2.2419 -1.5226

0.3646 0.0001 0.0359 0.1428

Significance F 0.0009

Lower 99% -84.0702 3.0024 -23.7176 -14.5905

173. Referring to SCENARIO 13-11, what is the experimental unit for this analysis? a) A clinic b) A client on a weight-loss program c) A month d) A morning, afternoon, or evening session ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: model building

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Upper 99% 42.6106 11.4919 204.1138 4.3857

13-44

Multiple Regression

174. Referring to SCENARIO 13-11, what null hypothesis would you test to determine whether the slope of the linear relationship between weight loss (Y) and time on the program (X1) varies according to time of session? a) H 0 : 1  0 b)

H 0 : 2  0

c)

H 0 : 3  0

d)

H 0 : 1  2  0

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: interaction, form of hypothesis 175. Referring to SCENARIO 13-11, in terms of the  s in the model, give the mean change in weight loss (Y) for every 1 month increase in time on the program (X1) when not attending the morning session. a) 1

1   2 c) 1  3 d) 2  3 b)

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: interaction, slope, interpretation 176. Referring to SCENARIO 13-11, in terms of the  s in the model, give the mean change in weight loss (Y) for every 1 month increase in time on the program (X1) when attending the morning session. a) 1

1   2 c) 1  3 d) 2  3 b)

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: interaction, slope, interpretation

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Multiple Regression 13-45 177. True or False: Referring to SCENARIO 13-11, the overall model for predicting weight loss (Y) is statistically significant at the 0.05 level.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: interaction, F test on the entire regression, decision, conclusion 178. Referring to SCENARIO 13-11, which of the following statements is supported by the analysis shown? a) There is sufficient evidence (at  = 0.05) of curvature in the relationship between weight loss (Y) and months on program(X1). b) There is sufficient evidence (at  = 0.05) to indicate that the relationship between weight loss (Y) and months on program (X1) varies with session time. c) There is insufficient evidence (at  = 0.05) of curvature in the relationship between weight loss (Y) and months on program(X1). d) There is insufficient evidence (at  = 0.05) to indicate that the relationship between weight loss (Y) and months on program(X1) varies with session time.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: interaction, t test on slope, decision, conclusion 179. In a multiple regression model, the adjusted r 2 a) cannot be negative. b) can sometimes be negative. c) can sometimes be greater than +1. d) has to fall between 0 and +1.

ANSWER: b TYPE: MC DIFFICULTY: Difficult KEYWORDS: adjusted r-square, properties

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13-46

Multiple Regression

SCENARIO 13-12 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price ($) per hour of parking, blocks to the quadrangle, and whether the parking is on or off campus. The population regression model hypothesized is Yi    1 X1i  2 X 2i   where Y is the meter price per hour X1 is the number of blocks to the quad X2 is a dummy variable that takes the value 1 if the meter is located on campus and 0 otherwise The following Excel results are obtained.

Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.5536 0.3064 0.2812 0.4492 58

ANOVA df Regression Residual Total

Intercept Block Campus

SS 2 55 57

4.9035 11.0984 16.0019

Coefficients

Standard Error

1.6500 -0.2504 0.1552

0.2028 0.0529 0.1297

MS

F

2.4518 0.2018

12.1501

t Stat

P-value

8.1359 -4.7355 1.1966

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0.0000 0.0000 0.2366

Significance F 0.0000

Lower 99% 1.1089 -0.3915 -0.1908

Upper 99% 2.1912 -0.1093 0.5011

Multiple Regression 13-47 180. Referring to SCENARIO 13-12, what is the correct interpretation for the estimated coefficient for X2? a) Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus. b) Holding the effect of the distance from the quad constant, the estimated mean costs for parking off campus is $0.16 per hour more than parking on campus. c) Holding the effect of the distance from the quad constant, the estimated mean costs for parking on campus is $0.16 per hour more than parking off campus for each additional block away from the quad. d) Holding the effect of the distance from the quad constant, the estimated mean costs for parking off campus is $0.16 per hour more than parking on campus for each additional block away from the quad.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: dummy variable, slope, interpretation 181. Referring to SCENARIO 13-12, predict the cost per hour if one parks off campus and 3 blocks from the quad.

ANSWER: $ 0.90 TYPE: PR DIFFICULTY: Easy KEYWORDS: prediction of individual values 182. Referring to SCENARIO 13-12, if one is already off campus but decides to park 3 more blocks from the quad, the estimated mean parking meter rate will decrease by ____.

ANSWER $0.25*3 = $0.75 TYPE: FI DIFFICULTY: Moderate KEYWORDS: dummy variable, slope, interpretation 183. True or False: An interaction term in a multiple regression model may be used when the relationship between X1 and Y changes for differing values of X2.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: interaction, properties 184. True or False: When a dummy variable is included in a multiple regression model, the interpretation of the estimated slope coefficient does not make any sense anymore.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: dummy variable, slope, interpretation

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13-48

Multiple Regression

185. True or False: In trying to construct a model to estimate grades on a statistics test, a professor wanted to include, among other factors, whether the person had taken the course previously. To do this, the professor included a dummy variable in her regression model that was equal to 1 if the person had previously taken the course, and 0 otherwise. The interpretation of the coefficient associated with this dummy variable would be the mean amount the repeat students tended to be above or below non-repeaters, with all other factors the same.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: dummy variable, slope, interpretation SCENARIO 13-13 An econometrician is interested in evaluating the relationship of demand for building materials to mortgage rates in Los Angeles and San Francisco. He believes that the appropriate model is Y = 10 + 5X1 + 8X2 where

X1 = mortgage rate in % X2 = 1 if SF, 0 if LA Y = demand in $100 per capita

186. Referring to SCENARIO 13-13, holding constant the effect of city, each additional increase of 1% in the mortgage rate would lead to an estimated increase of ________ in the mean demand.

ANSWER: $500 per capita TYPE: FI DIFFICULTY: Moderate KEYWORDS: slope, interpretation 187. Referring to SCENARIO 13-13, the effect of living in San Francisco rather than Los Angeles is to increase the mean demand by an estimated ________.

ANSWER: $800 per capita TYPE: FI DIFFICULTY: Moderate KEYWORDS: dummy variable, slope, interpretation 188. Referring to SCENARIO 13-13, the predicted demand in Los Angeles when the mortgage rate is 8% is ________.

ANSWER: $5,000 per capita TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values, dummy variable

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Multiple Regression 13-49 189. Referring to SCENARIO 13-13, the predicted demand in San Francisco when the mortgage rate is 10% is ________.

ANSWER: $6,800 per capita TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values, dummy variable 190. Referring to SCENARIO 13-13, the fitted model for predicting demand in Los Angeles is ________. a) 10 + 5X1 b) 10 + 13X1 c) 15 + 8X2 d) 18 + 5X2 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values, dummy variable 191. Referring to SCENARIO 13-13, the fitted model for predicting demand in San Francisco is ________. a) 10 + 5X1 b) 10 + 13X1 c) 15 + 8X2 d) 18 + 5X1 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values, dummy variable SCENARIO 13-14 An automotive engineer would like to be able to predict automobile mileages. She believes that the two most important characteristics that affect mileage are horsepower and the number of cylinders (4 or 6) of a car. She believes that the appropriate model is Y = 40 – 0.05X1 + 20X2 – 0.1X1X2 where X1 = horsepower X2 = 1 if 4 cylinders, 0 if 6 cylinders Y = mileage.

192. Referring to SCENARIO 13-14, the predicted mileage for a 300 horsepower, 6-cylinder car is ________.

ANSWER: 25 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values, dummy variable

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13-50

Multiple Regression

193. Referring to SCENARIO 13-14, the predicted mileage for a 200 horsepower, 4-cylinder car is ________.

ANSWER: 30 TYPE: FI DIFFICULTY: Moderate KEYWORDS: prediction of individual values, dummy variable 194. Referring to SCENARIO 13-14, the fitted model for predicting mileages for 6-cylinder cars is ________. a) 40 – 0.05X1 b) 40 – 0.10X1 c) 60 – 0.10X1 d) 60 – 0.15X1 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values, dummy variable 195. Referring to SCENARIO 13-14, the fitted model for predicting mileages for 4-cylinder cars is ________. a) 40 – 0.05X1 b) 40 – 0.10X1 c) 60 – 0.10X1 d) 60 – 0.15X1 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: prediction of individual values, dummy variable

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Multiple Regression 13-51 SCENARIO 13-15 The superintendent of a school district wanted to predict the percentage of students passing a sixthgrade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), mean teacher salary in thousands of dollars (Salaries), and instructional spending per pupil in thousands of dollars (Spending) of 47 schools in the state.

Following is the multiple regression output with Y = % Passing as the dependent variable, X 1 = Salaries and X 2 = Spending: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.4276 0.1828 0.1457 5.7351 47

ANOVA df Regression Residual Total

Intercept Salary Spending

SS 2 44 46

323.8284 1447.2094 1771.0378

Coefficients

Standard Error

-72.9916 2.7939 0.3742

45.9106 0.8974 0.9782

MS

F

161.9142 32.8911

4.9227

t Stat

P-value

-1.5899 3.1133 0.3825

0.1190 0.0032 0.7039

Significance F 0.0118

Lower 95% -165.5184 0.9853 -1.5972

Upper 95% 19.5352 4.6025 2.3455

196. Referring to SCENARIO 13-15, which of the following is a correct statement? a) The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars. b) The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1%. c) The mean percentage of students passing the proficiency test is estimated to go up by 2.79% when mean teacher salary increases by one thousand dollars holding constant the instructional spending per pupil. d) The mean teacher salary is estimated to go up by 2.79% when mean percentage of students passing the proficiency test increases by 1% holding constant the instructional spending per pupil.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, slope

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13-52

Multiple Regression

197. Referring to SCENARIO 13-15, which of the following is a correct statement? a) 18.28% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary and instructional spending per pupil. b) 18.28% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary and instructional spending per pupil after adjusting for the number of predictors and sample size. c) 18.28% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary holding constant the effect of instructional spending per pupil. d) 18.28% of the total variation in the percentage of students passing the proficiency test can be explained by instructional spending per pupil holding constant the effect of mean teacher salary.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, coefficient of multiple determination 198. Referring to SCENARIO 13-15, which of the following is a correct statement? a) 14.57% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary and instructional spending per pupil. b) 14.57% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary and instructional spending per pupil after adjusting for the number of predictors and sample size. c) 14.57% of the total variation in the percentage of students passing the proficiency test can be explained by mean teacher salary holding constant the effect of instructional spending per pupil. d) 14.57% of the total variation in the percentage of students passing the proficiency test can be explained by instructional spending per pupil holding constant the effect of mean teacher salary.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, adjusted r-square 199. Referring to SCENARIO 13-15, what is the standard error of estimate?

ANSWER: 5.7351 (%) TYPE: PR DIFFICULTY: Easy KEYWORDS: standard error of estimate 200. Referring to SCENARIO 13-15, predict the percentage of students passing the proficiency test for a school which has a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

ANSWER: 39.5127 (%) TYPE: PR DIFFICULTY: Easy KEYWORDS: prediction of individual values

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Multiple Regression 13-53 201. Referring to SCENARIO 13-15, estimate the mean percentage of students passing the proficiency test for all the schools that have a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

ANSWER: 39.5127 (%) TYPE: PR DIFFICULTY: Easy KEYWORDS: estimation of mean values 202. Referring to SCENARIO 13-15, which of the following is the correct null hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary? a)

H0 : 0  0

b)

H0 : 1  0

c)

H0 : 2  0

d)

H0 : 3  0

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, form of hypothesis 203. Referring to SCENARIO 13-15, which of the following is the correct alternative hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary? a) H1 : 0  0 b) H 1 :  1  0 c) H 1 :  2  0 d)

H1 : 3  0

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, form of hypothesis 204. Referring to SCENARIO 13-15, what is the value of the test statistic when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary?

ANSWER: 0.3825 TYPE: PR DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic

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13-54

Multiple Regression

205. Referring to SCENARIO 13-15, what is the p-value of the test statistic when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary?

ANSWER: 0.7039 TYPE: PR DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 206. True or False: Referring to SCENARIO 13-15, the null hypothesis should be rejected at a 5% level of significance when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test, considering the effect of mean teacher salary.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: t test on slope, decision 207. True or False: Referring to SCENARIO 13-15, there is sufficient evidence that instructional spending per pupil has an effect on percentage of students passing the proficiency test while holding constant the effect of mean teacher salary at a 5% level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: t test on slope, conclusion 208. Referring to SCENARIO 13-15, which of the following is the correct null hypothesis to test whether mean teacher salary has any effect on percentage of students passing the proficiency test, considering the effect of instructional spending per pupil? a)

H0 : 0  0

b)

H0 : 1  0

c)

H0 : 2  0

d)

H0 : 3  0

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, form of hypothesis

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Multiple Regression 13-55 209. Referring to SCENARIO 13-15, which of the following is the correct alternative hypothesis to test whether mean teacher salary has any effect on percentage of students passing the proficiency test, considering the effect of instructional spending per pupil? a) H1 : 0  0 b) H 1 :  1  0 c) H 1 :  2  0 d)

H1 : 3  0

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, form of hypothesis 210. Referring to SCENARIO 13-15, what is the value of the test statistic when testing whether mean teacher salary has any effect on percentage of students passing the proficiency test, considering the effect of instructional spending per pupil?

ANSWER: 3.1133 TYPE: PR DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic 211. Referring to SCENARIO 13-15, what is the p-value of the test statistic when testing whether mean teacher salary has any effect on percentage of students passing the proficiency test, considering the effect of instructional spending per pupil?

