Business Statistics, 6E David M Levine Timothy C Krehbiel Test Bank

Business Statistics, 6E

By Levine & Krehbiel

Email: richard@qwconsultancy.com

Business Statistics: A First Course, 6e (Levine) Chapter 1 Introduction 1) The process of using data collected from a small group to reach conclusions about a large group is called A) statistical inference.

B) the scientific method.

C) sampling.

D) descriptive statistics.

Answer: A 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) the scientific method.

C) sampling.

D) descriptive statistics.

Answer: D 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) a parameter.

D) a statistic.

Answer: B Difficulty: Easy Keywords: descriptive statistics 4) The estimation of the population's 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) a parameter.

D) a statistic.

Answer: A Difficulty: Easy Keywords: inferential statistics

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5) The universe or "totality of items or things" under consideration is called A) a sample.

B) a population.

C) a parameter.

D) a statistic.

Answer: B Difficulty: Easy Keywords: population 6) The portion of the universe that has been selected for analysis is called A) a sample.

B) a frame.

C) a parameter.

D) a statistic.

Answer: A Difficulty: Easy Keywords: sample 7) A summary measure that is computed to describe a characteristic from only a sample of the population is called A) a parameter.

B) a census.

C) a statistic.

D) the scientific method.

Answer: C Difficulty: Easy Keywords: statistic 8) A summary measure that is computed to describe a characteristic of an entire population is called A) a parameter.

B) a census.

C) a statistic.

D) the scientific method.

Answer: A Difficulty: Easy Keywords: parameter 9) Which of the following is most likely a population as opposed to a sample?

A) respondents to a newspaper survey B) the first five students completing an assignment C) every third person to arrive at the bank D) registered voters in a county Answer: D Difficulty: Moderate Keywords: population, sample

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10) 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 Difficulty: Moderate Keywords: parameter, statistic 11) Which of the following is NOT an element of descriptive statistical problems?

A) an inference made about the population based on the sample B) the population or sample of interest C) tables, graphs, or numerical summary tools D) identification of patterns in the data Answer: A Difficulty: Moderate Keywords: descriptive statistics 12) A study is under way in Yosemite National Forest to determine the height of adult 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 Difficulty: Moderate Keywords: population, sample 13) A study is under way in Yosemite National Forest to determine the height of adult 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 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 Difficulty: Easy Keywords: variable

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14) A study is under way in Yosemite National Forest to determine the height of adult 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 Difficulty: Easy Keywords: population, sample 15) 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 wanted 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 Difficulty: Easy Keywords: population, sample 16) 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 wanted 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 Difficulty: Easy Keywords: variable

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17) 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 wanted 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 Difficulty: Easy Keywords: population, sample 18) 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 finds 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 Difficulty: Moderate Keywords: population, sample 19) The average number of units earned per semester by college students is suspected to be 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. Identify the variable of interest to the researcher.

A) the number of students enrolled at Calendula College during the spring term B) the average indebtedness of Calendula College students enrolled in the spring C) the age of Calendula College students enrolled in the spring D) the number of units earned by Calendula College students during the spring term Answer: D Difficulty: Easy Keywords: variable 20) 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 Difficulty: Easy Keywords: discrete random variable, types of data

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21) 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 produced by a cow in one 24-hour period D) the number of gallons of milk sold at the local grocery store yesterday Answer: C Difficulty: Easy Keywords: continuous random variable, types of data 22) To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot every 30 minutes for 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 during each period of time, then X is an example of A) a categorical random variable.

B) a discrete random variable.

C) a continuous random variable.

D) a statistic.

Answer: B Difficulty: Moderate Keywords: discrete random variable, types of data 23) 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, then X is an example of A) a categorical random variable.

B) a discrete random variable.

C) a continuous random variable.

D) a parameter.

Answer: C Difficulty: Moderate Keywords: continuous random variable, types of data 24) The classification of student class designation (freshman, sophomore, junior, senior) is an example of A) a categorical random variable.

B) a discrete random variable.

C) a continuous random variable.

D) a parameter.

Answer: A Difficulty: Easy Keywords: categorical random variable, types of data

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25) The classification of student major (accounting, economics, management, marketing, other) is an example of A) a categorical random variable.

B) a discrete random variable.

C) a continuous random variable.

D) a parameter.

Answer: A Difficulty: Easy Keywords: categorical random variable, types of data 26) 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 population.

B) a sample.

C) a parameter.

D) a statistic.

Answer: C Difficulty: Moderate Keywords: parameter 27) 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 population.

B) a sample.

C) a parameter.

D) a statistic Answer: D Difficulty: Moderate Keywords: statistic 28) 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 random variable.

B) a discrete random variable.

C) a continuous random variable.

D) a parameter.

Answer: A Difficulty: Easy Keywords: categorical random variable, types of data

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TABLE 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 DVD player made by the company over the past 12 months are satisfied with their products.

29) Referring to Table 1-1, the population of interest is A) all the customers who have bought a DVD player made by the company over the past 12 months.

B) all the customers who have bought a DVD player made by the company and brought it in for repair over the past 12 months.

C) all the customers who have used a DVD player over the past 12 months.

D) all the customers who have ever bought a DVD player made by the company.

Answer: A Difficulty: Difficult Keywords: population 30) Referring to Table 1-1, the possible responses to the question "How many DVD players made by other manufacturers have you used?" are values from a A) discrete random variable.

B) continuous random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Easy Keywords: discrete random variable, types of data 31) Referring to Table 1-1, the possible responses to the question "Are you happy, indifferent, or unhappy with the performance per dollar spent on the DVD player?" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: C Difficulty: Easy Keywords: categorical random variable, types of data 32) Referring to Table 1-1, the possible responses to the question "What is your annual income rounded to the nearest thousand?" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Explanation: A) Even though money is usually considered as a continuous random variable, it should be considered as a discrete random variable when rounded to the nearest thousands.

Difficulty: Difficult Keywords: discrete random variable, types of data

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33) Referring to Table 1-1, the possible responses to the question "How much time do you use the DVD player every week on the average?" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: B Difficulty: Easy Keywords: continuous random variable, types of data 34) Referring to Table 1-1, the possible responses to the question "How many people are there in your household?" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Easy Keywords: discrete random variable, types of data 35) Referring to Table 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 random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: C Difficulty: Easy Keywords: categorical random variable, types of data 36) Referring to Table 1-1, the possible responses to the question "What brand of DVD player did you purchase?" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: C Difficulty: Easy Keywords: categorical random variable, types of data

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37) Referring to Table 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 random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Moderate Keywords: discrete random variable, types of data 38) Referring to Table 1-1, the possible responses to the question "In which year were you born?" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Moderate Keywords: discrete random variable, types of data 39) True or False: A population is the totality of items or things under consideration.

Answer: TRUE Difficulty: Easy Keywords: population 40) True or False: A sample is the portion of the universe that is selected for analysis.

Answer: TRUE Difficulty: Easy Keywords: sample 41) 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 Difficulty: Easy Keywords: statistical package 42) 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.

Answer: TRUE Difficulty: Easy Keywords: reasons for learning statistics 43) 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 Difficulty: Moderate Keywords: continuous random variable, types of data 1-10 .

44) 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 Difficulty: Moderate Keywords: discrete random variable, types of data 45) 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 Difficulty: Moderate Keywords: continuous random variable, types of data 46) True or False: Faculty rank (professor to lecturer) is an example of discrete numerical data.

Answer: FALSE Difficulty: Easy Keywords: categorical random variable, types of data 47) True or False: Student grades (A to F) are an example of continuous numerical data.

Answer: FALSE Difficulty: Moderate Keywords: categorical random variables, types of data 48) True or False: The amount of coffee consumed by an individual in a day is an example of a discrete numerical variable.

Answer: FALSE Difficulty: Moderate Keywords: continuous random variables, types of data 49) True or False: A statistic is usually used to provide an estimate for a usually unobserved parameter.

Answer: TRUE Difficulty: Moderate Keywords: statistic, parameter, inferential statistics 50) True or False: A statistic is usually unobservable while a parameter is usually observable.

Answer: FALSE Difficulty: Moderate Keywords: statistic, parameter, inferential statistic 51) True or False: The answer to the question "What is your favorite color?" is an example of a continuous variable.

Answer: FALSE Difficulty: Easy Keywords: continuous random variable 52) True or False: The answer to the question "How do you rate the quality of your business statistics course" is an example of a qualitative variable.

Answer: TRUE Difficulty: Easy Keywords: categorical random variable 1-11 .

53) 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 discrete variable.

Answer: TRUE Difficulty: Easy Keywords: discrete random variable 54) True or False: The answer to the question "What is your sleeping bag temperature rating?" is an example of a categorical variable.

Answer: FALSE Difficulty: Easy Keywords: categorical random variable 55) True or False: A professor computing the sample average exam score of 20 students and using it to estimate the average exam score for the 1,500 students taking the exam is an example of inferential statistics.

Answer: TRUE Difficulty: Easy Keywords: descriptive statistics, inferential statistics 56) 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 Difficulty: Easy Keywords: descriptive statistics, inferential statistics 57) 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 Difficulty: Easy Keywords: descriptive statistics, inferential statistics 58) 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. All the employees in the corporation constitute the ________.

Answer: population Difficulty: Easy Keywords: population 59) 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 500 employees who will participate in this study constitute the ________.

Answer: sample Difficulty: Easy Keywords: sample

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60) 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 Difficulty: Easy Keywords: statistic 61) 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 Difficulty: Easy Keywords: parameter 62) 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 Difficulty: Easy Keywords: descriptive statistics 63) 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 Difficulty: Easy Keywords: inferential statistics 64) The oranges grown on 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 six-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 Difficulty: Moderate Keywords: statistic

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65) The oranges grown on 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 six-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 on a daily basis to estimate the respective true population ________.