ANSWER: 0.0032 TYPE: PR DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 212. True or False: Referring to SCENARIO 13-15, the null hypothesis should be rejected at a 5% level of significance when testing whether mean teacher salary has any effect on percentage of students passing the proficiency test, considering the effect of instructional spending per pupil.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: t test on slope, decision 213. True or False: Referring to SCENARIO 13-15, there is sufficient evidence that mean teacher salary has an effect on percentage of students passing the proficiency test while holding constant the effect of instructional spending per pupil at a 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: t test on slope, conclusion

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13-56

Multiple Regression

214. Referring to SCENARIO 13-15, which of the following is the correct null hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables? a)

H0 : 0  1  2  0

b)

H0 : 1  2  0

c)

H0 : 0  1  2  0

d)

H0 : 1  2  0

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on the entire regression, form of hypothesis 215. Referring to SCENARIO 13-15, which of the following is the correct alternative hypothesis to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables? a)

H1 : 0  1  2  0

b)

H1 : 1  2  0

c)

H 1 : At least one of  j  0 for j = 0, 1, 2

d)

H 1 : At least one of  j  0 for j = 1, 2

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on the entire regression, form of hypothesis 216. Referring to SCENARIO 13-15, the null hypothesis H0 : 1  2  0 implies that percentage of students passing the proficiency test is not affected by either of the explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 217. Referring to SCENARIO 13-15, the null hypothesis H0 : 1  2  0 implies that percentage of students passing the proficiency test is not affected by one of the explanatory variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis

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Multiple Regression 13-57 218. Referring to SCENARIO 13-15, the null hypothesis H0 : 1  2  0 implies that percentage of students passing the proficiency test is not related to either of the explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 219. Referring to SCENARIO 13-15, the null hypothesis H0 : 1  2  0 implies that percentage of students passing the proficiency test is not related to one of the explanatory variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 220. Referring to SCENARIO 13-15, the alternative hypothesis H 1 : At least one of  j  0 for j = 1, 2 implies that percentage of students passing the proficiency test is related to both of the explanatory variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 221. Referring to SCENARIO 13-15, the alternative hypothesis H 1 : At least one of  j  0 for j = 1, 2 implies that percentage of students passing the proficiency test is related to at least one of the explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 222. Referring to SCENARIO 13-15, the alternative hypothesis H 1 : At least one of  j  0 for j = 1, 2 implies that percentage of students passing the proficiency test is affected by both of the explanatory variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis

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13-58

Multiple Regression

223. Referring to SCENARIO 13-15, the alternative hypothesis H 1 : At least one of  j  0 for j = 1, 2 implies that percentage of students passing the proficiency test is affected by at least one of the explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 224. Referring to SCENARIO 13-15, what are the numerator and denominator degrees of freedom, respectively, for the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

ANSWER: 2 and 44 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on the entire regression, degrees of freedom 225. Referring to SCENARIO 13-15, what is the value of the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

ANSWER: 4.9227 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on the entire regression, test statistic 226. Referring to SCENARIO 13-15, what is the p-value of the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

ANSWER: 0.0118 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on the entire regression, p-value 227. True or False: Referring to SCENARIO 13-15, the null hypothesis should be rejected at a 5% level of significance when testing whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, decision

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Multiple Regression 13-59 228. True or False: Referring to SCENARIO 13-15, there is sufficient evidence that at least one of the explanatory variables is related to the percentage of students passing the proficiency test at a 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, conclusion 229. True or False: Referring to SCENARIO 13-15, there is sufficient evidence that the percentage of students passing the proficiency test depends on at least one of the explanatory variables at a 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, conclusion 230. True or False: Referring to SCENARIO 13-15, there is sufficient evidence that both of the explanatory variables are related to the percentage of students passing the proficiency test at a 5% level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: F test on the entire regression, conclusion 231. True or False: Referring to SCENARIO 13-15, there is sufficient evidence that the percentage of students passing the proficiency test depends on both of the explanatory variables at a 5% level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: F test on the entire regression, conclusion 232. Referring to SCENARIO 13-15, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one thousand dollars increase in instructional spending per pupil on the mean percentage of students passing the proficiency test?

ANSWER:  (%) to 2.3455 (%) TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, slope, interpretation

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13-60

Multiple Regression

233. Referring to SCENARIO 13-15, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one thousand dollar increase in mean teacher salary on the mean percentage of students passing the proficiency test?

ANSWER:  (%) to 4.6025 (%) TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, slope, interpretation 234. True or False: Referring to SCENARIO 13-15, you can conclude that mean teacher salary has no impact on the mean percentage of students passing the proficiency test, considering the effect of instructional spending per pupil, at a 5% level of significance using the confidence interval estimate for 1 .

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, t test on slope, decision 235. True or False: Referring to SCENARIO 13-15, you can conclude that instructional spending per pupil has no impact on the mean percentage of students passing the proficiency test, considering the effect of mean teacher salary, at a 5% level of significance using the confidence interval estimate for 2 .

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: confidence interval, t test on slope, decision 236. True or False: Referring to SCENARIO 13-15, you can conclude definitively that mean teacher salary individually has no impact on the mean percentage of students passing the proficiency test, considering the effect of instructional spending per pupil, at a 1% level of significance based solely on but not actually computing the 99% confidence interval estimate for 1 .

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, t test on slope, decision

EXPLANATION: You know that the 99% confidence interval estimate for 1 will be wider than the 95% confidence interval but you cannot tell definitively if 0 will still be outside the 99% confidence interval without actually computing the 99% confidence interval.

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Multiple Regression 13-61 237. True or False: Referring to SCENARIO 13-15, you can conclude definitively that instructional spending per pupil individually has no impact on the mean percentage of students passing the proficiency test, considering the effect of mean teacher salary, at a 1% level of significance based solely on but not actually computing the 99% the confidence interval estimate for 2 .

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, t test on slope, decision

EXPLANATION: You know that the 99% confidence interval estimate for 2 will be wider than the 95% confidence interval and, hence, should still contain 0.

238. True or False: Referring to SCENARIO 13-15, you can conclude definitively that mean teacher salary individually has no impact on the mean percentage of students passing the proficiency test, considering the effect of that instructional spending per pupil, at a 10% level of significance based solely on but not actually computing the 90% confidence interval estimate for 1 .

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, t test on slope, decision

EXPLANATION: You know that the 90% confidence interval estimate for 1 will be narrower than the 95% confidence interval and, hence, should still not contain 0.

239. True or False: Referring to SCENARIO 13-15, you can conclude definitively that instructional spending per pupil individually has no impact on the mean percentage of students passing the proficiency test, considering the effect of mean teacher salary, at a 10% level of significance based solely on but not actually computing the 90% confidence interval estimate for 2 .

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, t test on slope, decision

EXPLANATION: You know that the 90% confidence interval estimate for 2 will be narrower than the 95% confidence interval but not definitively whether it will still contain 0 without actually computing the 90% confidence interval.

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13-62

Multiple Regression

SCENARIO 13-16 What are the factors that determine the acceleration time (in sec.) from 0 to 60 miles per hour of a car? Data on the following variables for 30 different vehicle models were collected: Y (Accel Time): Acceleration time in sec.

X1 (Engine Size): cubic centimeters (cc) X2 (Sedan): 1 if the vehicle model is a sedan and 0 otherwise The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.

Regression Statistics Multiple R 0.6096 R Square 0.3716 Adjusted R Square 0.3251 Standard Error 1.4629 Observations 30 ANOVA df Regression Residual Total

2 27 29

SS 34.1744 57.7856 91.9600

Intercept Engine Size Sedan

Coefficients 7.1052 -0.0005 0.7264

Standard Error 0.6574 0.0001 0.5564

MS 17.0872 2.1402

F 7.9839

Significance F 0.0019

t Stat 10.8086 -3.6477 1.3056

P-value 0.0000 0.0011 0.2027

Lower 95% 5.7564 -0.0008 -0.4152

The various residual plots are as shown below.

Residuals versus Predicted Y

Residuals

4 2 0 -2 -4

0

2

4

6

8

Predicted Y

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Upper 95% 8.4540 -0.0002 1.8681

Multiple Regression 13-63

Residual Plot for Engine Size 4 3

Residuals

2 1 0 -1 -2 -3 -4 0

2000

4000 Engine

6000

8000

Residual Plot for Sedan 4 3

Residuals

2 1 0 -1 -2 -3 -4 0

0.2

0.4

0.6 Sedan

0.8

1

1.2

2

3

Normal Probability Plot 4 3

Residual

2 1 0 -1 -2 -3 -4 -3

-2

-1

0 Z Value

1

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13-64

Multiple Regression 2

2

The coefficient of partial determinations rY 12 and rY 21 are 0.3301, and 0.0594, respectively.

The coefficient of determination for the regression model using each of the 2 independent variables as 2

the dependent variable and the other independent variable as independent variables ( Rj ) are, respectively 0.0077, and 0.0077.

240. Referring to SCENARIO 13-16, what is the correct interpretation for the estimated coefficient for X1? a) As the 0 to 60 miles per hour acceleration time increases by one second, the mean engine size will decrease by an estimated 0.0005 c.c. without taking into consideration the other independent variable included in the model. b) As the engine size increases by one c.c., the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0005 seconds without taking into consideration the other independent variable included in the model. c) As the 0 to 60 miles per hour acceleration time increases by one second, the mean engine size will decrease by an estimated 0.0005 c.c. taking into consideration the other independent variable included in the model. d) As the engine size increases by one c.c., the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0005 seconds taking into consideration the other independent variable included in the model.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, interpretation 241. Referring to SCENARIO 13-16, what is the correct interpretation for the estimated coefficient for X2? a) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds lower than that of a non-sedan after considering the effect of the engine size. b) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds higher than that of a non-sedan after considering the effect of the engine size. c) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds lower than that of a non-sedan without considering the effect of the engine size. d) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds higher than that of a non-sedan without considering the effect of the engine size.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: slope, interpretation, dummy variable 242. True or False: Referring to SCENARIO 13-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7264 seconds higher than that of a non-sedan with the same engine size.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: slope, interpretation, dummy variable

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Multiple Regression 13-65 243. True or False: Referring to SCENARIO 13-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7264 seconds lower than that of a non-sedan with the same engine size.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: slope, interpretation, dummy variable 244. True or False: Referring to SCENARIO 13-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.0005 seconds higher than that of a non-sedan with the same engine size.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: slope, interpretation, dummy variable 245. True or False: Referring to SCENARIO 13-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.0005 seconds lower than that of a non-sedan with the same engine size.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: slope, interpretation, dummy variable 246. Referring to SCENARIO 13-16, what is the value of the test statistic to determine whether engine size makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance?

ANSWER: -3.6477 TYPE: PR DIFFICULTY: Easy KEYWORDS: model building, t test on slope, test statistic 247. Referring to SCENARIO 13-16, what is the p-value of the test statistic to determine whether engine size makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance?

ANSWER: 0.0011 TYPE: PR DIFFICULTY: Easy KEYWORDS: model building, t test on slope, p-value

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13-66

Multiple Regression

248. True or False: Referring to SCENARIO 13-16, there is enough evidence to conclude that engine size makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: model building, t test on slope, decision 249. Referring to SCENARIO 13-16, what is the value of the test statistic to determine whether being a sedan or not makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance?

ANSWER: 1.3056 TYPE: PR DIFFICULTY: Easy KEYWORDS: model building, t test on slope, test statistic 250. Referring to SCENARIO 13-16, what is the p-value of the test statistic to determine whether being a sedan or not makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance?

ANSWER: 0.2027 TYPE: PR DIFFICULTY: Easy KEYWORDS: model building, t test on slope, p-value 251. True or False: Referring to SCENARIO 13-16, there is enough evidence to conclude that being a sedan or not makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: model building, t test on slope, decision 252. Referring to SCENARIO 13-16, ________ of the variation in Accel Time can be explained by the two independent variables after taking into consideration the number of independent variables and the number of observations.

ANSWER: 0.3251 or 32.51% TYPE: FI DIFFICULTY: Moderate KEYWORDS: model building, adjusted r-square

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Multiple Regression 13-67 253. Referring to SCENARIO 13-16, ________ of the variation in Accel Time can be explained by the two independent variables.

ANSWER: 0.3716 or 37.16% TYPE: FI DIFFICULTY: Moderate KEYWORDS: model building, coefficient of multiple determination 254. Referring to SCENARIO 13-16, which of the following assumptions is most likely violated based on the residual plot of the residuals versus predicted Y? a) Independence of errors. b) Normality of errors. c) Equal variance. d) None.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: assumption, homoscedasticity 255. Referring to SCENARIO 13-16, which of the following assumptions is most likely violated based on the residual plot for Engine Size? a) Linearity. b) Normality of errors. c) Independence of errors. d) None.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: assumption, linearity 256. Referring to SCENARIO 13-16, which of the following assumptions is most likely violated based on the normal probability plot? a) Linearity. b) Normality. c) Equal variance. d) Independence.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: assumption, normality EXPLANATION: Possible left skew in the data.

257. True or False: Referring to SCENARIO 13-16, the error appears to be left-skewed.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: assumption, normality EXPLANATION: Page 238-239, text.

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13-68

Multiple Regression

258. True or False: Referring to SCENARIO 13-16, the errors (residuals) appear to be right-skewed.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: assumption, normality SCENARIO 13-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age) and a dummy variable for management position (Manager: 1 = yes, 0 = no).

The results of the regression analysis are given below: Regression Statistics Multiple R

0.6391

R Square

0.4085

Adjusted R Square

0.3765

Standard Error

18.8929

Observations

40

ANOVA df

SS

MS

F 12.7740

Regression

2

9119.0897

4559.5448

Residual

37

13206.8103

356.9408

Total

39

22325.9

Coefficients

Standard Error

t Stat

Significance F

P-value

Intercept

-0.2143

11.5796

-0.0185

0.9853

Age

1.4448

0.3160

4.5717

0.0000

-22.5761

11.3488

-1.9893

0.0541

Manager

0.0000

259. Referring to SCENARIO 13-17, which of the following is a correct statement? a) On average, a worker who is a year older is estimated to stay jobless shorter by approximately 0.2143 weeks while holding constant the effects of the manager dummy variable. b) On average, a worker who is a year older is estimated to stay jobless longer by approximately 0.2143 weeks while holding constant the effects of the manager dummy variable. c) On average, a worker who is a year older is estimated to stay jobless shorter by approximately 1.4448 weeks while holding constant the effects of the manager dummy variable. d) On average, a worker who is a year older is estimated to stay jobless longer by approximately 1.4448 weeks while holding constant the effects of the manager dummy variable.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, slope Copyright ©2020 Pearson Education, Inc.

Multiple Regression 13-69 260. Referring to SCENARIO 13-17, which of the following is a correct statement? a) On average, those who are in a management position are estimated to stay jobless shorter by approximately 1.4448 weeks while holding constant the effects of age. b) On average, those who are in a management position are estimated to stay jobless longer by approximately 1.4448 weeks while holding constant the effects of age. c) On average, those who are in a management position are estimated to stay jobless shorter by approximately 22.5761 weeks while holding constant the effects of age. d) On average, those who are in a management position are estimated to stay jobless longer by approximately 22.5761 weeks while holding constant the effects of age.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, slope 261. Referring to SCENARIO 13-17, which of the following is a correct statement? a) 40.85% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager. b) 40.85% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the number of predictors and sample size. c) 40.85% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the level of significance d) 40.85% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager holding constant the effect of all the independent variables.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, coefficient of multiple determination 262. Referring to SCENARIO 13-17, which of the following is a correct statement? a) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager. b) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the number of predictors and sample size. c) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager after adjusting for the level of significance d) 37.65% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker and whether the worker is a manager holding constant the effect of all the independent variables.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: interpretation, adjusted r-square

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13-70

Multiple Regression

263. Referring to SCENARIO 13-17, what is the standard error of estimate?

ANSWER: 18.8929 TYPE: PR DIFFICULTY: Easy KEYWORDS: standard error of estimate 264. Referring to SCENARIO 13-17, predict the number of weeks being unemployed due to a layoff for a worker who is a thirty-year old and is a manager.

ANSWER: 20.5536 TYPE: PR DIFFICULTY: Easy KEYWORDS: prediction of individual values 265. Referring to SCENARIO 13-17, which of the following is the correct null hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable? a) H 0 : 1  0 b) H 0 : 1  0 c) H 0 :  2  0 d) H 0 :  2  0 ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, form of hypothesis 266. Referring to SCENARIO 13-17, which of the following is the correct alternative hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable? a) H1 : 1  0 b) H1 : 1  0 c) H1 :  2  0 d) H1 :  2  0 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: t test on slope, form of hypothesis 267. Referring to SCENARIO 13-17, what is the value of the test statistic when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable?

ANSWER: 4.5717 TYPE: PR DIFFICULTY: Easy KEYWORDS: t test on slope, test statistic

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Multiple Regression 13-71 268. Referring to SCENARIO 13-17, what is the p-value of the test statistic when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable?

ANSWER: 0.0000 TYPE: PR DIFFICULTY: Easy KEYWORDS: t test on slope, p-value 269. True or False: Referring to SCENARIO 13-17, the null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: t test on slope, decision 270. True or False: Referring to SCENARIO 13-17, there is sufficient evidence that age has an effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable at a 10% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: t test on slope, conclusion 271. Referring to SCENARIO 13-17, which of the following is the correct null hypothesis to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables? a)

H0 : 0  1  2  0

b)

H0 : 1  2  0

c)

H0 : 0  1  2

d)

H0 : 1  2

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: F test on the entire regression, form of hypothesis 272. Referring to SCENARIO 13-17, the null hypothesis H0 : 1  2  0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by any of the explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis Copyright ©2020 Pearson Education, Inc.

13-72

Multiple Regression

273. Referring to SCENARIO 13-17, the null hypothesis H0 : 1  2  0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by some of the explanatory variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 274. Referring to SCENARIO 13-17, the null hypothesis H0 : 1  2  0 implies that the number of weeks a worker is unemployed due to a layoff is not related to any of the explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 275. Referring to SCENARIO 13-17, the null hypothesis H0 : 1  2  0 implies that the number of weeks a worker is unemployed due to a layoff is not related to one of the explanatory variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 276. Referring to SCENARIO 13-17, the alternative hypothesis H 1 : At least one of  j  0 for j = 1, 2 implies that the number of weeks a worker is unemployed due to a layoff is related to all of the explanatory variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis

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Multiple Regression 13-73 277. Referring to SCENARIO 13-17, the alternative hypothesis H 1 : At least one of  j  0 for j = 1, 2 implies that the number of weeks a worker is unemployed due to a layoff is related to at least one of the explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 278. Referring to SCENARIO 13-17, the alternative hypothesis H 1 : At least one of  j  0 for j = 1, 2 implies that the number of weeks a worker is unemployed due to a layoff is affected by all of the explanatory variables.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 279. Referring to SCENARIO 13-17, the alternative hypothesis H 1 : At least one of  j  0 for j = 1, 2 implies that the number of weeks a worker is unemployed due to a layoff is affected by at least one of the explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, interpretation, form of hypothesis 280. Referring to SCENARIO 13-17, what are the numerator and denominator degrees of freedom, respectively, for the test statistic to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

ANSWER: 2 and 37 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on the entire regression, degrees of freedom 281. Referring to SCENARIO 13-17, what is the value of the test statistic to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

ANSWER: 12.7740 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on the entire regression, test statistic

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13-74

Multiple Regression

282. Referring to SCENARIO 13-17, what is the p-value of the test statistic to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

ANSWER: 0.0000 TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on the entire regression, p-value 283. True or False: Referring to SCENARIO 13-17, the null hypothesis should be rejected at a 10% level of significance when testing whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, decision 284. True or False: Referring to SCENARIO 13-17, there is sufficient evidence that at least one of the explanatory variables is related to the number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

ANSWER: True TYPE: PR DIFFICULTY: Easy KEYWORDS: F test on the entire regression, conclusion 285. True or False: Referring to SCENARIO 13-17, there is sufficient evidence that the number of weeks a worker is unemployed due to a layoff depends on at least one of the explanatory variables at a 10% level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: F test on the entire regression, conclusion 286. True or False: Referring to SCENARIO 13-17, there is sufficient evidence that all of the explanatory variables are related to the number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: F test on the entire regression, conclusion

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Multiple Regression 13-75 287. True or False: Referring to SCENARIO 13-17, there is sufficient evidence that the number of weeks a worker is unemployed due to a layoff depends on all of the explanatory variables at a 10% level of significance.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: F test on the entire regression, conclusion 288. Referring to SCENARIO 13-17, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one-year increase in age on the mean number of weeks a worker is unemployed due to a layoff after taking into consideration the effect of all the other independent variables?

ANSWER: 0.8045 to 2.0851 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, slope, interpretation 289. Referring to SCENARIO 13-17, what are the lower and upper limits of the 95% confidence interval estimate for the difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not after taking into consideration the effect of all the other independent variables?

ANSWER: -45.5710 to 0.4188 TYPE: PR DIFFICULTY: Moderate KEYWORDS: confidence interval, slope, interpretation 290. True or False: Referring to SCENARIO 13-17, you can conclude that, holding constant the effect of the other independent variable, age has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 5% level of significance if we use only the information of the 95% confidence interval estimate for the effect of a one year increase in age on the mean number of weeks a worker is unemployed due to a layoff.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, t test on slope, decision 291. True or False: Referring to SCENARIO 13-17, we can conclude that, holding constant the effect of the other independent variable, there is a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not at a 5% level of significance if we use only the information of the 95% confidence interval estimate for the difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: confidence interval, t test on slope, decision

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13-76

Multiple Regression

292. True or False: Referring to SCENARIO 13-17, we can conclude definitively that, holding constant the effect of the other independent variable, age has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 1% level of significance if all we have is the information of the 95% confidence interval estimate for the effect of a one year increase in age on the mean number of weeks a worker is unemployed due to a layoff.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, t test on slope, decision

EXPLANATION: Since the 99% confidence interval estimate for 1 will be wider than the 95% confidence interval, which may or may not contain 0, we cannot conclude definitively that holding constant the effect of the other independent variable, age has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 1% level of significance.

293. True or False: Referring to SCENARIO 13-17, we can conclude definitively that, holding constant the effect of the other independent variables, there is not a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not at a 1% level of significance if all we have is the information of the 95% confidence interval estimate for the difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not.

ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, t test on slope, decision

EXPLANATION: Since the 99% confidence interval estimate for 2 will be wider than the 95% confidence interval and will still contain 0, we can conclude definitively that, holding constant the effect of the other independent variables, there is not a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not at a 1% level of significance.

294. True or False: Referring to SCENARIO 13-17, we can conclude definitively that, holding constant the effect of the other independent variable, age has an impact on the mean number of weeks a worker is unemployed due to a layoff at a 10% level of significance if all we have is the information of the 95% confidence interval estimate for the effect of a one year increase in age on the mean number of weeks a worker is unemployed due to a layoff.

ANSWER: True TYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, t test on slope, decision

EXPLANATION: Since the 90% confidence interval estimate for 1 will be narrower than the 95% confidence interval and we can be sure that it still will not contain 0, you can conclude definitively that holding constant the effect of the other independent variables, age has an impact on the mean number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

Copyright ©2020 Pearson Education, Inc.

Multiple Regression 13-77 295. True or False: Referring to SCENARIO 13-17, we can conclude definitively that, holding constant the effect of the other independent variables, there is not a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not at a 10% level of significance if all we have is the information of the 95% confidence interval estimate for the difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: confidence interval, t test on slope, decision-------

EXPLANATION: Since the 90% confidence interval estimate for 2 will be narrower than the 95% confidence interval and we are not sure if it will still contain 0, we cannot conclude definitively that, holding constant the effect of the other independent variables, there is not a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is in a management position and one who is not at a 10% level of significance.

SCENARIO 13-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT) at the university or college and whether the TOEFL criterion is at least 90 (Toefl90 = 1 if yes, 0 otherwise.) The dependent variable, Y, is school type (Type = 1 if private and 0 otherwise). There are 80 universities in the sample.

The PHStat output is given below: Binary Logistic Regression Predictor

Coefficients

SE Coef

Z

Intercept SAT Toefl90:1

-3.9594 0.0028 0.1928

1.6741 0.0011 0.5827

-2.3650 2.5459 0.3309

Deviance

101.9826

p-Value 0.0180 0.0109 0.7407

296. Referring to SCENARIO 13-18, which of the following is the correct expression for the estimated model? a) Y  3.9594  0.0028 SAT  0.1928 Toefl 90 b) Yˆ   3.9594  0.0028 SA T  0.1928 T oefl 90 c) ln  o d d s ratio    3.9 5 9 4  0 .0 0 2 8 S A T  0 .1 9 2 8 T o efl 9 0 d)

ln  estim ated o d d s ratio    3.9 5 9 4  0 .0 0 2 8 S A T  0 .1 9 2 8 T o efl 9 0

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: logistic regression, estimation Copyright ©2020 Pearson Education, Inc.

13-78

Multiple Regression

297. Referring to SCENARIO 13-18, what is the estimated odds ratio for a school with a mean SAT score of 1250 and a TOEFL criterion that is at least 90?

ANSWER: 0.7660 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 298. Referring to SCENARIO 13-18, what is the estimated probability that a school is a private one with a mean SAT score of 1250 and a TOEFL criterion that is at least 90?

ANSWER: 0.4337 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 299. Referring to SCENARIO 13-18, what is the estimated odds ratio for a school with a mean SAT score of 1100 and a TOEFL criterion that is not at least 90?

ANSWER: 0.4150 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 300. Referring to SCENARIO 13-18, what is the estimated probability that a school with a mean SAT score of 1100 and a TOEFL criterion that is not at least 90?

ANSWER: 0.2933 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 301. Referring to SCENARIO 13-18, which of the following is the correct interpretation for the SAT slope coefficient? a) Holding constant the effect of Toefl90, the estimated mean value of school type increases by 0.0028 for each increase of one point in average SAT score. b) Holding constant the effect of Toefl90, the estimated school type increases by 0.0028 for each increase of one point in average SAT score. c) Holding constant the effect of Toefl90, the estimated probability of the school being a private school increases by 0.0028 for each increase of one point in mean SAT score. d) Holding constant the effect of Toefl90, the estimated natural logarithm of the odds ratio of the school being a private school increases by 0.0028 for each increase of one point in mean SAT score.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: logistic regression, slope, interpretation

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Multiple Regression 13-79 302. Referring to SCENARIO 13-18, which of the following is the correct interpretation for the Toefl90 slope coefficient? a) Holding constant the effect of SAT, the estimated mean value of school type is 0.1928 higher when the school has a TOEFL criterion that is at least 90. b) Holding constant the effect of SAT, the estimated school type increases by 0.1928 when the school has a TOEFL criterion that is at least 90. c) Holding constant the effect of SAT, the estimated natural logarithm of the odds ratio of the school being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not. d) Holding constant the effect of SAT, the estimated probability of the school being a private school is 0.1928 higher for a school that has a TOEFL criterion that is at least 90 than one that does not.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: logistic regression, slope, interpretation 303. Referring to SCENARIO 13-18, what are the degrees of freedom for the chi-square distribution when testing whether the model is a good-fitting model?

ANSWER: 77 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, deviance statistic, degrees of freedom 304. Referring to SCENARIO 13-18, what is the p-value of the test statistic when testing whether SAT makes a significant contribution to the model in the presence of Toefl90?

ANSWER: 0.0109 TYPE: PR DIFFICULTY: Easy KEYWORDS: logistic regression, Wald statistic, p-value 305. Referring to SCENARIO 13-18, what should be the decision (‘reject’ or ‘do not reject’) on the null hypothesis when testing whether SAT makes a significant contribution to the model in the presence of Toefl90 at a 0.05 level of significance?

ANSWER: Reject TYPE: PR DIFFICULTY: Easy KEYWORDS: logistic regression, Wald statistic, decision 306. True or False: Referring to SCENARIO 13-18, there is not enough evidence to conclude that SAT score makes a significant contribution to the model in the presence of Toefl90 at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: moderate KEYWORDS: logistic regression, Wald statistic, conclusion Copyright ©2020 Pearson Education, Inc.

13-80

Multiple Regression

307. Referring to SCENARIO 13-18, what is the p-value of the test statistic when testing whether Toefl90 makes a significant contribution to the model in the presence of SAT? ANSWER: 0.7407 TYPE: PR DIFFICULTY: Easy KEYWORDS: logistic regression, Wald statistic, p-value 308. Referring to SCENARIO 13-18, what should be the decision (‘reject’ or ‘do not reject’) on the null hypothesis when testing whether Toefl90 makes a significant contribution to the model in the presence of SAT at a 0.05 level of significance?