Answer: parameters Difficulty: Easy Keywords: parameters 66) The oranges grown on 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 six-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 Difficulty: Moderate Keywords: inferential statistics 67) The oranges grown on 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 six-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 Difficulty: Moderate Keywords: descriptive statistics 68) 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 Difficulty: Easy Keywords: statistic

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69) 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 Difficulty: Easy Keywords: parameter 70) 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 Difficulty: Moderate Keywords: statistic 71) 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 Difficulty: Easy Keywords: parameter 72) 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 Difficulty: Moderate Keywords: inferential statistics 73) 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 Difficulty: Easy Keywords: descriptive statistics 74) 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 three years is an example of a ________ numerical variable.

Answer: discrete Difficulty: Easy Keywords: discrete random variable, types of data

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75) 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 Difficulty: Easy Keywords: continuous random variable, types of data 76) 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 Difficulty: Easy Keywords: continuous random variable, types of data 77) 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 Difficulty: Moderate Keywords: continuous random variable, types of data 78) 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 three years is an example of a ________ numerical variable.

Answer: discrete Difficulty: Easy Keywords: discrete random variable, types of data 79) In purchasing an automobile, there are a number of variables to consider. The body style of the car (sedan, coupe, wagon, etc.) is an example of a ________ variable.

Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data 80) In purchasing an automobile, there are a number of variables to consider. The classification of the car as a subcompact, compact, standard, or luxury size is an example of a ________ variable.

Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data 81) In purchasing an automobile, there are a number of variables to consider. The color of the car is an example of a ________ variable.

Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data

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82) Most colleges admit students based on their achievements in a number of different areas. Whether a student has taken any advanced placement courses is an example of a ________ variable.

Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data 83) Most colleges admit students based on their achievements in a number of different areas. The grade obtained in senior level English (A, B, C, D, or F) is an example of a ________ variable.

Answer: categorical Difficulty: Moderate Keywords: categorical random variable, types of data 84) Most colleges admit students based on their achievements in a number of different areas. The total SAT score achieved by a student is an example of a ________ numerical variable.

Answer: discrete Difficulty: Moderate Keywords: discrete random variable, types of data 85) The Dean of Students conducted a survey on campus. The gender of the student is an example of a ________ variable.

Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data 86) The Dean of Students conducted a survey on campus. Class designation (Freshman, Sophomore, Junior, Senior) is an example of a ________ variable.

Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data 87) The Dean of Students conducted a survey on campus. The major area of study is an example of a ________ variable.

Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data 88) The Dean of Students conducted a survey on campus. The SAT score in mathematics is an example of a ________ numerical variable.

Answer: discrete Difficulty: Easy Keywords: continuous random variable, types of data 89) The Dean of Students conducted a survey on campus. Grade point average (GPA) is an example of a ________ numerical variable.

Answer: continuous Difficulty: Easy Keywords: continuous random variable, types of data

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90) The Dean of Students conducted a survey on campus. The number of credits currently enrolled for is an example of a ________ numerical variable.

Answer: discrete Difficulty: Easy Keywords: discrete random variable, types of data 91) The Dean of Students conducted a survey on campus. The number of clubs, groups, teams, and organizations affiliated with on campus is an example of a ________ numerical variable.

Answer: discrete Difficulty: Easy Keywords: discrete random variable, types of data 92) A personal computer user survey was conducted. The computer brand primarily used is an example of a ________ variable.

Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data 93) A personal computer user survey was conducted. The number of personal computers owned is an example of a ________ numerical variable.

Answer: discrete Difficulty: Easy Keywords: discrete random variable, types of data 94) A personal computer user survey was conducted. The number of years using a personal computer is an example of a ________ numerical variable.

Answer: continuous Difficulty: Moderate Keywords: continuous random variable, types of data 95) A personal computer user survey was conducted. The hours of personal computer use per week is an example of a ________ numerical variable Answer: continuous Difficulty: Moderate Keywords: continuous random variable, types of data 96) A personal computer user survey was conducted. The primary word processing package used is an example of a ________ variable Answer: categorical Difficulty: Easy Keywords: categorical random variable, types of data 97) A personal computer user survey was conducted. The number of computer magazine subscriptions is an example of a ________ numerical variable.

Answer: discrete Difficulty: Moderate Keywords: discrete random variable, types of data

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98) True or False: The brand of TV one owns is an example of a numerical variable.

Answer: False Difficulty: Easy Keywords: categorical random variable 99) True or False: Whether the university is private or public is an example of a categorical variable.

Answer: TRUE Difficulty: Easy Keywords: categorical random variable 100) True or False: Marital status is an example of a numerical variable.

Answer: FALSE Difficulty: Easy Keywords: categorical random variable 101) True or False: The grade level (K-12) of a student is an example of a numerical variable.

Answer: FALSE Difficulty: Easy Keywords: categorical random variable 102) True or False: 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 Difficulty: Easy Keywords: categorical random variable 103) True or False: The quality ("terrible", "poor", "fair", "acceptable", "very good" and "excellent") of a day care center is an example of a numerical variable.

Answer: FALSE Difficulty: Easy Keywords: categorical random variable 104) True or False: The amount of alcohol consumed by a person per week is an example of a continuous variable.

Answer: TRUE Difficulty: Easy Keywords: continuous random variable 105) True or False: The number of defective apples in a single box is an example of a continuous variable.

Answer: FALSE Difficulty: Easy Keywords: discrete random variable, continuous random variable 106) True or False: The amount of calories contained in a 12-ounce package of cheese is an example of a discrete variable.

Answer: FALSE Difficulty: Easy Keywords: discrete random variable, continuous random variable 1-19 .

107) True or False: The amount of time a student spent studying for an exam is an example of a continuous variable.

Answer: TRUE Difficulty: Easy Keywords: continuous random variable TABLE 1-2 A Wall Street Journal poll asked 2,150 adults in the United States a series of questions to find out their view on the U.S. economy.

108) Referring to Table 1-2, the population of interest is A) all the males living in the United States when the poll was taken.

B) all the females living in the United States when the poll was taken.

C) all the adults living in the United States when the poll was taken.

D) all the people living in the United States when the poll was taken.

Answer: C Difficulty: Easy Keywords: population 109) Referring to Table 1-2, the 2,150 adults make up A) the population.

B) the sample.

C) the parameter.

D) the statistic.

Answer: B Difficulty: Easy Keywords: sample 110) Referring to Table 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 random variable.

B) continuous random variable.

C) categorical random variable.

D) parameter.

Answer: C Difficulty: Easy Keywords: categorical random variable, types of data 111) Referring to Table 1-2, the possible responses to the question "How many people in your household are unemployed currently?" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Easy Keywords: discrete random variable, types of data

1-20 .

112) Referring to Table 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 random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Moderate Keywords: discrete random variable, types of data 113) Referring to Table 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 random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Easy Keywords: discrete random variable, types of data 114) Referring to Table 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 random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Explanation: A) The percentage of voters is the ratio of two discrete variables and, hence, the ratio is also a discrete variable.

Difficulty: Easy Keywords: discrete random variable, types of data 115) Referring to Table 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 random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: C Difficulty: Easy Keywords: categorical random variable, types of data

1-21 .

116) Referring to Table 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 random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: C Difficulty: Easy Keywords: categorical random variable, types of data 117) Referring to Table 1-2, the possible responses to the question "In which year do you think the last recession in the United States started?" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Easy Keywords: discrete random variable, types of data 118) Referring to Table 1-2, the possible responses to the question "On the scale of 1 to 100 with 1 being extremely anxious and 100 being not anxious at all, rate your level of anxiety in this U.S. economy" are values from a A) discrete numerical random variable.

B) continuous numerical random variable.

C) categorical random variable.

D) parameter.

Answer: A Difficulty: Moderate Keywords: discrete random variable, types of data

1-22 .

Business Statistics: A First Course, 6e (Levine) Chapter 2 Organizing and Visualizing Data 1) 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 Difficulty: Easy Keywords: sources of data 2) The British Airways Internet site provides a questionnaire instrument that can be answered electronically. Which of the four methods of data collection is involved when people complete the questionnaire?

A) published sources B) experimentation C) surveying D) observation Answer: C Difficulty: Easy Keywords: sources of data 3) 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 four 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 Difficulty: Easy Keywords: sources of data 4) 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 (inflationadjusted) salary over the last three years. Which of the four methods of data collection was involved when he used the Consumer Price Index?

A) published sources B) experimentation C) surveying D) observation Answer: A Difficulty: Easy Keywords: sources of data

2-1 .

5) Which of the four 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 Difficulty: Moderate Keywords: sources of data 6) 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 collection method as A) a designed experiment.

B) observational data.

C) a random sample.

D) a published source.

Answer: D Difficulty: Easy Keywords: sources of data 7) 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 Difficulty: Easy Keywords: sources of data 8) 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 Difficulty: Easy Keywords: sources of data

2-2 .

TABLE 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 three years, with the following results.

X 1 2 3 4 5

f 14 18 12 5 1

9) Referring to Table 2-1, how many drivers are represented in the sample?

A) 5 B) 15 C) 18 D) 50 Answer: D Difficulty: Easy Keywords: frequency distribution 10) Referring to Table 2-1, how many total claims are represented in the sample?

A) 15 B) 50 C) 111 D) 250 Answer: C Difficulty: Moderate Keywords: interpretation, frequency distribution 11) 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 Difficulty: Easy Keywords: Pareto chart

2-3 .

TABLE 2-2 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 1 2 3 4 5

f 7 3 11 8 9

12) Referring to Table 2-2, how many regional offices are represented in the survey results?

A) 5 B) 11 C) 15 D) 40 Answer: D Difficulty: Easy Keywords: interpretation, frequency distribution 13) Referring to Table 2-2, across all of the regional offices, how many total employees were supervised by those surveyed?

A) 15 B) 40 C) 127 D) 200 Answer: C Difficulty: Moderate Keywords: interpretation, frequency distribution 14) 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 Difficulty: Easy Keywords: frequency distribution

2-4 .

TABLE 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 have to 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.

15) Referring to the histogram from Table 2-3, how many graduating seniors attended the luncheon?

A) 4 B) 152 C) 275 D) 388 Answer: C Explanation: C) The number of graduating seniors is the sum of all the frequencies, f.