ANSWER: Do not reject TYPE: PR DIFFICULTY: Easy KEYWORDS: logistic regression, Wald statistic, decision 309. True or False: Referring to SCENARIO 13-18, there is not enough evidence to conclude that Toefl90 makes a significant contribution to the model in the presence of SAT at a 0.05 level of significance.

ANSWER: True TYPE: TF DIFFICULTY: moderate KEYWORDS: logistic regression, Wald statistic, conclusion

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Multiple Regression 13-81 SCENARIO 13-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service. A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0) and 19 had a lawn service (code 1). Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars) and lawn size (Lawn Size, in thousands of square feet).

The PHStat output is given below: Binary Logistic Regression Predictor

Coefficients

SE Coef

Z

Intercept Income Lawn Size

-7.8562 0.0304 1.2804

3.8224 0.0133 0.6971

-2.0553 2.2897 1.8368

Deviance

25.3089

p-Value 0.0398 0.0220 0.0662

310. Referring to SCENARIO 13-19, which of the following is the correct expression for the estimated model? a) Y  7.8562  0.0304 Income  1.2804 LawnSize b) Yˆ   7.8562  0.0304 Income  1.2804 LawnSize (odds ratio) = −7.8562 + 0.0304 c) + 1.2804 (estimated odds ratio) = −7.8562 + 0.0304 + 1.2804 d) ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: logistic regression, estimation 311. Referring to SCENARIO 13-19, what is the estimated odds ratio for a home owner with a family income of $100,000 and a lawn size of 5,000 square feet?

ANSWER: 4.8832 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 312. Referring to SCENARIO 13-19, what is the estimated probability that a home owner with a family income of $100,000 and a lawn size of 5,000 square feet will purchase a lawn service?

ANSWER: 0.8300 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 313. Referring to SCENARIO 13-19, what is the estimated odds ratio for a home owner with a family income of $50,000 and a lawn size of 5,000 square feet?

Copyright ©2020 Pearson Education, Inc.

13-82

Multiple Regression

ANSWER: 1.0680 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 314. Referring to SCENARIO 13-19, what is the estimated probability that a home owner with a family income of $50,000 and a lawn size of 5,000 square feet will purchase a lawn service?

ANSWER: 0.5164 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 315. Referring to SCENARIO 13-19, what is the estimated odds ratio for a home owner with a family income of $50,000 and a lawn size of 2,000 square feet?

ANSWER: 0.0229 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 316. Referring to SCENARIO 13-19, what is the estimated probability that a home owner with a family income of $50,000 and a lawn size of 2,000 square feet will purchase a lawn service?

ANSWER: 0.0224 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 317. Referring to SCENARIO 13-19, what is the estimated odds ratio for a home owner with a family income of $100,000 and a lawn size of 2,000 square feet?

ANSWER: 0.1048 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation 318. Referring to SCENARIO 13-19, what is the estimated probability that a home owner with a family income of $100,000 and a lawn size of 2,000 square feet will purchase a lawn service?

ANSWER: 0.0949 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, odds ratio, estimation

Copyright ©2020 Pearson Education, Inc.

Multiple Regression 13-83 319. Referring to SCENARIO 13-19, which of the following is the correct interpretation for the Income slope coefficient? a) Holding constant the effect of lawn size, the estimated number of lawn services purchased increases by 0.0304 for each increase of one thousand dollars in family income. b) Holding constant the effect of lawn size, the estimated average number of lawn services purchased increases by 0.0304 for each increase of one thousand dollars in family income. c) Holding constant the effect of lawn size, the estimated probability of purchasing a lawn service increases by 0.0304 for each increase of one thousand dollars in family income. d) Holding constant the effect of lawn size, the estimated natural logarithm of the odds ratio of purchasing a lawn service increases by 0.0304 for each increase of one thousand dollars in family income.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: logistic regression, slope, interpretation 320. Referring to SCENARIO 13-19, which of the following is the correct interpretation for the Lawn Size slope coefficient? a) Holding constant the effect of income, the estimated number of lawn services purchased increases by 1.2804 for each increase of one thousand square feet in lawn size. b) Holding constant the effect of income, the estimated average number of lawn services purchased increases by 1.2804 for each increase of one thousand square feet in lawn size. c) Holding constant the effect of income, the estimated probability of purchasing a lawn service increases by 1.2804 for each increase of one thousand square feet in lawn size. d) Holding constant the effect of income, the estimated natural logarithm of the odds ratio of purchasing a lawn service increases by 1.2804 for each increase of one thousand square feet in lawn size.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: logistic regression, slope, interpretation 321. Referring to SCENARIO 13-19, what are the degrees of freedom for the chi-square distribution when testing whether the model is a good-fitting model?

ANSWER: 27 TYPE: PR DIFFICULTY: Moderate KEYWORDS: logistic regression, deviance statistic, degrees of freedom 322. Referring to SCENARIO 13-19, what is the p-value of the test statistic when testing whether the model is a good-fitting model?

ANSWER: 0.5572 TYPE: PR DIFFICULTY: Difficult KEYWORDS: logistic regression, deviance statistic, p-value EXPLANATION: Use =CHISQ.DIST.RT(25.3089,27) in Excel to obtain the p-value.

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13-84

Multiple Regression

323. True or False: Referring to SCENARIO 13-19, the null hypothesis that the model is a goodfitting model cannot be rejected when allowing for a 5% probability of making a type I error.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: logistic regression, deviance statistic, decision 324. True or False: Referring to SCENARIO 13-19, there is not enough evidence to conclude that the model is not a good-fitting model at a 0.05 level of significance.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: logistic regression, deviance statistic, conclusion 325. Referring to SCENARIO 13-19, what is the p-value of the test statistic when testing whether Income makes a significant contribution to the model in the presence of LawnSize?

ANSWER: 0.0220 TYPE: PR DIFFICULTY: Easy KEYWORDS: logistic regression, Wald statistic, p-value 326. Referring to SCENARIO 13-19, what should be the decision (‘reject’ or ‘do not reject’) on the null hypothesis when testing whether Income makes a significant contribution to the model in the presence of LawnSize at a 0.05 level of significance?

ANSWER: reject TYPE: PR DIFFICULTY: Easy KEYWORDS: logistic regression, Wald statistic, decision 327. True or False: Referring to SCENARIO 13-19, there is not enough evidence to conclude that Income makes a significant contribution to the model in the presence of LawnSize at a 0.05 level of significance.

ANSWER: False TYPE: TF DIFFICULTY: moderate KEYWORDS: logistic regression, Wald statistic, conclusion 328. Referring to SCENARIO 13-19, what is the p-value of the test statistic when testing whether LawnSize makes a significant contribution to the model in the presence of Income?

ANSWER: 0.0662 TYPE: PR DIFFICULTY: Easy KEYWORDS: logistic regression, Wald statistic, p-value

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Multiple Regression 13-85 329. Referring to SCENARIO 13-19, what should be the decision (‘reject’ or ‘do not reject’) on the null hypothesis when testing whether LawnSize makes a significant contribution to the model in the presence of Income at a 0.05 level of significance?

ANSWER: Do not reject TYPE: PR DIFFICULTY: Easy KEYWORDS: logistic regression, Wald statistic, decision 330. True or False: Referring to SCENARIO 13-19, there is not enough evidence to conclude that LawnSize makes a significant contribution to the model in the presence of Income at a 0.05 level of significance.

ANSWER: True TYPE: TF DIFFICULTY: moderate KEYWORDS: logistic regression, Wald statistic, conclusion 331. Which of the following is used to determine observations that have influential effect on the fitted model? a) Durbin Watson statistic b) Variance inflationary factor c) The Cp statistic d) Cook’s distance statistic ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: influence analysis 332. Which of the following is NOT used to determine observations that have influential effect on the fitted model? a) The hat matrix elements hi b) The studentized deleted residuals ti c) The Cp statistic d) Cook’s distance statistic ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: influence analysis

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13-86

Multiple Regression

333. Using the hat matrix elements hi to determine influential points in a multiple regression model with k independent variable and n observations, Xi is an influential point if a)

hi  2  k  1 / n

b) hi  2  k  1 / n c)

hi  n  k  1 / 2

d) hi  n  k  1 / 2 ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: influence analysis 334. Using the Studentized residuals ti to determine influential points in a multiple regression model with k independent variable and n observations and letting tn-k-2 denote the upper critical value of a two-tail t test with a 0.10 level of significance, Xi is an influential point if a)

ti  tnk 1

b)

ti  tnk 1

c)

ti  tnk 2

d)

ti  tnk 2

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: influence analysis 335. Using the Cook’s distance statistic Di to determine influential points in a multiple regression model with k independent variable and n observations and letting F1,2 denote the critical value of an F distribution with  1 and  2 degrees of freedom at a 0.50 level of significance, Xi is an influential point if a)

Di  Fk1,nk1

b)

Di  Fk1,nk1

c)

Di  Fnk1,k1

d)

Di  Fnk1,k1

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: influence analysis

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Multiple Regression 13-87 336. True or False: Only when all three of the hat matrix elements hi, the Studentized deleted residuals ti and the Cook’s distance statistic Di reveal consistent result should an observation be removed from the regression analysis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: influence analysis 341. A plot of the residuals versus an independent X shows evidence of a curvilinear effect. Which of the following statements is a possible solution? a. b. c. d.

Transform the Y variable.

Use the Durbin-Watson statistic to determine if there is autocorrelation.

Add a curvilinear independent variable to the multiple regression model.

Check for autocorrelation among the residuals.

ANSWER: c TYPE: MC DIFFICULTY: Difficult KEYWORDS: multiple regression residual analysis, page 546, text.

342. True or False: To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Dummy variable, interactive term, cross-product term, page 557 text 343.

True or False: The following two statements are equivalent in meaning: A. B.

The test of significance for a specific regression coefficient in a multiple regression model is a test of significance for adding that variable into the model given the other variable is included.

The t test for a regression coefficient is actually a test for the contribution of that independent variable.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: tests of hypothesis, t tests, page 549 text

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Business Analytics

14-1

CHAPTER 14: BUSINESS ANALYTICS 1. Which of the following disciplines is typically NOT involved in business analytics? a) Economics b) Statistics c) Information system d) Management science

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: analytic methods, definition 2. Which of the following is NOT among the three broad categories of analytic methods? a) Predictive analytics b) Prescriptive analytics c) Productive analytics d) Descriptive analytics

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: analytic methods, definition 3. Which of the following finds relationships in data that may not be readily apparent? a) Predictive analytics b) Prescriptive analytics c) Productive analytics d) Descriptive analytics ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: analytic methods, predictive analytics 4. Which of the following investigates what should occur and suggest the best course of action for the future? a) Predictive analytics b) Prescriptive analytics c) Productive analytics d) Descriptive analytics ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: analytic methods, prescriptive analytics, definition

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14-2

Business Analytics

5. Which of the following explores business activities that have occurred or are occurring in the present moment? a) Predictive analytics b) Prescriptive analytics c) Productive analytics d) Descriptive analytics ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, definition 6. Dashboards may contain which of the following? a) Treemaps b) Gauges c) Contingency table d) All of the above ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, dashboards, treemaps, gauges, bullet graphs 7. True or False: Most information design specialists prefer bullet graphs over gauges because bullet graphs foster the direct comparison of each measurement.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, dashboards, bullet graphs, gauges 8. True or False: Treemaps that use color to represent the value of a second variable, thereby increasing the data density of the displays, is an example of chartjunk.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, dashboards treemaps, chartjunk

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Business Analytics

14-3

9. True or False: Bullet graphs that use color to represent the value of a second variable, thereby increasing the data density of the displays, is an example of chartjunk.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, dashboards bullet graphs, chartjunk 10. True or False: Double-clicking a cell in a PivotTable causes Excel to drill down and display the underlying data in a new worksheet.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, data discovery, drill down, PivotTable, multidimensional contingency table, organizing and visualizing many variables 11. True or False: You can compute any of the numerical descriptive statistics for the variables of the new worksheet that a drill-down in a PivotTable creates.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, data discovery, drill down, PivotTable, multidimensional contingency table, organizing and visualizing many variables 12. True or False: Some business analytics are performed by adding variables to see if unforeseen relationships are uncovered.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, data discovery

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14-4

Business Analytics

13. True or False: Some business analytics involve starting with many variables, followed by filtering the data by exploring specific combinations of categorical values or numerical range.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, data discovery, filter 14. True or False: Some business analytics involve starting with many variables, followed by filtering the data by exploring specific combinations of categorical values or numerical range. In Excel, this approach is mimicked by using a drill-down.

ANSWER: False TYPE: TF DIFFICULTY: Moderate EXPLANATION: Excel has no drill-down except as a pivot table.

KEYWORDS: analytic methods, descriptive analytics, data discovery, filter, PivotTable, drill-down 15. True or False: Some business analytics involve starting with many variables, followed by filtering the data by exploring specific combinations of categorical values or numerical range. In Excel, this approach is mimicked by using a slicer.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, data discovery, filter, PivotTable, slicer 16. True or False: Some business analytics involve starting with many variables, followed by filtering the data by exploring specific combinations of categorical values or numerical range. In Excel, this approach is mimicked by using gauges.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, data discovery, filter, PivotTable, gauges 17. True or False: In real-world business analytics, filtering is typically performed on large data based on complex conditional relationships.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, data discovery, filter, PivotTable 18. True or False: There is no significant difference between filtering performed in a complex realworld business analytic and filtering performed using the slicers in a PivotTable in Excel.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, data discovery, filter, PivotTable, slicer

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Business Analytics

14-5

SCENARIO 14-1 The table below contains the sparklines for the rates of return (in percentage) for three different stocks from 2007 to 2013.

Stock

2007

2008

2009

Year 2010

A

15.9

36.9

-41.3

55.9

42.5

-21.1

18

B

23.2

11.2

25.1

23.9

10.2

30.8

0.1

C

20.5

42.6

-26.9

49.3

83.7

-9.8

21.5

2011

2012

2013

19. Referring to SCENARIO 14-1, the rates of return of stock ____ have the smallest variation among the three.

ANSWER: B TYPE: FI DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, sparklines 20. Referring to SCENARIO 14-1, the pattern of the rates of return of stock ____ and stock ____ are similar.