Difficulty: Difficult Keywords: interpretation, histogram 16) Referring to the histogram from Table 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 Difficulty: Difficult Keywords: interpretation, histogram

2-5 .

17) 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?

A) 14% B) 44% C) 54% D) 86% Answer: D Difficulty: Easy Keywords: interpretation, pie chart 18) 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 Difficulty: Easy Keywords: polygon, histogram 19) 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: B Difficulty: Easy Keywords: percentage polygon

2-6 .

TABLE 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 3 4 5 6 7 8 9

Leaves 23 03478999 0112345 12566 01 2

20) Referring to Table 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 Difficulty: Easy Keywords: stem-and-leaf display, interpretation 21) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, interpretation 22) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, interpretation

2-7 .

TABLE 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

23) Referring to Table 2-5, what is the width of each class?

A) 1 minute B) 5 minutes C) 2% D) 100% Answer: B Difficulty: Easy Keywords: class interval, relative frequency distribution 24) Referring to Table 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 Difficulty: Moderate Keywords: relative frequency distribution, interpretation 25) Referring to Table 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 Difficulty: Moderate Keywords: relative frequency distribution, interpretation

2-8 .

26) Referring to Table 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 Difficulty: Moderate Keywords: relative frequency distribution, interpretation 27) Referring to Table 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 Difficulty: Easy Keywords: cumulative relative frequency 28) Referring to Table 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 Difficulty: Moderate Keywords: cumulative relative frequency 29) Referring to Table 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 Difficulty: Easy Keywords: relative frequency distribution, interpretation 30) Referring to Table 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 Difficulty: Moderate Keywords: relative frequency distribution, interpretation 2-9 .

31) Referring to Table 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 Difficulty: Moderate Keywords: relative frequency distribution, interpretation 32) Referring to Table 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 Difficulty: Difficult Keywords: relative frequency distribution, interpretation 33) Which of the following is appropriate for displaying data collected on the different brands of cars that students at a major university drive?

A) a Pareto chart B) a two-way classification table C) a histogram D) a scatter plot Answer: A Difficulty: Easy Keywords: Pareto diagram 34) 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 Difficulty: Easy Keywords: time-series plot 35) 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 Difficulty: Easy Keywords: contingency table 2-10 .

36) 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 Difficulty: Easy Keywords: choice of chart, histogram 37) 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 Difficulty: Easy Keywords: choice of chart, percentage polygon 38) 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 Difficulty: Easy Keywords: choice of chart, stem-and-leaf 39) In a survey, 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 Difficulty: Easy Keywords: choice of chart, bar chart 40) You have collected information on the market share of five different search engines used by U.S. Internet users in January 2011. 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 Difficulty: Easy Keywords: choice of chart, pie chart 2-11 .

41) 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 Explanation: B) Even though a pie chart can also be used, the Pareto chart is preferable for separating the "vital few" from the "trivial many".

Difficulty: Moderate Keywords: choice of chart, Pareto chart 42) 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 Difficulty: Easy Keywords: choice of chart, scatter plot 43) You have collected data on the number of U.S. households actively using online banking and/or online bill payment from 1995 to 2010. 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 Difficulty: Easy Keywords: choice of chart, time-series plot 44) You have collected data on the monthly seasonally adjusted civilian unemployment rate for the United States from 1998 to 2010. 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 Difficulty: Easy Keywords: choice of chart, time-series plot

2-12 .

45) You have collected data on the number of complaints for six different brands of automobiles sold in the United States in 2006 and in 2010. 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 Difficulty: Moderate Keywords: choice of chart, side-by-side bar chart 46) 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 Difficulty: Moderate Keywords: choice of chart, contingency table TABLE 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

47) Referring to Table 2-6, of the students in the sample who went bar hopping the weekend before the midterm, ________ percent did well on the midterm.

A) 15 B) 27.27 C) 30 D) 55 Answer: C Difficulty: Easy Keywords: contingency table, interpretation

2-13 .

48) Referring to Table 2-6, of the students in the sample who did well on the midterm, ________ percent went bar hopping the weekend before the midterm.

A) 15 B) 27.27 C) 30 D) 50 Answer: B Difficulty: Easy Keywords: contingency table, interpretation 49) Referring to Table 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 Difficulty: Easy Keywords: contingency table, interpretation 50) Referring to Table 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 Difficulty: Easy Keywords: contingency table, interpretation 51) Referring to Table 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 Difficulty: Easy Keywords: contingency table, interpretation 52) Referring to Table 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 Difficulty: Moderate Keywords: contingency table, interpretation 2-14 .

53) Referring to Table 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 Difficulty: Moderate Keywords: contingency table, interpretation 54) 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 Difficulty: Moderate Keywords: contingency table 55) 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?

A) 35% B) 50% C) 65% D) 85% Answer: C Difficulty: Easy Keywords: bar chart, interpretation

2-15 .

TABLE 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 1 2 3 4 5 6

Leaves 234447899 22223455678889 0011135778 02345579 112466 158

56) Referring to Table 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 Difficulty: Easy Keywords: stem-and-leaf display, interpretation 57) Referring to Table 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 Difficulty: Easy Keywords: stem-and-leaf display, interpretation 58) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, interpretation 59) Referring to Table 2-7, ________ percent of the cases were adjudicated within the first two years.

Answer: 30 Difficulty: Moderate Keywords: stem-and-leaf display, interpretation 60) Referring to Table 2-7, ________ percent of the cases were not adjudicated within the first four years.

Answer: 20 Difficulty: Moderate Keywords: stem-and-leaf display, interpretation 61) Referring to Table 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 Difficulty: Easy Keywords: stem-and-leaf display, interpretation

2-16 .

62) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, relative frequency distribution 63) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, cumulative percentage distribution TABLE 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 0 1 2 3 4 5 6 7 8 9

Leaves 012222233333344566666667789999 1111222234444455669999 00011223455556889 0000446799 011345567 0077 8 67 3 0247

64) Referring to Table 2-8, the person who has the largest leaf associated with the smallest stem visited the facility ________ times.

Answer: 9 Difficulty: Moderate Keywords: stem-and-leaf display, interpretation 65) Referring to Table 2-8, the person who visited the health club less than anyone else in the sample visited the facility ________ times.

Answer: 0 or no Difficulty: Easy Keywords: stem-and-leaf display, interpretation 66) Referring to Table 2-8, the person who visited the health club more than anyone else in the sample visited the facility ________ times.

Answer: 97 Difficulty: Easy Keywords: stem-and-leaf display, interpretation

2-17 .

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

Answer: 10 Difficulty: Moderate Keywords: stem-and-leaf display, interpretation 68) Referring to Table 2-8, ________ of the 100 members visited the health club no more than 12 times in a year.

Answer: 38 Difficulty: Moderate Keywords: stem-and-leaf display, interpretation 69) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, frequency distribution 70) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, relative frequency distribution 71) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, cumulative percentage distribution 72) Referring to Table 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 Difficulty: Moderate Keywords: stem-and-leaf display, class midpoint

2-18 .

TABLE 2-9 The frequency distribution below represents the rents of 250 randomly selected federally subsidized apartments in a small town.

Rent in $ Frequency 300 but less than 400 113 400 but less than 500 85 500 but less than 600 32 600 but less than 700 16 700 but less than 800 4 73) Referring to Table 2-9, ________ apartments rented for at least $400 but less than $600.

Answer: 117 Difficulty: Easy Keywords: frequency distribution 74) Referring to Table 2-9, ________ percent of the apartments rented for $600 or more.

Answer: 8 or 20/250 Difficulty: Easy Keywords: frequency distribution, cumulative percentage distribution 75) Referring to Table 2-9, ________ percent of the apartments rented for at least $500.

Answer: 20.8 or 52/250 Difficulty: Moderate Keywords: frequency distribution, cumulative percentage distribution 76) Referring to Table 2-9, the class midpoint of the second class is ________.

Answer: 450 Difficulty: Easy Keywords: frequency distribution, class midpoint 77) Referring to Table 2-9, the relative frequency of the second class is ________.

Answer: 85/250 or 17/50 or 34% or 0.34 Difficulty: Easy Keywords: frequency distribution, relative frequency distribution 78) Referring to Table 2-9, the percentage of apartments renting for less than $600 is ________.

Answer: 230/250 or 23/25 or 92% or 0.92 Difficulty: Moderate Keywords: frequency distribution, cumulative percentage distribution

2-19 .

TABLE 2-10 The histogram below represents scores achieved by 200 job applicants on a personality profile.

79) Referring to the histogram from Table 2-10, ________ percent of the job applicants scored between 10 and 20.

Answer: 20 Difficulty: Easy Keywords: histogram, percentage distribution 80) Referring to the histogram from Table 2-10, ________ percent of the job applicants scored below 50.

Answer: 80 Difficulty: Moderate Keywords: histogram, percentage distribution 81) Referring to the histogram from Table 2-10, the number of job applicants who scored between 30 and below 60 is ________.

Answer: 80 Difficulty: Moderate Keywords: histogram 82) Referring to the histogram from Table 2-10, the number of job applicants who scored 50 or above is ________.

Answer: 40 Difficulty: Moderate Keywords: histogram 83) Referring to the histogram from Table 2-10, 90% of the job applicants scored above or equal to ________.

Answer: 10 Difficulty: Moderate Keywords: histogram, cumulative percentage distribution

2-20 .

84) Referring to the histogram from Table 2-10, half of the job applicants scored below ________.

Answer: 30 Difficulty: Moderate Keywords: histogram, cumulative percentage distribution 85) Referring to the histogram from Table 2-10, ________ percent of the applicants scored below 20 or at least 50.

Answer: 50 Difficulty: Moderate Keywords: histogram, cumulative percentage distribution 86) Referring to the histogram from Table 2-10, ________ percent of the applicants scored between 20 and below 50.