ANSWER: A, C TYPE: FI DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, sparklines 21. True or False: Referring to SCENARIO 14-1, the sparklines enable you to draw conclusions on the historical trend of the rates of return of the three stocks.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, sparklines 22. True or False: Referring to SCENARIO 14-1, the sparklines enable you to conclude that the rates of return of the stock market in general are volatile from 2007 to 2013.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, sparklines 23. True or False: Referring to SCENARIO 14-1, the sparklines enable you to predict that the rates of return of the stock market in 2014 will be higher than in 2013.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, sparklines Copyright ©2020 Pearson Education, Inc.

14-6

Business Analytics

24. True or False: Referring to SCENARIO 14-1, the sparklines enable you to predict that the rates of return of the stock market in 2014 will be about the same as in 2013.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, sparklines SCENARIO 14-2 The treemap below shows the amounts (size) measured in billions of US dollars and percentage changes from prior year (color) of business-to-consumer ecommerce sales last year for North America, Asia Pacific, Western Europe, Central & Eastern Europe, Latin America, and Middle East & Africa.

25. Referring to SCENARIO 14-2, which region has the largest amount of business-to-consumer ecommerce sales last year?

ANSWER: North America TYPE: PR DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, treemaps 26. Referring to SCENARIO 14-2, which region has the fastest growth in business-to-consumer ecommerce sales last year?

ANSWER: Asia Pacific TYPE: PR DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, treemaps

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Business Analytics

14-7

27. Referring to SCENARIO 14-2, which region has the smallest amount of business-to-consumer ecommerce sales last year?

ANSWER: Middle East & Africa TYPE: PR DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, treemaps 28. Referring to SCENARIO 14-2, which region has the slowest growth in business-to-consumer ecommerce sales last year?

ANSWER: Western Europe TYPE: PR DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, treemaps 29. True or False: Referring to SCENARIO 14-2, the Asia Pacific region has the largest amount of business-to-consumer ecommerce sales last year.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, treemaps 30. True or False: Referring to SCENARIO 14-2, the Western Europe region has the largest amount of business-to-consumer ecommerce sales last year.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, treemaps 31. True or False: Referring to SCENARIO 14-2, the Middle East & Africa region has the slowest growth in business-to-consumer ecommerce sales last year.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, treemaps 32. True or False: Referring to SCENARIO 14-2, the North America region has the fastest growth in business-to-consumer ecommerce sales last year.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: analytic methods, descriptive analytics, treemaps

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14-8

Business Analytics

33. Which of the following is NOT one of the categories of predictive analytics methods? a) Clustering b) Recommendation c) Association d) Prediction

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Predictive Analytics, definition 34. Which of the following is NOT one of the categories of predictive analytics methods? a) Classification b) Clustering c) Association d) Description

ANSWER: d TYPE: MC DIFFICULTY: Easy KEYWORDS: Predictive Analytics, definition 35. Which of the following is NOT among the predictive analytics methods covered in the book? a) Principle component analysis b) Neural networks c) Cluster analysis d) Multidimensional scaling

ANSWER: a or b TYPE: MC DIFFICULTY: Easy KEYWORDS: Predictive Analytics, definition 36. Which of the following is NOT among the predictive analytics methods covered in the book? a) Neural networks b) Simple component analysis c) Cluster analysis d) Multidimensional scaling

ANSWER: a or b TYPE: MC DIFFICULTY: Easy KEYWORDS: Predictive Analytics, definition

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Business Analytics

14-9

37. Which of the following is NOT among the predictive analytics methods covered in the book? a) Neural networks b) Cluster analysis c) Factor analysis d) Multidimensional scaling

ANSWER: c or d TYPE: MC DIFFICULTY: Easy KEYWORDS: Predictive Analytics, definition 38. True or False: Data mining is used mostly in the mining industry.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: Predictive Analytics, data mining, definition 39. True or False: Data mining uses various techniques to extract useful information from huge depositories of data.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: Predictive Analytics, data mining, definition 40. True or False: In a classification tree, the dependent variable is a categorical variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree 41. True or False: In a regression tree, the dependent variable is a categorical variable.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree 42. True or False: Successful implementation of a classification tree requires objective criteria for splitting the data at each node based on a dependent variable.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: classification, classification tree, characteristics

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14-10

Business Analytics

43. True or False: Successful implementation of a regression tree requires rules for deciding when a branch of the tree cannot be split any more.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, characteristics 44. True or False: Successful implementation of a regression tree requires a method to provide prediction for the target variable at each of the nodes.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, characteristics 45. True or False: Successful use of a regression tree requires a precise description of the parameters of the tree.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, characteristics 46. True or False: Successful implementation of a classification tree requires rules for splitting the data at each node based on an independent variable.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, characteristics 47. True or False: Splitting of a node might be followed by pruning if necessary in a classification tree.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, characteristics 48. True or False: Splitting is always followed by pruning in a classification tree.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, characteristics

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Business Analytics

14-11

49. True or False: Classification tree is not sensitive to the distribution of the independent variables.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, characteristics 50. True or False: The result of the regression tree is affected by the distribution of the independent variables.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: classification, regression tree, characteristics 51. True or False: The Akaike information criteria (AIC) or the corrected Akaike information criteria (AICc) can be used to compare alternative models chosen by the classification tree.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, Akaike information criteria, corrected Akaike information criteria 52. True or False: The Akaike information criteria (AIC) or the corrected Akaike information criteria (AICc) is a measure of the probability that can be attributed to the response that has occurred.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, Akaike information criteria, corrected Akaike information criteria 53. True or False: The LogWorth statistic is used to decide when to split a node of a regression tree.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, LogWorth statistic 54. True or False: The LogWorth statistic is a measure of the probability that can be attributed to the response that has occurred.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, LogWorth statistic

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14-12

Business Analytics 2

55. True or False: The likelihood ratio chi square statistic G is a measure of the probability that can be attributed to the response that has occurred.

ANSWER: True TYPE: TF DIFFICULTY: Easy 2 KEYWORDS: classification, classification tree, G statistic SCENARIO 14-3 The tree diagram below shows the results of the classification tree model that has been constructed to predict the probability of a cable company’s customers who will switch (“Yes” or “No”) into its bundled program offering based on the price ($30, $40, $50, $60) and whether the customer spends more than 5 hours a day watching TV (“Yes” or “No”) using the data set of 100 customers collected from a survey.

56. Referring to SCENARIO 14-3, what percentage of the variation in whether a customer will switch into its bundled program offering can be explained by the price and whether the customer spends more than 5 hours a day watching TV? ANSWER: 10.9% or 0.109 TYPE: PR DIFFICULTY: Easy KEYWORDS: classification, classification tree, interpretation

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Business Analytics

14-13

57. Referring to SCENARIO 14-3, the first split occurs at what price?

ANSWER: $50 TYPE: PR DIFFICULTY: Easy KEYWORDS: classification, classification tree, interpretation 58. Referring to SCENARIO 14-3, what is the highest rate of switching into the bundled offering?

ANSWER: 0.3889 or 38.89% TYPE: PR DIFFICULTY: Easy KEYWORDS: classification, classification tree, interpretation 59. Referring to SCENARIO 14-3, what is the lowest rate of switching into the bundled offering?

ANSWER: 0.0000 or 0.00% TYPE: PR DIFFICULTY: Easy KEYWORDS: classification, classification tree, interpretation 60. True or False: Referring to SCENARIO 14-3, the highest probability of switching is predicted to occur among customers who watch more than 5 hours of TV a day and are offered the bundled price of higher than $50.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, interpretation 61. True or False: Referring to SCENARIO 14-3, the highest probability of switching is predicted to occur among customers who watch more than 5 hours of TV a day and are offered the bundled price of between $30 and $40.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: classification, classification tree, interpretation 62. True or False: Referring to SCENARIO 14-3, the highest probability of switching is predicted to occur among customers who watch more than 5 hours of TV a day and are offered the bundled price of lower than $50.

ANSWER: False TYPE: TF DIFFICULTY: Difficult KEYWORDS: classification, classification tree, interpretation

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14-14

Business Analytics

63. True or False: Referring to SCENARIO 14-3, the highest probability of switching is predicted to occur among customers who watch more than 5 hours of TV a day and are offered the bundled price of higher than $40.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: classification, classification tree, interpretation 64. True or False: Referring to SCENARIO 14-3, the highest probability of switching is predicted to occur among customers who do not watch more than 5 hours of TV a day and are offered the bundled price of higher than $50.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, interpretation 65. True or False: Referring to SCENARIO 14-3, the highest probability of switching is predicted to occur among customers who do not watch more than 5 hours of TV a day and are offered the bundled price of lower than $50.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, classification tree, interpretation

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Business Analytics

14-15

SCENARIO 14-4 The regression tree below was obtained for predicting the weekend box office revenue of a newly released movie (in thousands of dollars) based on data collected in different cities on the expenditure (at $25, $30, $35, $40, $45, $50, $55, $60, $65 or $70 thousand) spent on TV advertising and the number of times (10, 15, 20, 25, 30 or 35) a day the advertisement appear on TV.

66. Referring to SCENARIO 14-4, what percentage of the variation in weekend box office revenue can be explained by the amount spent on TV advertising and the number of times a day the advertisement appears on TV? ANSWER: 78.2% or 0.782 TYPE: PR DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation 67. Referring to SCENARIO 14-4, how many cities were used in generating the regression tree?

ANSWER: 21 TYPE: PR DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation 68. True or False: Referring to SCENARIO 14-4, the first split occurs at $45 thousand spent on TV advertising.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation Copyright ©2020 Pearson Education, Inc.

14-16

Business Analytics

69. True or False: Referring to SCENARIO 14-4, the first split occurs at 25 TV appearances a day of the advertisement.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation 70. True or False: Referring to SCENARIO 14-4, the highest mean weekend box office revenue is predicted to occur with at least $45 thousand spent on TV advertisement and at least 25 advertisement appearances a day.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation 71. True or False: Referring to SCENARIO 14-4, the highest mean weekend box office revenue is predicted to occur with at least $45 thousand spent on TV advertisement and fewer than 25 advertisement appearances a day.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation 72. True or False: Referring to SCENARIO 14-4, the highest mean weekend box office revenue is predicted to occur with less than $45 thousand spent on TV advertisement and fewer than 25 advertisement appearances a day.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation 73. True or False: Referring to SCENARIO 14-4, the highest mean weekend box office revenue is predicted to occur with $55 thousand spent on TV advertisement and at least 25 advertisement appearances a day.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation 74. True or False: Referring to SCENARIO 14-4, the highest mean weekend box office revenue is predicted to occur with $30 thousand spent on TV advertisement and 30 advertisement appearances a day.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation Copyright ©2020 Pearson Education, Inc.

Business Analytics

14-17

75. True or False: Referring to SCENARIO 14-4, the highest mean weekend box office revenue is predicted to occur with $55 thousands spent on TV advertisement and 35 advertisement appearances a day.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: classification, regression tree, interpretation 76. True or False: Neural networks do not make any a priori assumption about the distribution of the data and, hence, are nonparametric methods.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: neural networks, properties 77. True or False: Multilayer perceptrons usually contain an input layer, a hidden layer and an output layer.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: neural networks, properties 78. True or False: The forward-and-backward computation among the three layers of a multilayer perceptron is repeated until the output layer detects that the difference between the predicted results and the target values has been minimized or is at an acceptable level.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: neural networks, properties 79. True or False: Neural networks require only training data but not validating data.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: neural networks, properties 80. True or False: Neural networks use the validating data to uncover a model and then the training data to see if the model can make the correct prediction or classification.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: neural networks, properties

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14-18

Business Analytics 81. True or False: Neural networks can suffer from poor quality of data, insufficient data, or overfitted models.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: neural networks, properties SCENARIO 14-5 The output below shows the results of the neural network model that has been constructed to predict the probability of a cable company’s customers who will switch (“Yes” or “No”) into its bundled program offering based on the price ($30, $40, $50, $60) and whether the customer spends more than 5 hours a day watching TV (“Yes” or “No”) using the data set of 100 customers collected from a survey.

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Business Analytics

14-19

82. Referring to SCENARIO 14-5, the misclassification rate of 0.2058824 in the validation data set means that how many customers in the validation data are incorrectly classified?

ANSWER: 7 TYPE: PR DIFFICULTY: Easy KEYWORDS: neural networks, interpretation 83. Referring to SCENARIO 14-5, out of the 27 customers who did not switch in the validation data set, how many are correctly classified by the neural network?

ANSWER: 27 TYPE: PR DIFFICULTY: Easy KEYWORDS: neural networks, interpretation 84. Referring to SCENARIO 14-5, out of the 7 customers who did switch in the validation data set, how many are correctly classified by the neural network?

ANSWER: 0 TYPE: PR DIFFICULTY: Easy KEYWORDS: neural networks, interpretation

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14-20

Business Analytics

SCENARIO 14-6 The neural network output below was obtained for predicting the weekend box office revenue of a newly released movie (in thousands of dollars) based on data collected in different cities on the expenditure (at $25, $30, $35, $40, $45, $50, $55, $60 $65 or $70 thousands) spent on TV advertising and the number of times (10, 15, 20, 25, 30 or 35) a day the advertisement appear on TV.

85. Referring to SCENARIO 14-6, what is the r-square of model for the validating data?

ANSWER: 0.7634434 TYPE: PR DIFFICULTY: Easy KEYWORDS: neural networks, interpretation

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Business Analytics

14-21

86. Referring to SCENARIO 14-6, what is the r-square of model for the training data?

ANSWER: 0.974434 TYPE: PR DIFFICULTY: Easy KEYWORDS: neural networks, interpretation 87. Referring to SCENARIO 14-6, how many hidden nodes are used in the neural network model?

ANSWER: 3 TYPE: PR DIFFICULTY: Easy KEYWORDS: neural networks, interpretation 88. True or False: Each observation is treated as its own cluster at the beginning in hierarchical clustering.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, properties 89. True or False: Each observation is treated as its own cluster at the beginning in k-means clustering.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, properties 90. True or False: In k-means clustering, observations that are assigned to a cluster may never be reassigned to a different cluster later in the process.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, properties 91. True or False: Complete linkage can be used to measure the distance between objects in cluster analysis.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, properties 92. True or False: Euclidean distance can be used to measure the distance between objects in cluster analysis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, properties Copyright ©2020 Pearson Education, Inc.

14-22

Business Analytics 93. True or False: Ward’s minimum variance can be used to measure the distance between clusters in cluster analysis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, properties 94. True or False: Single linkage can be used to measure the distance between objects in cluster analysis.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, properties 95. True or False: Average linkage can be used to measure the distance between clusters in cluster analysis.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, properties

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Business Analytics

14-23

SCENARIO 14-7 The output below shows the results of cluster analysis on the different regions of the world (North America, Asia Pacific, Western Europe, Central & Eastern Europe, Latin America, and Middle East & Africa) based on the amounts (in billions of US dollars) and the percentage changes from prior year of business-to-consumer ecommerce sales last year.

96. Referring to SCENARIO 14-7, what are the first group of countries that cluster together?

ANSWER: Central & Eastern Europe, Latin America TYPE: PR DIFFICULTY: Easy KEYWORDS: cluster analysis, interpretation, complete linkage, single linkage 97. True or False: Referring to SCENARIO 14-7, the “complete” method is used to measure the distance between objects within a cluster.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, interpretation, complete linkage

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14-24

Business Analytics 98. True or False: Referring to SCENARIO 14-7, the “complete” method is used to measure the distance between clusters.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, interpretation 99. True or False: Referring to SCENARIO 14-7, North America and Western Europe are the second groups of countries that cluster together.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, interpretation 100. True or False: Referring to SCENARIO 14-7, Middle East & Africa is the next region that clusters with the Central & Eastern Europe and Latin America cluster.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: cluster analysis, interpretation 101. True or False: Referring to SCENARIO 14-7, at the two-cluster level, Asia Pacific alone makes up one of the two clusters.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: cluster analysis, interpretation 102. True or False: In metric multidimensional scaling, the distance between objects is ratio scaled.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: multidimensional scaling, properties 103. True or False: In nonmetric multidimensional scaling, the distance between objects is ordinal scaled.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: multidimensional scaling, properties

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Business Analytics

14-25

104. True or False: In multidimensional scaling, the stress statistic is used to measure the distance between objects.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: multidimensional scaling, properties 105. True or False: In multidimensional scaling, the stress statistic is used to measure the goodness of fit of the results to the data.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: multidimensional scaling, properties 106. True or False: In multidimensional scaling, the general rule is to increase the number of dimensions as long as the stress statistic decreases substantially.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: multidimensional scaling, properties 107. True or False: In multidimensional scaling, the general rule in to increase the number of dimensions as long as the stress statistic increases substantially.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: multidimensional scaling, properties 108. True or False: In multidimensional scaling, the larger the stress statistic, the better is the fit.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: multidimensional scaling, properties 109. True or False: In multidimensional scaling, the Euclidean distance is most commonly used to measure the distance between objects.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: multidimensional scaling, properties

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14-26

Business Analytics 110.

Which of the following is not true concerning overfitting? a) b) c) d)

It may result from using the training data inappropriately It attempts to describe the random error thereby making the model less useful.

It does not violate the law of parsimony.

Over fitted models may work poorly when using new data.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: prescriptive analytics, supervised methods, page 680 111. Being able to monitor business activities in near real time is a feature most associated with: a) b) c) d)

Classification methods Prescriptive analytics Regression trees Descriptive analytics

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: analytic methods, descriptive analytics, dashboards page 682.

112. True or False: The prescriptive analytics technique in which the decision maker sets constraints that reflect resource limitations to determine how the process works most effectively is called simulation.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: Prescriptive analytics, optimization, simulation, page 555.

113. True or False: The prescriptive analytics technique in which the decision maker repeatedly runs a predictive analytics model while varying the assumptions or data in the model to create a set of results that offer choices about the business process being modeled is called simulation.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Prescriptive analytics, optimization, simulation, page 555.

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Statistical Applications in Quality Management

15-1

STATISTICAL APPLICATIONS IN QUALITY MANAGEMENT 1. The control chart a) focuses on the time dimension of a system. b) captures the natural variability in the system. c) can be used for categorical, discrete, or continuous variables. d) All of the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: control chart 2. Variation signaled by individual fluctuations or patterns in the data is called a) special or assignable causes. b) common or chance causes. c) explained variation. d) the standard deviation.

ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: special causes of variation 3. Variation due to the inherent variability in a system of operation is called a) special or assignable causes. b) common or chance causes. c) explained variation. d) the standard deviation.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: common causes of variation 4. The principal focus of the control chart is the attempt to separate special or assignable causes of variation from common causes of variation. Which causes of variation can be reduced only by changing the system? a) Special or assignable causes b) Common causes c) Total causes d) None of the above ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: common causes of variation

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15-2

Statistical Applications in Quality Management

5. Once the control limits are set for a control chart, one attempts to a) discern patterns that might exist in values over time. b) determine whether any points fall outside the control limits. c) Both of the above. d) None of the above.

ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: control chart 6. Which of the following situations suggests a process that appears to be operating in a state of statistical control? a) A control chart with a series of consecutive points that are above the center line and a series of consecutive points that are below the center line. b) A control chart in which no points fall outside either the upper control limit or the lower control limit and no patterns are present. c) A control chart in which several points fall outside the upper control limit. d) All of the above.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: control chart, statistical control 7. Which of the following situations suggests a process that appears to be operating out of statistical control? a) A control chart with a series of consecutive points that are above the center line and a series of consecutive points that are below the center line. b) A control chart in which points fall outside the lower control limit. c) A control chart in which several points fall outside the upper control limit. d) All of the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: control chart, statistical control 8. A process is said to be out of control if a) a point falls above the upper or below the lower control lines. b) eight or more consecutive points fall above the center line or eight or more consecutive points fall below the center line. c) Either of the above. d) None of the above.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: statistical control

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Statistical Applications in Quality Management

15-3

9. One of the morals of the red bead experiment is: a) variation is part of the process. b) only management can change the system. c) it is the system that primarily determines performance. d) All of the above.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: red bead experiment SCENARIO 15-1 A local newspaper has 10 delivery boys who each deliver the morning paper to 50 customers every day. The owner decides to record the number of papers delivered on time for a 10-day period for one of the delivery boys and construct a p chart to see whether the percentage is too erratic.

Number of Papers Day Delivered on Time 1 46 2 45 3 46 4 45 5 43 6 48 7 46 8 49 9 48 10 47 10. Referring to SCENARIO 15-1, what is the numerical value of the center line for the p chart? a) 0.926 b) 0.911 c) 0.885 d) 0.500 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: p chart, center line 11. Referring to SCENARIO 15-1, what is the numerical value of the lower control limit for the p chart? a) 0.920 b) 0.911 c) 0.815 d) 0.798 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: p chart, control limit Copyright ©2020 Pearson Education, Inc.

15-4

Statistical Applications in Quality Management

12. Referring to SCENARIO 15-1, what is the numerical value of the upper control limit for the p chart? a) 0.926 b) 0.961 c) 0.979 d) 1.037 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: p chart, control limit 13. Referring to SCENARIO 15-1, which expression best characterizes the p chart? a) Cycles b) Increasing trend c) In-control d) Individual outliers ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: p chart SCENARIO 15-2 A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to construct a p chart to see if the percentage favoring the incumbent candidate is too erratic.

Sample Number Favoring (Day) Incumbent Candidate 1 57 2 57 3 53 4 51 5 55 6 60 7 56 8 59 14. Referring to SCENARIO 15-2, what is the numerical value of the center line for the p chart? a) 0.53 b) 0.56 c) 0.63 d) 0.66 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: p chart, center line

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Statistical Applications in Quality Management

15-5

15. Referring to SCENARIO 15-2, what is the numerical value of the lower control limit for the p chart? a) 0.37 b) 0.41 c) 0.50 d) 0.71 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: p chart, control limit 16. Referring to SCENARIO 15-2, what is the numerical value of the upper control limit for the p chart? a) 0.92 b) 0.89 c) 0.71 d) 0.62 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: p chart, control limit 17. Referring to SCENARIO 15-2, which expression best characterizes the p chart? a) In-control b) Increasing trend c) Decreasing trend d) Individual outliers ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: p chart

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15-6

Statistical Applications in Quality Management

SCENARIO 15-3 A quality control analyst for a light bulb manufacturer is concerned that the time it takes to produce a batch of light bulbs is too erratic. Accordingly, the analyst randomly surveys 10 production periods each day for 14 days and records the sample mean and range for each day.

Day X (in minutes) R 1 58.5 5.1 2 47.6 7.8 3 64.3 6.1 4 60.6 5.7 5 63.7 6.2 6 57.5 6.0 7 55.0 5.4 8 54.9 6.1 9 55.0 5.9 10 62.7 5.0 11 61.9 7.1 12 60.0 6.5 13 58.3 5.9 14 52.0 5.2 18. Referring to SCENARIO 15-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the center line of this R chart? a) 4.8 b) 6.0 c) 6.9 d) 7.1 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: R chart, center line 19. Referring to SCENARIO 15-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the lower control limit for this R chart? a) 4.84 b) 3.37 c) 2.98 d) 1.34 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: R chart, control limit

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Statistical Applications in Quality Management

15-7

20. Referring to SCENARIO 15-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. What is the upper control limit for this R chart? a) 10.66 b) 9.37 c) 7.98 d) 6.34 ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: R chart, control limit 21. Referring to SCENARIO 15-3, suppose the analyst constructs an R chart to see if the variability in production times is in-control. The R chart is characterized by which of the following? a) Increasing trend b) Decreasing trend c) In-control d) Points outside the control limits ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: R chart 22. Referring to SCENARIO 15-3, suppose the sample mean and range data were based on 11 observations per day instead of 10. How would this change affect the lower and upper control limits of the R chart? a) LCL would increase; UCL would decrease. b) LCL would remain the same; UCL would decrease. c) Both LCL and UCL would remain the same. d) LCL would decrease; UCL would increase.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: control limit 23. Referring to SCENARIO 15-3, suppose the analyst constructs an X chart to see if the production process is in-control. What is the center line for this chart? a) 64.3 b) 59.5 c) 58.0 d) 57.1 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: XBar chart, center line

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15-8

Statistical Applications in Quality Management

24. Referring to SCENARIO 15-3, suppose the analyst constructs an X chart to see if the production process is in-control. What is the lower control limit (LCL) for this chart? a) 47.60 b) 56.15 c) 57.15 d) 58.05 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: XBar chart, control limit 25. Referring to SCENARIO 15-3, suppose the analyst constructs an X chart to see if the production process is in-control. What is the upper control limit (UCL) for this chart? a) 62.15 b) 60.95 c) 59.85 d) 58.75 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: XBar chart, control limit 26. Referring to SCENARIO 15-3, suppose the analyst constructs an X chart to see if the production process is in-control. Which expression best describes this chart? a) In-control b) Increasing trend c) Decreasing trend d) Individual outliers ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: XBar chart

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Statistical Applications in Quality Management

15-9

SCENARIO 15-4 A factory supervisor is concerned that the time it takes workers to complete an important production task (measured in seconds) is too erratic and adversely affects expected profits. The supervisor proceeds by randomly sampling 5 individuals per hour for a period of 10 hours. The sample mean and range for each hour are listed below.

Hour R X 1 18.4 25 2 16.9 27 3 23.0 30 4 21.2 23 5 21.0 24 6 24.0 25 7 19.3 12 8 15.8 14 9 20.0 13 10 23.0 11 She also decides that lower and upper specification limit for the critical-to-quality variable should be 10 and 30 seconds, respectively.

27. Referring to SCENARIO 15-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What is the center line of this R chart? a) 20.00 b) 20.56 c) 20.40 d) 24.00 ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: R chart, center line 28. Referring to SCENARIO 15-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. What are the lower and upper control limits for this R chart? a) – 2.33, 43.13 b) – 2.28, 42.28 c) 0, 42.28 d) 0, 43.13 ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: R chart, control limit

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15-10

Statistical Applications in Quality Management

29. Referring to SCENARIO 15-4, suppose the supervisor constructs an R chart to see if the variability in collection times is in-control. This R chart is characterized by which of the following? a) Decreasing trend b) Increasing trend c) In-control d) Individual outliers ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: R chart 30. Referring to SCENARIO 15-4, suppose the sample mean and range data were based on 6 observations per hour instead of 5. How would this change affect the lower and upper control limits of an R chart? a) LCL would increase; UCL would decrease. b) LCL would remain the same; UCL would decrease. c) Both LCL and UCL would remain the same. d) LCL would decrease; UCL would increase.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: R chart, control limit 31. Referring to SCENARIO 15-4, suppose the supervisor constructs an X chart to see if the process is in-control. What is the center line of the chart? a) 20.00 b) 20.26 c) 21.00 d) 24.26 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: XBar chart, center line 32. Referring to SCENARIO 15-4, suppose the supervisor constructs an X chart to see if the process is in-control. What are the lower and upper control limits of this chart? a) 10.00, 30.00 b) 8.49, 32.03 c) 5.39, 35.13 d) 4.96, 35.56 ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: XBar chart, control limit

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Statistical Applications in Quality Management

15-11

33. Referring to SCENARIO 15-4, suppose the supervisor constructs an X chart to see if the process is in-control. Which expression best describes this chart? a) Decreasing trend b) In-control c) Increasing trend d) Individual outliers ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: XBar chart 34. Referring to SCENARIO 15-4, what is the value of d 2 factor?

ANSWER: 2.326 TYPE: PR DIFFICULTY: Easy KEYWORDS: d2 factor 35. Referring to SCENARIO 15-4, what percentage of the time it takes workers to complete an important production task will fall inside the specification limits?

ANSWER: 0.75 TYPE: PR DIFFICULTY: Moderate KEYWORDS: process capacity 36. Referring to SCENARIO 15-4, what is the value of the C p index?

ANSWER: 0.38 TYPE: PR DIFFICULTY: Easy KEYWORDS: Cp index 37. Referring to SCENARIO 15-4, what is the value of the CPL index?