Answer: 50 Difficulty: Moderate Keywords: histogram, cumulative percentage distribution TABLE 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 4 5 5 6 7 9 9 12 12 15 17 20 21 23 23 25 26 27 27 28 29 29 87) Referring to Table 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 Difficulty: Easy Keywords: frequency distribution 88) Referring to Table 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 Difficulty: Moderate Keywords: relative frequency distribution 89) Referring to Table 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 Difficulty: Easy Keywords: frequency distribution 2-21 .

90) Referring to Table 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 Difficulty: Moderate Keywords: relative frequency distribution, percentage distribution 91) Referring to Table 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 Difficulty: Moderate Keywords: cumulative percentage distribution 92) Referring to Table 2-11, construct a histogram for the defects data, using "0 but less than 5" as the first class.

Answer:

Difficulty: Easy Keywords: histogram, frequency distribution

2-22 .

93) Referring to Table 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:

Difficulty: Moderate Keywords: cumulative percentage polygon 94) The point halfway between the boundaries of each class interval in a grouped frequency distribution is called the ________.

Answer: class midpoint Difficulty: Easy Keywords: cumulative percentage polygon, frequency distribution 95) A ________ is a vertical bar chart in which the rectangular bars are constructed at the boundaries of each class interval.

Answer: histogram Difficulty: Easy Keywords: histogram 96) It is essential that each class grouping or interval in a frequency distribution be ________ and ________.

Answer: non-overlapping and of equal width Difficulty: Moderate Keywords: frequency distribution, class interval 97) In order to compare one large set of numerical data to another, a ________ distribution must be developed from the frequency distribution.

Answer: relative frequency or percentage Difficulty: Easy Keywords: relative frequency distribution, percentage distribution

2-23 .

98) When comparing two or more large sets of numerical data, the distributions being developed should use the same ________.

Answer: class boundaries.

Difficulty: Easy Keywords: class boundaries 99) The width of each class grouping or interval in a frequency distribution should be ________.

Answer: the same or equal Difficulty: Easy Keywords: class interval, frequency distribution 100) In constructing a polygon, each class grouping is represented by its ________ and then these are consecutively connected to one another.

Answer: midpoint Difficulty: Easy Keywords: polygon, class interval, midpoint 101) A ________ is a summary table in which numerical data are tallied into class intervals or categories.

Answer: frequency distribution Difficulty: Easy Keywords: frequency distribution, class interval 102) True or False: In general, grouped frequency distributions should have between 5 and 15 class intervals.

Answer: TRUE Difficulty: Easy Keywords: frequency distribution, number of classes 103) True or False: The sum of relative frequencies in a distribution always equals 1.

Answer: TRUE Difficulty: Easy Keywords: relative frequency 104) True or False: The sum of cumulative frequencies in a distribution always equals 1.

Answer: FALSE Difficulty: Moderate Keywords: cumulative distribution 105) True or False: In graphing two categorical data, the side-by-side bar chart is best suited when comparing joint responses.

Answer: TRUE Difficulty: Moderate Keywords: side-by-side chart 106) True or False: When constructing a frequency distribution, classes should be selected so that they are of equal width.

Answer: TRUE Difficulty: Easy Keywords: frequency distribution 2-24 .

107) 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 Difficulty: Easy Keywords: frequency distribution, class interval 108) 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 Difficulty: Moderate Keywords: cumulative percentage distribution 109) 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 Difficulty: Easy Keywords: pie chart 110) 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 Difficulty: Easy Keywords: class interval, frequency distribution 111) True or False: Determining the class boundaries of a frequency distribution is highly subjective.

Answer: TRUE Difficulty: Easy Keywords: class boundaries, frequency distribution 112) True or False: The original data values cannot be determined once they are grouped into a frequency distribution table.

Answer: TRUE Difficulty: Easy Keywords: frequency distribution 113) True or False: The percentage distribution cannot be constructed from the frequency distribution directly.

Answer: FALSE Difficulty: Easy Keywords: percentage distribution, frequency distribution 114) 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 Difficulty: Easy Keywords: stem-and-leaf display, frequency distribution

2-25 .

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

Answer: TRUE Difficulty: Easy Keywords: relative frequency distribution 116) True or False: Ogives are plotted at the midpoints of the class groupings.

Answer: FALSE Difficulty: Easy Keywords: ogives, midpoint 117) True or False: Percentage polygons are plotted at the boundaries of the class groupings.

Answer: FALSE Difficulty: Easy Keywords: percentage polygons 118) True or False: The main principle behind the Pareto chart is the ability to separate the "vital few" from the "trivial many."

Answer: TRUE Difficulty: Easy Keywords: Pareto chart 119) True or False: A histogram can have gaps between the bars, whereas bar charts cannot have gaps.

Answer: FALSE Difficulty: Easy Keywords: histogram, bar chart 120) True or False: Histograms are used for numerical data while bar charts are suitable for categorical data.

Answer: TRUE Difficulty: Easy Keywords: histogram, bar chart 121) 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, the company has received 534 complaints.

One possible graphical method for representing these data would be a Pareto chart.

Answer: TRUE Difficulty: Moderate Keywords: Pareto chart 122) True or False: Apple Computer, Inc. collected information on the age of its customers. 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 Difficulty: Moderate Keywords: Pareto chart

2-26 .

123) True or False: Apple Computer, Inc. collected information on the age of its customers. 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 Difficulty: Moderate Keywords: pie chart 124) True or False: Apple Computer, Inc. collected information on the age of its customers. 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 Difficulty: Moderate Keywords: percentage polygon 125) True or False: Apple Computer, Inc. collected information on the age of its customers. 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 Difficulty: Moderate Keywords: ogive 126) 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 Difficulty: Moderate Keywords: Ogive 127) True or False: An ogive is a cumulative percentage polygon.

Answer: TRUE Difficulty: Easy Keywords: Ogive, cumulative percentage polygon 128) True or False: A side-by-side chart is two histograms plotted side-by-side.

Answer: FALSE Difficulty: Moderate Keywords: side-by-side chart 129) 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 Difficulty: Easy Keywords: number of classes 130) True or False: In general, a frequency distribution should have at least 8 class groups but no more than 20.

Answer: FALSE Difficulty: Easy Keywords: number of classes

2-27 .

131) True or False: True of False: To determine the width of class interval, divide the number of class groups by the range of the data.

Answer: FALSE Difficulty: Easy Keywords: class interval 132) 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 Difficulty: Easy Keywords: percentage polygon 133) True or False: A polygon can be constructed from a bar chart.

Answer: FALSE Difficulty: Moderate Keywords: polygon 134) True or False: 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 Difficulty: Easy Keywords: contingency table, cross-classification table 135) True or False: Relationships in a contingency table can be examined more fully if the frequencies are converted into ________.

Answer: percentages or proportions Difficulty: Easy Keywords: contingency table TABLE 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 Neutral Against Totals 38 54 12 104 12 36 48 96 50 90 60 200

136) Referring to Table 2-12, construct a table of row percentages.

Answer: For Neutral Against Totals Female 36.54 51.92 11.54 100.00 Male 2.50 37.50 50.00 100.00 Totals 25.00 45.00 30.00 100.00 Difficulty: Easy Keywords: row percentages

2-28 .

137) Referring to Table 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 Difficulty: Easy Keywords: column percentages 138) Referring to Table 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 Difficulty: Easy Keywords: total percentages 139) Referring to Table 2-12, of those for the plan in the sample, ________ percent were females.

Answer: 76 Difficulty: Moderate Keywords: contingency table, column percentages 140) Referring to Table 2-12, of those neutral in the sample, ________ percent were males.

Answer: 40 Difficulty: Moderate Keywords: contingency table, column percentages 141) Referring to Table 2-12, of the males in the sample, ________ percent were for the plan.

Answer: 12.50 Difficulty: Moderate Keywords: contingency table 142) Referring to Table 2-12, of the females in the sample, ________ percent were against the plan.

Answer: 11.54 Difficulty: Moderate Keywords: contingency table 143) Referring to Table 2-12, of the females in the sample, ________ percent were either neutral or against the plan.

Answer: 63.46 or (51.92+11.54) Difficulty: Moderate Keywords: contingency table 144) Referring to Table 2-12, ________ percent of the 200 were females who were against the plan.

Answer: 6 Difficulty: Moderate Keywords: contingency table

2-29 .

145) Referring to Table 2-12, ________ percent of the 200 were males who were neutral.

Answer: 18 Difficulty: Moderate Keywords: contingency table 146) Referring to Table 2-12, ________ percent of the 200 were females who were either neutral or against the plan.

Answer: 33 Difficulty: Difficult Keywords: contingency table 147) Referring to Table 2-12, ________ percent of the 200 were males who were not against the plan.

Answer: 24 Difficulty: Difficult Keywords: contingency table 148) Referring to Table 2-12, ________ percent of the 200 were not neutral.

Answer: 55 Difficulty: Difficult Keywords: contingency table, row percentages 149) Referring to Table 2-12, ________ percent of the 200 were against the plan.

Answer: 30 Difficulty: Moderate Keywords: contingency table, row percentages 150) Referring to Table 2-12, ________ percent of the 200 were males.

Answer: 48 Difficulty: Easy Keywords: contingency table, column percentages 151) Referring to Table 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 Difficulty: Moderate Keywords: contingency table, row percentages 152) Referring to Table 2-12, if the sample is a good representation of the population, we can expect ________ percent of the population will be males.

Answer: 48 Difficulty: Moderate Keywords: contingency table, column percentages 153) Referring to Table 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 Difficulty: Moderate Keywords: contingency table

2-30 .

154) Referring to Table 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 Difficulty: Moderate Keywords: contingency table 155) Referring to Table 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) Difficulty: Moderate Keywords: contingency table TABLE 2-13 Given below is the stem-and-leaf display representing the amount of detergent used in gallons (with leaves in tenths of gallons) in a day by 25 drive-through car wash operations in Phoenix.

9 | 147 10 | 02238 11 | 135566777 12 | 223489 13 | 02 156) Referring to Table 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 Difficulty: Easy Keywords: frequency distribution 157) Referring to Table 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% Difficulty: Moderate Keywords: relative frequency distribution, percentage distribution 158) Referring to Table 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% Difficulty: Easy Keywords: percentage distribution, cumulative relative frequency 159) Referring to Table 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% Difficulty: Easy Keywords: relative frequency distribution, percentage distribution 2-31 .