ANSWER: 0.39 TYPE: PR DIFFICULTY: Easy KEYWORDS: CPL index 38. Referring to SCENARIO 15-4, what is the value of the CPU index?

ANSWER: 0.37 TYPE: PR DIFFICULTY: Easy KEYWORDS: CPU index

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Statistical Applications in Quality Management

39. Referring to SCENARIO 15-4, what is the value of the C pk index?

ANSWER: 0.37 TYPE: PR DIFFICULTY: Easy KEYWORDS: Cpk index 40. True or False: The control limits are based on the standard deviation of the process.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: control limit 41. True or False: The purpose of a control chart is to eliminate common cause variation.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: control chart, common causes of variation 42. True or False: Special or assignable causes of variation are signaled by individual fluctuations or patterns in the data.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: special causes of variation 43. True or False: Common causes of variation represent variation due to the inherent variability in the system.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: common causes of variation 44. True or False: Common causes of variation are correctable without modifying the system.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: common causes of variation 45. True or False: Changes in the system to reduce common cause variation are the responsibility of management.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: common causes of variation Copyright ©2020 Pearson Education, Inc.

Statistical Applications in Quality Management

15-13

46. True or False: One of the morals of the red bead experiment is that variation is part of any process.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: red bead experiment 47. True or False: In the United States, the control limits on a control chart are placed so that they are 3 standard deviations above and below a central line.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: control chart, control limit 48. True or False: The p chart is a control chart used for monitoring the proportion of items that meet given specifications.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: p chart 49. True or False: The R chart is a control chart used to monitor a process mean.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: R chart 50. True or False: It is not possible for the X chart to be out-of-control when the R chart is in control.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: XBar chart, R chart, statistical control 51. The cause of variation that can be reduced only by changing the system is ______ cause variation.

ANSWER: common TYPE: FI DIFFICULTY: Easy KEYWORDS: common causes of variation

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Statistical Applications in Quality Management

52. _______ causes of variation are correctable without modifying the system.

ANSWER: Special TYPE: FI DIFFICULTY: Easy KEYWORDS: special causes of variation SCENARIO 15-5 A manufacturer of computer disks took samples of 240 disks on 15 consecutive days. The number of disks with bad sectors was determined for each of these samples. The results are in the table that follows.

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Bad 9 7 4 6 8 3 6 10 16 24 15 9 4 8 6

% Bad 0.037500 0.029167 0.016667 0.025000 0.033333 0.012500 0.025000 0.041667 0.066667 0.100000 0.062500 0.037500 0.016667 0.033333 0.025000

53. Referring to SCENARIO 15-5, the best estimate of the mean proportion of disks with bad sectors is __________.

ANSWER: 0.0375 TYPE: FI DIFFICULTY: Moderate KEYWORDS: p chart, center line 54. Referring to SCENARIO 15-5, a p control chart is to be made for these data. The center line of the control chart is __________.

ANSWER: 0.0375 TYPE: FI DIFFICULTY: Moderate KEYWORDS: p chart, center line

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Statistical Applications in Quality Management

15-15

55. Referring to SCENARIO 15-5, a p control chart is to be made for these data. The estimate of the standard error of the proportion of disks with bad sectors is __________.

ANSWER: 0.03679/3 or 0.01226 TYPE: FI DIFFICULTY: Moderate KEYWORDS: p chart, standard error 56. Referring to SCENARIO 15-5, a p control chart is to be made for these data. The upper control limit is __________, and the lower control limit is __________.

ANSWER: 0.0743; 0.00071 TYPE: FI DIFFICULTY: Moderate KEYWORDS: p chart, control limit 57. Referring to SCENARIO 15-5, construct a p control chart for these data.

ANSWER: Proportion of Bad Disks in Samples of Size 240 p Chart 0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0

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Sample Number

TYPE: PR DIFFICULTY: Difficult KEYWORDS: p chart 58. True or False: Referring to SCENARIO 15-5, the process seems to be in control.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: p chart, statistical control

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Statistical Applications in Quality Management

SCENARIO 15-6 The maker of a packaged candy wants to evaluate the quality of her production process. On each of 16 consecutive days, she samples 600 bags of candy and determines the number in each day's sample that she considers to be of poor quality. The data that she developed follow.

Number Proportion Day Poor Poor 1 33 0.0550000 2 29 0.0483333 3 31 0.0516667 4 32 0.0533333 5 43 0.0716667 6 45 0.0750000 7 46 0.0766667 8 48 0.0800000 9 48 0.0800000 10 46 0.0766667 11 28 0.0466667 12 32 0.0533333 13 28 0.0466667 14 32 0.0533333 15 31 0.0516667 16 24 0.0400000 59. Referring to SCENARIO 15-6, the estimate of the proportion of poor-quality bags of candy is __________.

ANSWER: 0.06 TYPE: FI DIFFICULTY: Moderate KEYWORDS: p chart, center line 60. Referring to SCENARIO 15-6, a p control chart is to be constructed for these data. The center line for the chart should be located at __________.

ANSWER: 0.06 TYPE: FI DIFFICULTY: Moderate KEYWORDS: p chart, center line 61. Referring to SCENARIO 15-6, a p control chart is to be constructed for these data. The estimate of the standard error of the sample proportion is __________.

ANSWER: 0.009695 TYPE: FI DIFFICULTY: Moderate KEYWORDS: p chart, standard error

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Statistical Applications in Quality Management

15-17

62. Referring to SCENARIO 15-6, a p control chart is to be constructed for these data. The lower control limit is __________, while the upper control limit is __________.

ANSWER: 0.0309, 0.0891 TYPE: FI DIFFICULTY: Moderate KEYWORDS: p chart, control limit 63. Referring to SCENARIO 15-6, construct a p control chart for these data.

ANSWER: P Chart: Sample Sizes = 600

p Chart 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0

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Sample Number TYPE: PR DIFFICULTY: Difficult KEYWORDS: p chart 64. True or False: Referring to SCENARIO 15-6, the process seems to be in control.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: p chart, statistical control

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Statistical Applications in Quality Management

SCENARIO 15-7 A supplier of silicone sheets for producers of computer chips wants to evaluate her manufacturing process. She takes samples of size 5 from each day's output and counts the number of blemishes on each silicone sheet. The results from 20 days of such evaluations are presented below.

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 8 8 10 5 8 9 10 10 6 6 8 6 7 5 7 7 8 11 6 6

Sheet 2 10 13 12 9 3 7 10 9 10 9 5 4 5 8 12 11 4 4 10 12

3 14 6 7 12 8 9 5 10 6 8 6 7 7 8 10 4 5 11 6 12

4 6 6 7 7 9 6 7 6 9 6 10 7 6 7 6 7 4 11 10 6

5 5 10 9 10 10 9 6 5 9 8 10 12 9 6 10 8 7 10 10 8

Mean 8.6 8.6 9.0 8.6 7.6 8.0 7.6 8.0 8.0 7.4 7.8 7.2 6.8 6.8 9.0 7.4 5.6 9.4 8.4 8.8

Range 9 7 5 7 7 3 5 5 4 3 5 8 4 3 6 7 4 7 4 6

She also decides that the upper specification limit is 10 blemishes.

65. Referring to SCENARIO 15-7, an R chart is to be constructed for the number of blemishes. The center line of this R chart is located at __________.

ANSWER: 5.45 TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, center line 66. Referring to SCENARIO 15-7, an R chart is to be constructed for the number of blemishes. One way to create the lower control limit involves multiplying the mean of the sample ranges by D3.

For this data set, the value of D3 is ________.

ANSWER: 0 TYPE: FI DIFFICULTY: Easy KEYWORDS: R chart, D3 factor

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Statistical Applications in Quality Management

15-19

67. Referring to SCENARIO 15-7, an R chart is to be constructed for the number of blemishes. One way to create the upper control limit involves multiplying the mean of the sample ranges by D4.

For this data set, the value of D4 is ________.

ANSWER: 2.114 TYPE: FI DIFFICULTY: Easy KEYWORDS: R chart, D4 factor 68. Referring to SCENARIO 15-7, an R chart is to be constructed for the number of blemishes. The lower control limit for this data set is ________.

ANSWER: 0 or has no limit TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, control limit 69. Referring to SCENARIO 15-7, an R chart is to be constructed for the number of blemishes. The upper control limit for this data set is ________.

ANSWER: 11.52 TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, control limit 70. Referring to SCENARIO 15-7, construct an R chart for the number of blemishes.

ANSWER: R Chart 12 10 8 6 4 2 0 0

5

10

15

Sample Number

TYPE: PR DIFFICULTY: Difficult KEYWORDS: R chart

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20

15-20

Statistical Applications in Quality Management

71. True or False: Referring to SCENARIO 15-7, based on the R chart, it appears that the process is out of control.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: R chart, statistical control 72. Referring to SCENARIO 15-7, an X chart is to be used for the number of blemishes. The center line of this chart is located at __________.

ANSWER: 7.930 TYPE: FI DIFFICULTY: Moderate KEYWORDS: XBar chart, center line 73. Referring to SCENARIO 15-7, an X chart is to be used for the number of blemishes. One way to obtain the control limits is to take the grand mean and add and subtract the product of A2 times the mean of the sample ranges. For this data set, the value of A2 is ________.

ANSWER: 0.577 TYPE: FI DIFFICULTY: Easy KEYWORDS: XBar chart, A2 factor 74. Referring to SCENARIO 15-7, an X chart is to be used for the number of blemishes. The lower control limit for this data set is ________, while the upper control limit is ________.

ANSWER: 4.785; 11.075 TYPE: FI DIFFICULTY: Moderate KEYWORDS: XBar chart, control limit

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Statistical Applications in Quality Management

15-21

75. Referring to SCENARIO 15-7, construct an X chart for the number of blemishes.

ANSWER:

Mean Chart 12 10 8 6 4 2 0 0

5

10

15

20

Sample Number TYPE: PR DIFFICULTY: Difficult KEYWORDS: XBar chart 76. True or False: Referring to SCENARIO 15-7, based on the X chart for the number of blemishes, it appears that the process is out of control.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: XBar chart, statistical control 77. Referring to SCENARIO 15-7, what is the value of d 2 factor?

ANSWER: 2.326 TYPE: PR DIFFICULTY: Easy KEYWORDS: d2 factor 78. Referring to SCENARIO 15-7, what percentage of the chips will fall below the upper specification limit?

ANSWER: 0.81 TYPE: PR DIFFICULTY: Moderate KEYWORDS: process capacity Copyright ©2020 Pearson Education, Inc.

15-22

Statistical Applications in Quality Management

79. Referring to SCENARIO 15-7, what is the value of the CPU index?

ANSWER: 0.29 TYPE: PR DIFFICULTY: Easy KEYWORDS: CPU index SCENARIO 15-8 Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time (hours) students are spending on the computer registering under the new system. She decides to randomly select 8 students on each of the 12 days of the registration and determine the time each spends on the computer registering. The range, mean, and standard deviation of the times required to register are in the table that follows.

Day Range Mean Std.Dev. 1 10 5.250 3.4949 2 31 15.250 10.3060 3 13 20.375 4.9262 4 21 22.875 8.3911 5 35 8.500 11.3767 6 18 7.875 6.9372 7 25 11.250 8.5815 8 30 7.875 9.5235 9 17 10.250 6.3640 10 22 9.500 7.8740 11 27 7.875 8.7086 12 26 12.875 9.3723 80. Referring to SCENARIO 15-8, an R chart is to be constructed for the time required to register.

The center line of this R chart is located at __________.

ANSWER: 22.92 TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, center line 81. Referring to SCENARIO 15-8, an R chart is to be constructed for the time required to register.

One way to create the lower control limit involves multiplying the mean of the sample ranges by D3. For this data set, the value of D3 is ________.

ANSWER: 0.136 TYPE: FI DIFFICULTY: Easy KEYWORDS: R chart, D3 factor

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Statistical Applications in Quality Management

15-23

82. Referring to SCENARIO 15-8, an R chart is to be constructed for the time required to register.

One way to create the upper control limit involves multiplying the mean of the sample ranges by D4. For this data set, the value of D4 is ________.

ANSWER: 1.864 TYPE: FI DIFFICULTY: Easy KEYWORDS: R chart, D4 factor 83. Referring to SCENARIO 15-8, an R chart is to be constructed for the time required to register.

The lower control limit for this data set is ________.

ANSWER: 3.117 TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, control limit 84. Referring to SCENARIO 15-8, an R chart is to be constructed for the time required to register.

The upper control limit for this data set is ________.

ANSWER: 42.72 TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, control limit 85. Referring to SCENARIO 15-8, construct an R chart for the time required to register.

ANSWER: R Chart 45 40 35 30 25 20 15 10 5 0 0

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Sample Number

TYPE: PR DIFFICULTY: Difficult KEYWORDS: R chart Copyright ©2020 Pearson Education, Inc.

10

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Statistical Applications in Quality Management

86. True or False: Referring to SCENARIO 15-8, based on the R chart, it appears that the process is out of control.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: R chart, statistical control 87. Referring to SCENARIO 15-8, an X chart is to be used for the time required to register. The center line of this chart is located at __________.

ANSWER: 11.65 TYPE: FI DIFFICULTY: Moderate KEYWORDS: XBar chart, center line 88. Referring to SCENARIO 15-8, an X chart is to be used for the time required to register. One way to obtain the control limits is to take the grand mean and add and subtract the product of A2 times the mean of the sample ranges. For this data set, the value of A2 is ________.

ANSWER: 0.373 TYPE: FI DIFFICULTY: Easy KEYWORDS: XBar chart, A2 factor 89. Referring to SCENARIO 15-8, an X chart is to be used for the time required to register. The lower control limit for this data set is ________, while the upper control limit is ________.

ANSWER: 3.098; 20.194 TYPE: FI DIFFICULTY: Moderate KEYWORDS: XBar chart, control limit

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Statistical Applications in Quality Management

15-25

90. Referring to SCENARIO 15-8, construct an X chart for the time required to register.

ANSWER:

Mean Chart 25 20 15 10 5 0 0

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Sample Number TYPE: PR DIFFICULTY: Difficulty KEYWORDS: XBar char 91. True or False: Referring to SCENARIO 15-8, based on the X chart, it appears that the process is in control.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: XBar chart, statistical control 92. Which of the following is a method for breaking process into a series of steps in order to eliminate defects and produce near perfect results? a) Deming’s 14 points management. b) Six Sigma management. c) Shewhart-Deming cycle. d) R chart and X chart.

ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: six sigma management

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Statistical Applications in Quality Management

93. Which of the following is not part of the DMAIC process in Six Sigma management? a) Define b) Do c) Analyze d) Control ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: six sigma management 94. Developing operational definitions for each critical-to-quality characteristic involves which part of the DMAIC process? a) Define b) Measure c) Analyze d) Improve e) Control ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: six sigma management 95. Determining the root causes of why defects can occur along with the variables in the process that cause these defects to occur involves which part of the DMAIC process? a) Define b) Measure c) Analyze d) Improve e) Control ANSWER: c TYPE: MC DIFFICULTY: Easy KEYWORDS: six sigma management 96. Maintaining the gains that have been made with a revised process in the long term by avoiding potential problems that can occur when a process is changed involves which part of the DMAIC process? a) Define b) Measure c) Analyze d) Improve e) Control ANSWER: e TYPE: MC DIFFICULTY: Easy KEYWORDS: six sigma management

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Statistical Applications in Quality Management 97. True or False: The focus of Lean Six Sigma is on removing non-value added steps and waste which can exist in any part of an organization.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 98. True or False: SS method is among the tools of Lean Six Sigma.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 99. True or False: Total Production Maintenance is among the tools of Lean Six Sigma.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 100.

True or False: Quick Changeover Techniques is among the tools of Lean Six Sigma.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 101.

True or False: Poke-Yoke devices is among the tools of Lean Six Sigma.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 102.

True or False: Champions is among the tools of Lean Six Sigma.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 103.

True or False: A master black belt is among the tools of Lean Six Sigma.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma

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Statistical Applications in Quality Management

104. True or False: The SS method involves methods that enable participants to reduce setup time for equipment and resources and materials needed for changeover.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 105. True or False: Quick Changeover Techniques involve methods that enable participants to reduce setup time for equipment and resources and materials needed for changeover.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 106. True or False: Total Productive Maintenance focuses on methods that enable participants to reduce setup time for equipment and resources and materials needed for changeover.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 107. True or False: Mistake Proofing devices focus on methods that enable participants to reduce setup time for equipment and resources and materials needed for changeover.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 108.

True or False: Mistake Proofing (Poke-Yoke) devices focus on preventing the causes of defects.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 109.

True or False: SS method focuses on preventing the causes of defects.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 110.

True or False: Total Productive Maintenance focuses on preventing the causes of defects.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma Copyright ©2020 Pearson Education, Inc.

Statistical Applications in Quality Management 111.

15-29

True or False: SMED focuses on preventing the causes of defects.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 112. True or False: The SS method establishes ways to organize necessary housekeeping aspects of a work environment.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 113. True or False: The SS method establishes ways to clean and maintain the necessary housekeeping aspects of a work environment.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 114. True or False: The SS method establishes ways to eliminate unnecessary housekeeping aspects of a work environment.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 115. True or False: Quick Changeover Techniques establish ways to clean and maintain the necessary housekeeping aspects of a work environment.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 116. True or False: Quick Changeover Techniques establish ways to eliminate unnecessary housekeeping aspects of a work environment.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma

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Statistical Applications in Quality Management

117. True or False: Poke-Yoke devices establish ways to clean and maintain the necessary housekeeping aspects of a work environment.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 118. True or False: Poke-Yoke devices establish ways to eliminate unnecessary housekeeping aspects of a work environment.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 119. True or False: TPM establishes ways to clean and maintain the necessary housekeeping aspects of a work environment.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 120. True or False: TPM establishes ways to eliminate unnecessary housekeeping aspects of a work environment.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 121. True or False: SMED establishes ways to clean and maintain the necessary housekeeping aspects of a work environment.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma 122. True or False: SMED establishes ways to eliminate unnecessary housekeeping aspects of a work environment.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: lean six sigma

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Statistical Applications in Quality Management

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123. Which of the following best measures the ability of a process to consistently meet specified customer-driven requirements? a) Process capability. b) Specification limits c) Upper control limit d) Lower control limit ANSWER: a TYPE: MC DIFFICULTY: Easy KEYWORDS: process capability 124. True or False: An in-control process must be achieved before being able to estimate process capability.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: process capability 125. True or False: A process capability is estimated by the percentage of product or service that falls outside the specification limits.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: process capability 126. True or False: The smaller the capability index, the more capable a process is of meeting customer requirements.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: capability index 127. True or False: The Cp index measures the potential of a process, not its actual performance.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: capability index 128. True or False: C p >1 indicates that if the process average can be centered, then more than 99.73% of the observations will fall inside the specification limits.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: capability index

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Statistical Applications in Quality Management

129. True or False: The CPL and CPU indexes are used to measure process’ actual performance rather than its potential.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: capability index 130. True or False: The Cpk is a one-sided specification limit.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: capability index 131. True or False: CPL >1 implies that the process mean is more than 3 standard deviation away from the lower specification limit.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: capability index 132. True or False: C pk > 1 indicates that the process average is exactly 3 standard deviations away from the closest specification limit.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: capability index 133. True or False: Larger C pk indicates larger capability of meeting the requirements.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: capability index

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Statistical Applications in Quality Management

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SCENARIO 15-9 The manufacturer of canned food constructed control charts and analyzed several quality characteristics. One characteristic of interest is the weight of the filled cans. The lower specification limit for weight is 2.95 pounds. The table below provides the range and mean of the weights of five cans tested every fifteen minutes during a day’s production.

Number XBar Range Number XBar Range 1 3.05072 0.0215 16 3.04646 0.073 2 3.01228 0.087 17 3.03868 0.0696 3 3.03558 0.0851 18 3.03338 0.0329 4 3.01014 0.0674 19 3.03322 0.0455 5 3.00858 0.0983 20 3.05078 0.0215 6 3.02704 0.0527 21 3.04808 0.0396 7 3.04268 0.0508 22 3.05348 0.0581 8 3.01052 0.0791 23 3.05516 0.0682 9 3.03464 0.0663 24 3.03426 0.0325 10 3.02034 0.0538 25 3.0516 0.0641 11 3.03764 0.0584 26 3.05562 0.0809 12 3.0409 0.0434 27 3.04402 0.0374 13 3.0519 0.0762 28 3.06458 0.0284 14 3.03994 0.0833 29 3.0544 0.0738 15 3.03788 0.0601 134. Referring to SCENARIO 15-9, an R chart is to be constructed for the weight. The center line of this R chart is located at __________.

ANSWER: 0.0589 TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, center line 135. Referring to SCENARIO 15-9, an R chart is to be constructed for the weight. One way to create the lower control limit involves multiplying the mean of the sample ranges by D3. For this data set, the value of D3 is ________.

ANSWER: 0 TYPE: FI DIFFICULTY: Easy KEYWORDS: R chart, D3 factor 136. Referring to SCENARIO 15-9, an R chart is to be constructed for the weight. One way to create the upper control limit involves multiplying the mean of the sample ranges by D4. For this data set, the value of D4 is ________.

ANSWER: 2.114 TYPE: FI DIFFICULTY: Easy KEYWORDS: R chart, D4 factor

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Statistical Applications in Quality Management

137. Referring to SCENARIO 15-9, an R chart is to be constructed for the weight. The lower control limit for this data set is ________.

ANSWER: 0 TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, control limit 138. Referring to SCENARIO 15-9, an R chart is to be constructed for the weight. The upper control limit for this data set is ________.

ANSWER: 0.1246 TYPE: FI DIFFICULTY: Moderate KEYWORDS: R chart, control limit 139. Referring to SCENARIO 15-9, construct an R chart for the time required to register.

ANSWER: Control Chart Calculations 0.14 UCL

0.12 0.1 0.08 0.06

RBar

0.04 0.02 0 0

5

10

15

20

25

LCL 30

35

TYPE: PR DIFFICULTY: Difficult KEYWORDS: R chart 140. True or False: Referring to SCENARIO 15-9, based on the R chart, it appears that the process is out of control.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: R chart, statistical control

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Statistical Applications in Quality Management

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141. Referring to SCENARIO 15-9, an X chart is to be used for the weight. The center line of this chart is located at __________.

ANSWER: 3.0388 TYPE: FI DIFFICULTY: Moderate KEYWORDS: XBar chart, center line 142. Referring to SCENARIO 15-9, an X chart is to be used for the weight. One way to obtain the control limits is to take the grand mean and add and subtract the product of A2 times the mean of the sample ranges. For this data set, the value of A2 is ________.

ANSWER: 0.577 TYPE: FI DIFFICULTY: Easy KEYWORDS: XBar chart, A2 factor 143. Referring to SCENARIO 15-9, an X chart is to be used for the weight. The lower control limit for this data set is ________, while the upper control limit is ________.

ANSWER: 3.0048; 3.0728 TYPE: FI DIFFICULTY: Moderate KEYWORDS: XBar chart, control limit 144. Referring to SCENARIO 15-9, construct an X chart for the weight.

ANSWER: Control Chart Calculations 3.08 UCL

3.07 3.06 3.05 3.04

XBar

3.03 3.02 3.01 LCL

3 0

5

10

15

20

25

TYPE: PR DIFFICULTY: Difficult KEYWORDS: XBar char

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35

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Statistical Applications in Quality Management

145. True or False: Referring to SCENARIO 15-9, based on the X chart, it appears that the process is in control.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: XBar chart, statistical control 146. Referring to SCENARIO 15-9, estimate the percentage of the cans whose weight is inside the specification limit.

ANSWER: 0.9998 or 99.98% TYPE: FI DIFFICULTY: Difficult KEYWORDS: XBar chart, control limit SCENARIO 15-10 Below is the number of defective items from a production line over twenty consecutive morning shifts.

Day Nonconformances Day Nonconformances 1 26 11 22 2 27 12 26 3 23 13 21 4 21 14 22 5 26 15 19 6 20 16 17 7 35 17 21 8 30 18 18 9 21 19 16 10 25 20 17

147. Referring to SCENARIO 15-10, a c chart is to be constructed for the number of defective items.

The center line of this c chart is located at __________.

ANSWER: 22.65 TYPE: FI DIFFICULTY: Moderate KEYWORDS: c chart, center line 148. Referring to SCENARIO 15-10, a c chart is to be constructed for the number of defective items.

The lower control limits is ________.

ANSWER: 8.3724 TYPE: FI DIFFICULTY: Easy KEYWORDS: c chart, control limit

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Statistical Applications in Quality Management

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149. Referring to SCENARIO 15-10, a c chart is to be constructed for the number of defective items.

The upper control limits is ________.

ANSWER: 36.9276 TYPE: FI DIFFICULTY: Easy KEYWORDS: c chart, control limit 150. Referring to SCENARIO 15-10, construct a c chart for the number of defective items.

ANSWER:

TYPE: PR DIFFICULTY: Difficult KEYWORDS: c chart 151. True or False: Referring to SCENARIO 15-10, based on the c chart, it appears that the process is out of control.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: c chart, statistical control 152. True or False: Referring to SCENARIO 15-10, based on the c chart, there appears to be a special cause of variation in the process.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: c chart, statistical control, special causes of variation

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Statistical Applications in Quality Management

153. True or False: Referring to SCENARIO 15-10, based on the c chart, no opportunity appears to be present to render an improvement in the process.

ANSWER: False TYPE: TF DIFFICULTY: Easy KEYWORDS: c chart, statistical control, special causes of variation 154. True or False: Referring to SCENARIO 15-10, the c chart suggests that the special cause of variation must be incorporated into the process to become part of the permanent ongoing process.

ANSWER: True TYPE: TF DIFFICULTY: Easy KEYWORDS: c chart, statistical control, special causes of variation 155. Which of the following is not one of Deming's 14 points? a) Belief in mass inspection. b) Create constancy of purpose for improvement of product or service. c) Adopt and institute leadership. d) Drive out fear.

ANSWER: a TYPE: MC DIFFICULTY: Moderate KEYWORDS: Deming’s 14 points 156. Which of the following is not one of Deming's 14 points? a) Create constancy of purpose for improvement of product or service. b) Award business on the basis of price tag alone. c) Break down barriers between staff areas. d) Drive out fear.

ANSWER: b TYPE: MC DIFFICULTY: Moderate KEYWORDS: Deming’s 14 points 157. Which of the following is not part of the Shewhart-Deming cycle? a) Plan b) Do c) React d) Act ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Shewhart-Deming cycle

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Statistical Applications in Quality Management

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158. The Shewhart-Deming cycle plays an important role in which of the following Deming’s 14 points for management? a) Adopt the new philosophy. b) Break down barriers between staff areas. c) Create constancy of purpose for improvement of product and services. d) Eliminate slogans, exhortation, and targets for the workforce.

ANSWER: c TYPE: MC DIFFICULTY: Moderate KEYWORDS: Shewhart-Deming cycle 159. Which famous statistician developed the 14 Points of Quality? a) Shewhart b) Deming c) Chebyshev d) Taguchi ANSWER: b TYPE: MC DIFFICULTY: Easy KEYWORDS: Deming’s 14 points 160. True or False: Treating common cause variation as special cause variation is known as interference.

ANSWER: False TYPE: TF DIFFICULTY: Moderate KEYWORDS: tampering, common cause variation, page 19-3 161. Which of the following is true regarding either instances or treatment of common cause variation? a) Reductions in variation require changes in the process. b) Process changes are the responsibility of management. c) They occur by chance alone. d) All of the above are true.

ANSWER: d TYPE: MC DIFFICULTY: Moderate KEYWORDS: Causes of process variation, pages 19-2,19-3 and 19-6.

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Statistical Applications in Quality Management

162. True or False: A capability index is used to measure the ability of a process to meet customer driven requirements.

ANSWER: True TYPE: TF DIFFICULTY: Moderate KEYWORDS: Capability indices EXPLANATION: Capability index measures a process’s ability to meet specification limits (page19-23). Process capability is the ability to meet customer-driven requirements using CTQ variables (page 19-21).

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