160) Referring to Table 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 but less than 13 gallons of detergent in a day?

Answer: 80% Difficulty: Easy Keywords: relative frequency distribution, percentage distribution 161) Referring to Table 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 Difficulty: Moderate Keywords: frequency distribution 162) Referring to Table 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 Difficulty: Moderate Keywords: relative frequency distribution, percentage distribution 163) Referring to Table 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 Difficulty: Moderate Keywords: cumulative percentage distribution

2-32 .

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

Answer:

Difficulty: Moderate Keywords: histogram, frequency distribution 165) Referring to Table 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:

Difficulty: Moderate Keywords: cumulative percentage polygon

2-33 .

166) Referring to Table 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:

Difficulty: Moderate Keywords: percentage distribution, percentage polygon TABLE 2-14 The table below contains the number of people who own a portable DVD player in a sample of 600 broken down by gender.

Own a Portable DVD Player Yes No

Male 96 224

Female 40 240

167) Referring to Table 2-14, construct a table of row percentages.

Answer: Own Male Female Total Yes 70.59% 29.41% 100.00% No 48.28% 51.72% 100.00% Total 53.33% 46.67% 100.00% Difficulty: Easy Keywords: row percentages 168) Referring to Table 2-14, construct a table of column percentages.

Answer: Own Male Female Total Yes 30.00% 14.29% 22.67% No 70.00% 85.71% 77.33% Total 100.00% 100.00% 100.00% Difficulty: Easy Keywords: column percentages

2-34 .

169) Referring to Table 2-14, construct a table of total percentages.

Answer: Own Male Female Total Yes 16.00% 6.67% 22.67% No 37.33% 40.00% 77.33% Total 53.33% 46.67% 100.00% Difficulty: Easy Keywords: total percentages 170) Referring to Table 2-14, of those who owned a portable DVD in the sample, ________ percent were females.

Answer: 29.41 Difficulty: Moderate Keywords: contingency table, row percentages 171) Referring to Table 2-14, of those who did not own a portable DVD in the sample, ________ percent were males.

Answer: 48.28 Difficulty: Moderate Keywords: contingency table, row percentages 172) Referring to Table 2-14, of the males in the sample, ________ percent owned a portable DVD. Answer: 30 Difficulty: Moderate Keywords: contingency table, column percentages 173) Referring to Table 2-14, of the females in the sample, ________ percent did not own a portable DVD. Answer: 85.71 Difficulty: Moderate Keywords: contingency table, column percentages 174) Referring to Table 2-14 of the females in the sample, ________ percent owned a portable DVD. Answer: 14.29 Difficulty: Moderate Keywords: contingency table, column percentages 175) Referring to Table 2-14, ________ percent of the 600 were females who owned a portable DVD. Answer: 6.67 Difficulty: Moderate Keywords: contingency table, total percentage 176) Referring to Table 2-14, ________ percent of the 600 were males who owned a portable DVD. Answer: 16 Difficulty: Moderate Keywords: contingency table, total percentage

2-35 .

177) Referring to Table 2-14, ________ percent of the 600 were females who either owned or did not own a portable DVD. Answer: 46.67 Difficulty: Moderate Keywords: contingency table, total percentage 178) Referring to Table 2-14, ________ percent of the 600 were males who did not own a portable DVD. Answer: 37.33 Difficulty: Moderate Keywords: contingency table, total percentage 179) Referring to Table 2-14, ________ percent of the 600 owned a portable DVD. Answer: 22.67 Difficulty: Moderate Keywords: contingency table, column percentages 180) Referring to Table 2-14, ________ percent of the 600 did not own a portable DVD. Answer: 77.33 Difficulty: Moderate Keywords: contingency table, column percentages 181) Referring to Table 2-14, ________ percent of the 600 were females.

Answer: 46.67 Difficulty: Easy Keywords: contingency table, row percentages 182) Referring to Table 2-14, if the sample is a good representation of the population, we can expect ________ percent of the population will own a portable DVD. Answer: 22.67 Difficulty: Moderate Keywords: contingency table, column percentages 183) Referring to Table 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 Difficulty: Moderate Keywords: contingency table, column percentages 184) Referring to Table 2-14, if the sample is a good representation of the population, we can expect ________ percent of those who own a portable DVD in the population will be males.

Answer: 70.59 Difficulty: Moderate Keywords: contingency table, row percentages 185) Referring to Table 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 DVD. Answer: 30 Difficulty: Moderate Keywords: contingency table, column percentages 2-36 .

186) Referring to Table 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 DVD. Answer: 85.71 Difficulty: Moderate Keywords: contingency table, column percentages TABLE 2-15 The figure below is the ogive for the amount of 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.

187) Referring to Table 2-15, roughly what percentage of pizza products contain less than 10 grams of fat?

A) 3% B) 14% C) 50% D) 75% Answer: B Difficulty: Easy Keywords: cumulative percentage polygon, ogive, interpretation 188) Referring to Table 2-15, what percentage of pizza products contain at least 20 grams of fat?

A) 5% B) 25% C) 75% D) 96% Answer: B Difficulty: Easy Keywords: cumulative percentage polygon, ogive, interpretation

2-37 .

189) Referring to Table 2-15, what percentage of pizza products contain between 10 and 25 grams of fat?

A) 14% B) 44% C) 62% D) 81% Answer: D Difficulty: Easy Keywords: cumulative percentage polygon, ogive, interpretation TABLE 2-16 The figure below is the percentage polygon for the amount of calories for a sample of 36 pizzas products where the upper limits of the intervals are: 310, 340, 370, 400 and 430.

190) Referring to Table 2-16, roughly what percentage of pizza products contain between 400 and 430 calories?

A) 0% B) 11% C) 89% D) 100% Answer: B Difficulty: Easy Keywords: percentage polygon, interpretation 191) Referring to Table 2-16, roughly what percentage of pizza products contain between 340 and 400 calories?

A) 22% B) 25% C) 28% D) 50% Answer: D Difficulty: Moderate Keywords: percentage polygon, interpretation

2-38 .

192) Referring to Table 2-16, roughly what percentage of pizza products contain at least 340 calories?

A) 25% B) 28% C) 39% D) 61% Answer: D Difficulty: Moderate Keywords: percentage polygon, interpretation TABLE 2-17 The following table presents total retail sales in millions of dollars for the leading apparel companies during April 2009 and April 2010.

Apparel Company Gap TJX Limited Kohl's Nordstrom Talbots AnnTaylor

April 2009 1,159.00 781.7 596.5 544.9 402.6 139.9 114.2

April 2010 962 899 620.4 678.9 418.3 130.1 124.8

193) Referring to Table 2-17, construct a table of column percentages.

Answer: Apparel Company April 2009 April 2010 Gap 31.00% 25.09% TJX 20.91% 23.45% Limited 15.95% 16.18% Kohl's 14.57% 17.71% Nordstrom 10.77% 10.91% Talbots 3.74% 3.39% AnnTaylor 3.05% 3.26% Total 100.00% 100.00% Difficulty: Moderate Keywords: column percentages

2-39 .

194) Referring to Table 2-17, construct a side-by-side bar chart.

Answer:

Difficulty: Moderate Keywords: column percentages, side-by-side chart 195) True or False: Referring to Table 2-17, in general, retail sales for the apparel industry have seen a modest growth between April 2008 and April 2009.

Answer: TRUE Difficulty: Easy Keywords: column percentages, side-by-side chart, interpretation 196) Referring to Table 2-17, among the 8 stores, ________ saw a sales decline.

Answer: Gap and Talbots Difficulty: Easy Keywords: column percentages, side-by-side chart, interpretation

2-40 .

TABLE 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.

197) Referring to Table 2-18, what was the highest level of satisfaction?

Answer: 97 Difficulty: Easy Keywords: stem-and-leaf display 198) Referring to Table 2-18, what was the lowest level of satisfaction?

Answer: 41 Difficulty: Easy Keywords: stem-and-leaf display 199) Referring to Table 2-18, how many students have a satisfaction level in the 50s?

Answer: 5 Difficulty: Easy Keywords: stem-and-leaf display 200) Referring to Table 2-18, how many students have a satisfaction level below 60?

Answer: 10 Difficulty: Easy Keywords: stem-and-leaf display 201) Referring to Table 2-18, how many students have a satisfaction level of at least 80?

Answer: 15 Difficulty: Easy Keywords: stem-and-leaf display 202) True or False: Referring to Table 2-18, the level of satisfaction is concentrated around 75.

Answer: TRUE Difficulty: Easy Keywords: stem-and-leaf display

2-41 .

203) True or False: Referring to Table 2-18, if a student is randomly selected, his/her most likely level of satisfaction among the 40s, 50s, 60s, 70s, 80s and 90s will be in the 70s.

Answer: TRUE Difficulty: Easy Keywords: stem-and-leaf display 204) True or False: Referring to Table 2-18, if a student is randomly selected, his/her most likely level of satisfaction among the 40s, 50s, 60s, 70s, 80s and 90s will be in the 60s.

Answer: FALSE Difficulty: Easy Keywords: stem-and-leaf display 205) 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.

Answer: TRUE Difficulty: Easy Keywords: scatter plot

2-42 .

206) 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.

Answer: FALSE Difficulty: Moderate Keywords: scatter plot 207) 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 Difficulty: Easy Keywords: scatter plot

2-43 .

208) 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.

Answer: FALSE Difficulty: Easy Keywords: scatter plot 209) 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.

Answer: TRUE Difficulty: Moderate Keywords: scatter plot

2-44 .

210) 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.

Answer: TRUE Difficulty: Moderate Keywords: scatter plot

2-45 .

Business Statistics: A First Course, 6e (Levine) 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 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) standard deviation Answer: C Difficulty: Easy Keywords: measure of central tendency, mode, arithmetic mean, median 3) Which of the arithmetic mean, median, and mode are resistant measures of central tendency?

A) the arithmetic only B) the median only C) the mode mean only D) the median and mode only Answer: D 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 Difficulty: Easy Keywords: shape 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 Difficulty: Easy Keywords: median, measure of central tendency, resistant to outliers, quartile

3-1 .

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 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 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 Difficulty: Easy Keywords: resistant to outliers, coefficient of variation, range, arithmetic mean, standard deviation, interquartile range, median, variance 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 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 Difficulty: Moderate Keywords: variation, arithmetic mean, interquartile range, standard deviation, coefficient of variation

3-2 .

11) Which descriptive summary measures are considered to be 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 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 Difficulty: Easy Keywords: shape, quartiles, arithmetic mean, mode 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 Difficulty: Easy Keywords: shape, quartiles, five-number summary, 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 Difficulty: Easy Keywords: shape, quartiles, five-number summary, quartiles

3-3 .

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 Difficulty: Moderate Keywords: empirical rule, normal distribution 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 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 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 median C) the mode D) the interquartile range Answer: D Difficulty: Easy Keywords: measure of central tendency, arithmetic mean, median, 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 Difficulty: Moderate Keywords: resistant to outliers, range, standard deviation, interquartile range, coefficient of variation

3-4 .

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 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 standard deviation Answer: C Difficulty: Easy Keywords: mode, arithmetic mean, median, standard deviation 22) According to the Chebyshev rule, at least 75% of all observations in any data set are contained within a distance of how many standard deviations around the mean?

A) 1 B) 2 C) 3 D) 4 Answer: B 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 a distance of how many standard deviations around the mean?

A) 1 B) 2 C) 3 D) 4 Answer: D Difficulty: Moderate Keywords: Chebyshev rule 24) According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 3 standard deviations around the mean?

A) 67% B) 75% C) 88.89% D) 99.7% Answer: C Difficulty: Easy Keywords: Chebyshev rule

3-5 .

25) According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 2 standard deviations around the mean?

A) 67% B) 75% C) 88.89% D) 95% Answer: B Difficulty: Easy Keywords: Chebyshev rule 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 were 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

A) right-skewed.

B) left-skewed.

C) symmetrical.

D) none of the above Answer: A Difficulty: Easy Keywords: boxplot

3-6 .

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 were collected. Below is the boxplot for the change in cost in dollars. The distribution of the change in cost is

A) right-skewed.

B) left-skewed.

C) symmetrical.

D) none of the above Answer: A Difficulty: Easy Keywords: boxplot TABLE 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 Table 3-1, calculate the arithmetic mean age of the senior citizens to the nearest hundredth of a year.

Answer: 74.04 years Difficulty: Easy Keywords: arithmetic mean 29) Referring to Table 3-1, determine the median age of the senior citizens.

Answer: 73 years Difficulty: Easy Keywords: median 30) Referring to Table 3-1 determine the first quartile of the ages of the senior citizens.

Answer: 65.5 years Difficulty: Moderate Keywords: quartiles

3-7 .

31) Referring to Table 3-1 determine the third quartile of the ages of the senior citizens.

Answer: 81.5 years Difficulty: Moderate Keywords: quartiles 32) Referring to Table 3-1, determine the interquartile range of the ages of the senior citizens.

Answer: 16 years Difficulty: Moderate Keywords: interquartile range 33) Referring to Table 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 of the above are correct.

Answer: A Difficulty: Moderate Keywords: quartiles, arithmetic mean 34) Referring to Table 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 of the above are correct.

Answer: C Difficulty: Moderate Keywords: quartiles 35) Referring to Table 3-1, what type of shape does the distribution of the sample appear to have?

Answer: Slightly positive or right-skewed.

Difficulty: Moderate Keywords: shape 36) Referring to Table 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 Difficulty: Moderate Keywords: variance 37) Referring to Table 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 Difficulty: Moderate Keywords: standard deviation 38) Referring to Table 3-1, calculate the coefficient of variation of the ages of the senior citizens.

Answer: 13.16% Difficulty: Moderate Keywords: coefficient of variation 3-8 .

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

Answer: FALSE Difficulty: Moderate Keywords: median 40) True or False: The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5 is 4.05.

Answer: FALSE Difficulty: Moderate Keywords: median 41) True or False: In a set of numerical data, the value for Q3 can never be smaller than the value for Q1.

Answer: TRUE Difficulty: Easy Keywords: quartiles 42) True or False: In a set of numerical data, the value for Q2 is always halfway between Q1 and Q3.

Answer: FALSE Difficulty: Easy Keywords: quartiles 43) 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 Difficulty: Moderate Keywords: boxplot, quartiles, shape 44) 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 Difficulty: Moderate Keywords: quartiles, shape 45) 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 Difficulty: Moderate Keywords: quartiles, shape 46) True or False: A boxplot is a graphical representation of a five-number summary.

Answer: TRUE Difficulty: Easy Keywords: boxplot, five-number summary 47) 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 Difficulty: Easy Keywords: five-number summary 3-9 .

48) True or False: In a boxplot, the box portion represents the data between the first and third quartile values.

Answer: TRUE Difficulty: Easy Keywords: boxplot 49) True or False: The line drawn within the box of the boxplot always represents the arithmetic mean.

Answer: FALSE Difficulty: Easy Keywords: boxplot, arithmetic mean 50) True or False: The line drawn within the box of the boxplot always represents the median.

Answer: TRUE Difficulty: Easy Keywords: boxplot, median 51) 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 Σ Xi = 600.

Answer: TRUE Difficulty: Easy Keywords: arithmetic mean 52) 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 Difficulty: Easy Keywords: arithmetic mean, standard deviation 53) True or False: In exploratory data analysis, a boxplot can be used to illustrate the median, quartiles, and extreme values.

Answer: TRUE Difficulty: Easy Keywords: boxplot, five-number summary 54) 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 Difficulty: Easy Keywords: median, arithmetic mean 55) True or False: The coefficient of variation measures variability in a data set relative to the size of the arithmetic mean.

Answer: TRUE Difficulty: Easy Keywords: coefficient of variation

3-10 .

56) True or False: The coefficient of variation is expressed as a percentage.

Answer: TRUE Difficulty: Easy Keywords: coefficient of variation 57) True or False: The coefficient of variation is a measure of central tendency in the data.

Answer: FALSE Difficulty: Easy Keywords: coefficient of variation, measure of variation 58) True or False: The interquartile range is a measure of variation or dispersion in a set of data.

Answer: TRUE Difficulty: Easy Keywords: interquartile range, measure of variation 59) True or False: The interquartile range is a measure of central tendency in a set of data.

Answer: FALSE Difficulty: Easy Keywords: interquartile range, measure of variation 60) True or False: The median is a measure of variation or dispersion in a set of data.

Answer: FALSE Difficulty: Easy Keywords: median, measure of central tendency 61) True or False: If a set of data is perfectly symmetrical, the arithmetic mean must be identical to the median.

Answer: TRUE Difficulty: Easy Keywords: shape, arithmetic mean, median 62) True or False: The coefficient of variation is a measure of relative variation.

Answer: TRUE Difficulty: Moderate Keywords: coefficient of variation 63) 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 Difficulty: Moderate Keywords: empirical rule, Chebyshev rule, normal distribution 64) If the arithmetic mean of a numerical data set is greater than the median, the data are considered to be ________-skewed.

Answer: positive or right Difficulty: Easy Keywords: shape, arithmetic mean, median

3-11 .

TABLE 3-2 The data below represent the amount 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 65) Referring to Table 3-2, the arithmetic mean carbohydrates in this sample is ________ grams.

Answer: 217/11 = 19.73 Difficulty: Moderate Keywords: arithmetic mean 66) Referring to Table 3-2, the median carbohydrate amount in the cereal is ________ grams.

Answer: 20 Difficulty: Moderate Keywords: median 67) Referring to Table 3-2, the first quartile of the carbohydrate amounts is ________ grams.

Answer: 15 Difficulty: Moderate Keywords: quartiles 68) Referring to Table 3-2, the third quartile of the carbohydrate amounts is ________ grams.

Answer: 23 Difficulty: Moderate Keywords: quartiles 69) Referring to Table 3-2, the range in the carbohydrate amounts is ________ grams.

Answer: 18 Difficulty: Easy Keywords: range 70) Referring to Table 3-2, the interquartile range in the carbohydrate amounts is ________ grams.

Answer: 8 Difficulty: Moderate Keywords: interquartile range 71) Referring to Table 3-2, the variance of the carbohydrate amounts is ________ (grams squared).

Answer: 26.02 Difficulty: Moderate Keywords: variance 72) Referring to Table 3-2, the standard deviation of the carbohydrate amounts is ________ grams.

Answer: 5.10 Difficulty: Moderate Keywords: standard deviation 73) Referring to Table 3-2, the coefficient of variation of the carbohydrate amounts is ________ percent.

Answer: 25.86 Difficulty: Moderate Keywords: coefficient of variation 3-12 .

74) Referring to Table 3-2, the five-number summary of the carbohydrate amounts consists of ________, ________, ________, ________, ________.

Answer: 11, 15, 20, 23, 29 Difficulty: Moderate Keywords: five-number summary 75) Referring to Table 3-2, construct a boxplot for the carbohydrate amounts.

Answer:

Difficulty: Moderate Keywords: boxplot TABLE 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.

76) Referring to Table 3-3, the arithmetic mean of the number of vitamin supplements sold in this sample is ________.

Answer: 28 Difficulty: Easy Keywords: arithmetic mean 77) Referring to Table 3-3, the first quartile of the number of vitamin supplements sold in this sample is ________.

Answer: 20 Difficulty: Moderate Keywords: quartiles 78) Referring to Table 3-3, the third quartile of the number of vitamin supplements sold in this sample is ________.

Answer: 35 Difficulty: Moderate Keywords: quartiles 3-13 .

79) Referring to Table 3-3, the median number of vitamin supplements sold in this sample is ________.

Answer: 26.5 Difficulty: Moderate Keywords: median 80) Referring to Table 3-3, the range of the number of vitamin supplements sold in this sample is ________.

Answer: 22 Difficulty: Easy Keywords: range 81) Referring to Table 3-3, the interquartile range of the number of vitamin supplements sold in this sample is ________.

Answer: 15 Difficulty: Moderate Keywords: interquartile range 82) Referring to Table 3-3, the variance of the number of vitamin supplements sold in this sample is ________.

Answer: 54.13 Difficulty: Easy Keywords: variance 83) Referring to Table 3-3, the standard deviation of the number of vitamin supplements sold in this sample is ________.

Answer: 7. 36 Difficulty: Easy Keywords: standard deviation 84) Referring to Table 3-3, the coefficient of variation of the number of vitamin supplements sold in this sample is ________ percent.

Answer: 26.3 Difficulty: Moderate Keywords: coefficient of variation 85) Referring to Table 3-3, the five-number summary of the data in this sample consists of ________, ________, ________, ________, ________.

Answer: 19, 20, 26.5, 35, 41 Difficulty: Moderate Keywords: five-number summary

3-14 .

86) Referring to Table 3-3, construct a boxplot for the data in this sample.

Answer:

Difficulty: Moderate Keywords: boxplot 87) Referring to Table 3-3, what type of shape does the distribution of the sample appear to have?

Answer: slightly positive- or right-skewed Difficulty: Moderate Keywords: shape TABLE 3-4 The ordered array below represents the number of cargo manifests approved by customs inspectors at 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.

88) Referring to Table 3-4, the arithmetic mean of the customs data is ________.

Answer: 23.9 Difficulty: Easy Keywords: arithmetic mean 89) Referring to Table 3-4, the median of the customs data is ________.

Answer: 23 Difficulty: Moderate Keywords: median 90) Referring to Table 3-4, the first quartile of the customs data is ________.

Answer: 21 Difficulty: Moderate Keywords: quartiles

3-15 .

91) Referring to Table 3-4, the third quartile of the customs data is ________.

Answer: 27 Difficulty: Moderate Keywords: quartiles 92) Referring to Table 3-4, the range of the customs data is ________.

Answer: 16 Difficulty: Easy Keywords: range 93) Referring to Table 3-4, the interquartile range of the customs data is ________.

Answer: 6 Difficulty: Moderate Keywords: interquartile range 94) Referring to Table 3-4, the variance of the customs data is ________.

Answer: 18.2 Difficulty: Easy Keywords: variance 95) Referring to Table 3-4, the standard deviation of the customs data is ________.

Answer: 4.3 Difficulty: Easy Keywords: standard deviation 96) Referring to Table 3-4, the coefficient of variation of the customs data is ________ percent.

Answer: 17.8 or 18 Difficulty: Moderate Keywords: coefficient of variation 97) Referring to Table 3-4, the five-number summary for the data in the customs sample consists of ________, ________, ________, ________, ________.

Answer: 16, 21, 23, 27, 32 Difficulty: Moderate Keywords: five-number summary

3-16 .

98) Referring to Table 3-4, construct a boxplot of this sample.

Answer:

Difficulty: Moderate Keywords: boxplot TABLE 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% 99) Referring to Table 3-5, compute the arithmetic mean rate of return per year.

Answer: 2.48% Difficulty: Easy Keywords: arithmetic mean 100) Referring to Table 3-5, what is the range of the rate of return?

Answer: 18.55% Difficulty: Easy Keywords: range 101) Referring to Table 3-5, construct a boxplot for the rate of return.

Answer:

Difficulty: Easy Keywords: boxplot

3-17 .

102) Referring to Table 3-5, what is the shape of the distribution for the rate of return?

Answer: left-skewed Difficulty: Easy Keywords: shape TABLE 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%.

103) Referring to Table 3-6, compute the arithmetic mean rate of return per year.

Answer: 15.30% Difficulty: Easy Keywords: arithmetic mean 104) Referring to Table 3-6, construct a boxplot for the rate of return Answer:

Difficulty: Moderate Keywords: boxplot 105) Referring to Table 3-6, what is the shape of the distribution for the rate of return?

Answer: right-skewed Difficulty: Moderate Keywords: shape 106) 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% Difficulty: Moderate Keywords: quartile 107) 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% Difficulty: Moderate Keywords: quartile

3-18 .

108) 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% Difficulty: Moderate Keywords: quartile 109) 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% Difficulty: Moderate Keywords: quartile 110) True or False: The Z scores can be used to identify outliers.

Answer: TRUE Difficulty: Easy Keywords: Z scores 111) True or False: The larger the Z score, the farther is the distance from the value to the median.

Answer: FALSE Difficulty: Moderate Keywords: Z scores 112) True or False: As a general rule, a value is considered an extreme value if its Z score is greater than -3.

Answer: FALSE Difficulty: Easy Keywords: Z score 113) True or False: As a general rule, a value is considered an extreme value if its Z score is greater than 3.

Answer: TRUE Difficulty: Easy Keywords: Z score 114) True or False: As a general rule, a value is considered an extreme value if its Z score is less than 3.

Answer: FALSE Difficulty: Easy Keywords: Z score 115) True or False: As a general rule, a value is considered an extreme value if its Z score is less than -3.

Answer: TRUE Difficulty: Easy Keywords: Z score 116) True or False: The Z score of a value can never be negative.

Answer: FALSE Difficulty: Moderate Keywords: Z score

3-19 .

117) True or False: The Z score of a value measures how many standard deviations the value is from the mean.

Answer: TRUE Difficulty: Moderate Keywords: Z score TABLE 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.

118) Referring to Table 3-7, what is the mean and median change in the cost?

Answer: $978, $895.5 Difficulty: Moderate Keywords: mean 119) Referring to Table 3-7, what is the five-number summary of the change in the cost?

Answer: $308, $593, $895.5, $1425, and $1720 Difficulty: Moderate Keywords: five-number summary 120) Referring to Table 3-7, what is the standard deviation of the change in the cost?

Answer: $491.8 Difficulty: Moderate Keywords: standard deviation 121) Referring to Table 3-7, what is the interquartile range of the change in the cost?

Answer: $832 Difficulty: Moderate Keywords: interquartile range 122) Referring to Table 3-7, what is the coefficient of variation of the change in cost?

Answer: 50.29% Difficulty: Moderate Keywords: coefficient of variation 123) Referring to Table 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 Difficulty: Moderate Keywords: Z scores 124) Referring to Table 3-7, are the data skewed? If so, how?

Answer: skewed to the right Difficulty: Moderate Keywords: shape

3-20 .

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

Bond Fund Vanguard GNMA Vanguard Total Bond Mkt. Index Bond Fund of America A Franklin Calif. Tax-Free Inc. A Vanguard Short-Term Corp.

Assets (Billions $) 19.5 16.8 13.7 12.8 10.9

125) Referring to Table 3-8, what is the mean for this population of the five largest bond funds?

Answer: $14.74 billions Difficulty: Easy Keywords: population mean 126) Referring to Table 3-8, what are the variance and standard deviation for this population?

Answer: 9.2984 squared billion dollars and $3.0493 billions, respectively Difficulty: Moderate Keywords: population variance, population standard deviation TABLE 3-9 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, 25.0 127) Referring to Table 3-9, what is the mean percentage of the total code that is part of the reuse database?

Answer: 44.69 Difficulty: Easy Keywords: population mean 128) Referring to Table 3-9, 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 Difficulty: Moderate Keywords: population variance, population standard deviation

3-21 .

TABLE 3-10 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.

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

129) Referring to Table 3-10, what is the sample covariance between the DJIA and the S&P 500 Index?

Answer: 31594.7333 Difficulty: Easy Keywords: covariance 130) Referring to Table 3-10, what is the sample correlation coefficient between the DJIA and the S&P 500 Index?

Answer: 0.9274 Difficulty: Easy Keywords: coefficient of correlation 131) Referring to Table 3-10, 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation 132) Referring to Table 3-10, 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation 133) Referring to Table 3-10, 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation

3-22 .

TABLE 3-11 Given below are the rating and performance scores of 15 laptop computers.

Performance Score 115 191 153 194 236 184 184 216 185 183 189 202 192 141 Overall Rating 74 78 79 80 84 76 77 92 83 78 77 78 78 73 134) Referring to Table 3-11, what is the sample covariance between the performance scores and the rating?

Answer: 88.8905 Difficulty: Moderate Keywords: covariance 135) Referring to Table 3-11, what is the sample correlation coefficient between the performance scores and the rating?

Answer: 0.6629 Difficulty: Moderate Keywords: coefficient of correlation 136) Referring to Table 3-11, 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation 137) Referring to Table 3-11, 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation 138) Referring to Table 3-11, 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation 3-23 .

TABLE 3-12 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 12-ounce energy drinks consumed by 10 college students within a week prior to the exam.

Exam Scores Number of Drinks

75

92

84

64

64

86

81

61

73

93

5

3

2

4

2

7

3

0

1

0

139) Referring to Table 3-12, what is the sample covariance between the exam scores and the number of energy drinks consumed?

Answer: 3.7667 Difficulty: Moderate Keywords: covariance 140) Referring to Table 3-12, what is the sample correlation coefficient between the exam scores and the number of energy drinks consumed?

Answer: 0.1450 Difficulty: Moderate Keywords: coefficient of correlation 141) Referring to Table 3-12, 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation 142) Referring to Table 3-12, 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 consumed as much energy drink.

B) be noticeably lower than the exam score had he/she not consumed as much energy drink.

C) not be noticeably different than the amount of energy drinks that he/she consumed.

D) not be noticeably different than the exam score had he/she not consumed as much.

Answer: D Difficulty: Moderate Keywords: coefficient of correlation, interpretation

3-24 .

143) Referring to Table 3-12, 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation

3-25 .

Business Statistics: A First Course, 6e (Levine) 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 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 Explanation: D) We do not know if they are mutually exclusive.

Difficulty: Moderate Keywords: collectively exhaustive, 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 Explanation: D) We do not know if they are collectively exhaustive.

Difficulty: Moderate Keywords: collectively exhaustive, mutually exclusive 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 Difficulty: Easy Keywords: mutually exclusive

4-1 .

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 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 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 Explanation: D) We do not know if they are equally likely events.

Difficulty: Moderate Keywords: collectively exhaustive, mutually exclusive 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 Difficulty: Easy Keywords: collectively exhaustive, mutually exclusive

4-2 .

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 Explanation: D) We do not know if they are collectively exhaustive.

Difficulty: Moderate Keywords: collectively exhaustive, mutually exclusive 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 Explanation: D) We do not know if they are mutually exclusive.

Difficulty: Moderate Keywords: collectively exhaustive, mutually exclusive 11) Selection of raffle tickets from a large bowl is an example of A) sampling with replacement.

B) sampling without replacement.

C) subjective probability.

D) none of the above Answer: B 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 Difficulty: Moderate Keywords: statistical independence 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 Difficulty: Easy Keywords: independence

4-3 .

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 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 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 Difficulty: Moderate Keywords: sample space 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 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 Difficulty: Easy Keywords: marginal probability

4-4 .

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 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 Difficulty: Easy Keywords: marginal 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).

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 5.19%?

A) 0.06 B) 0.41 C) 0.59 D) 1.00 Answer: B 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 Difficulty: Moderate Keywords: addition rule 4-5 .

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 Difficulty: Moderate Keywords: joint probability 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 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 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) 0.11 B) 0.195 C) 0.89 D) 0.90 Answer: A Difficulty: Moderate Keywords: joint probability, complement 4-6 .

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 increase during the next 6 months is ________.

A) 0.065 B) 0.15 C) 0.51 D) 0.89 Answer: B Explanation: B) 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) Difficulty: Difficult Keywords: joint probability, marginal probability, complement 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 Explanation: D) They are not statistically independent.

Difficulty: Moderate Keywords: joint probability, statistical independence 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 Difficulty: Moderate Keywords: mutually exclusive, collectively exhaustive, complement

4-7 .

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. Assuming that 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 Difficulty: Easy Keywords: 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. Assuming that 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 Difficulty: Easy Keywords: 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. Assuming that 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 Difficulty: Easy Keywords: independence, multiplication rule, addition rule, complement 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. Assuming that 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 Difficulty: Easy Keywords: independence, multiplication rule, joint probability, complement

4-8 .

34) According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household own two 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 Difficulty: Moderate Keywords: joint probability, conditional probability 35) According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household do not own two 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 Difficulty: Difficult Keywords: joint probability, complement, multiplication rule, conditional probability 36) According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents of a household own two 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: C Difficulty: Difficult Keywords: joint probability, complement, multiplication rule, conditional probability 37) According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that annual household income is over $50,000 if the residents of a household own two cars is ________.

A) 0.42 B) 0.48 C) 0.50 D) 0.69 Answer: D Difficulty: Difficult Keywords: conditional probability, Bayes' theorem

4-9 .

38) According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that annual household income is over $50,000 if the residents of a household do not own two cars is ________.

A) 0.12 B) 0.18 C) 0.40 D) 0.70 Answer: C Difficulty: Difficult Keywords: conditional probability, complement, Bayes' theorem 39) According to a survey of American households, the probability that the residents own two cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had two cars. The probability that the residents do not own two 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 Difficulty: Difficult Keywords: conditional probability, complement 40) A company has two 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 three 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 Difficulty: Easy Keywords: conditional probability, complement 41) A company has two 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 three 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 Difficulty: Moderate Keywords: marginal probability

4-10 .

42) A company has two 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 three 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 Difficulty: Difficult Keywords: conditional probability, Bayes' theorem TABLE 4-1 Mothers Against Drunk Driving is a very visible group whose main 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:

43) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, addition rule 44) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, joint probability

4-11 .

45) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, addition rule 46) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, marginal probability 47) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, conditional probability, addition rule 48) Referring to Table 4-1, given that three 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, conditional probability 49) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, conditional probability, complement

4-12 .

50) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, conditional probability, complement TABLE 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 Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, conditional probability 52) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, addition rule 53) Referring to Table 4-2, what is the probability that a randomly selected student did well on the midterm and also 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, joint probability

4-13 .

54) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, independence, joint probability 55) Referring to Table 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 Difficulty: Easy Keywords: contingency table, empirical classical probability, mutually exclusive, joint probability 56) Referring to Table 4-2, the events "Did Well on Midterm" and "Did Poorly on Midterm" are A) dependent.

B) mutually exclusive.

C) collective exhaustive.

D) all of the above Answer: D Difficulty: Easy Keywords: contingency table, empirical classical probability, independence, mutually exclusive, collective exhaustive, 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 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 Difficulty: Easy Keywords: sample space 59) True or False: If A and B cannot occur at the same time the events are called mutually exclusive.

Answer: TRUE Difficulty: Easy Keywords: mutually exclusive 60) True or False: If either A or B must occur the events are called mutually exclusive.

Answer: FALSE Difficulty: Easy Keywords: mutually exclusive, collective exhaustive

4-14 .

61) True or False: If either A or B must occur the events are called collectively exhaustive.

Answer: TRUE 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 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 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 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 Difficulty: Moderate Keywords: collective exhaustive 66) True or False: If P(A and B) = 0, then A and B must be mutually exclusive.

Answer: TRUE 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 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 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 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 Difficulty: Easy Keywords: statistical independence, multiplication rule 4-15 .

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 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 Difficulty: Easy Keywords: mutually exclusive, addition rule 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 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 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 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 Difficulty: Moderate Keywords: conditional probability TABLE 4-3 A survey is taken among customers of a fast-food restaurant to determine their 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 Table 4-3, the probability that a randomly selected individual is an adult is ________.

Answer: 125/200 or 62.5% Difficulty: Moderate Keywords: empirical classical probability, conditional probability, marginal probability

4-16 .

78) Referring to Table 4-3, the probability that a randomly selected individual is an adult or a child is ________.

Answer: 200/200 or 100% Difficulty: Moderate Keywords: empirical classical probability, addition rule 79) Referring to Table 4-3, the probability that a randomly selected individual is a child and prefers chicken is ________.

Answer: 20/200 or 10% Difficulty: Moderate Keywords: empirical classical probability, joint probability, multiplication rule 80) Referring to Table 4-3, the probability that a randomly selected individual is an adult and prefers chicken is ________.

Answer: 60/200 or 30% Difficulty: Moderate Keywords: empirical classical probability, joint probability, multiplication rule 81) Referring to Table 4-3, the probability that a randomly selected individual is a child or prefers hamburger is ________.

Answer: 140/200 or 70% Difficulty: Moderate Keywords: empirical classical probability, addition rule 82) Referring to Table 4-3, assume we know the person is a child. The probability that this individual prefers hamburger is ________.

Answer: 55/75 or 73.33% Difficulty: Moderate Keywords: empirical classical probability, conditional probability 83) Referring to Table 4-3, assume we know that a person prefers chicken. The probability that this individual is an adult is ________.

Answer: 60/80 or 75% Difficulty: Moderate Keywords: empirical classical probability, conditional probability, Bayes' theorem 84) Referring to Table 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% Difficulty: Moderate Keywords: empirical classical probability, conditional probability, Bayes' theorem

4-17 .

TABLE 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 Table 4-4, the probability a randomly selected patron prefers soda is ________.

Answer: 0.30 Difficulty: Moderate Keywords: addition rule, multiplication rule, marginal probability 86) Referring to Table 4-4, the probability a randomly selected patron is a female is ________.

Answer: 0.40 Difficulty: Moderate Keywords: addition rule, multiplication rule, marginal probability 87) Referring to Table 4-4, the probability a randomly selected patron is a female who prefers soda is ________.

Answer: 0.18 Difficulty: Difficult Keywords: addition rule, multiplication rule, joint probability 88) Referring to Table 4-4, the probability a randomly selected patron is a female who prefers water is ________.

Answer: 0.22 Difficulty: Difficult Keywords: addition rule, multiplication rule, joint probability 89) Referring to Table 4-4, suppose a randomly selected patron prefers soda. Then the probability the patron is a male is ________.

Answer: 0.40 Difficulty: Difficult Keywords: addition rule, multiplication rule, conditional probability 90) Referring to Table 4-4, suppose a randomly selected patron prefers water. Then the probability the patron is a male is ________.

Answer: 0.69 Difficulty: Difficult Keywords: addition rule, multiplication rule, conditional probability 91) Referring to Table 4-4, suppose a randomly selected patron is a female. Then the probability the patron prefers water is ________.

Answer: 0.55 Difficulty: Difficult Keywords: addition rule, multiplication rule, conditional probability 92) True or False: Referring to Table 4-4, the two events "preferring water" and "preferring soda" are independent.

Answer: FALSE Difficulty: Moderate Keywords: addition rule, multiplication rule, independence 4-18 .

93) True or False: Referring to Table 4-4, the two events "preferring water" and "being a male" are independent.

Answer: FALSE Difficulty: Moderate Keywords: addition rule, multiplication rule, independence TABLE 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 Table 4-5, if a package is selected at random, the probability that it will be properly sealed is ________.

Answer: 0.96 Difficulty: Moderate Keywords: addition rule, marginal probability 95) Referring to Table 4-5, if a package selected at random is improperly sealed, the probability that it came from machine A is ________.

Answer: 0.75 Difficulty: Difficult Keywords: conditional probability 96) Referring to Table 4-5, if a package selected at random came from Machine A, the probability that it is improperly sealed is ________.

Answer: 0.05 Difficulty: Difficult Keywords: conditional probability 97) Referring to Table 4-5, if a package selected at random came from Machine B, the probability that it is properly sealed is ________.

Answer: 0.975 Difficulty: Difficult Keywords: conditional probability, complement, addition rule 98) Referring to Table 4-5, if a package selected at random came from Machine B, the probability that it is improperly sealed is ________.

Answer: 0.025 Difficulty: Difficult Keywords: conditional probability, complement, addition rule

4-19 .

TABLE 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 Table 4-6, the probability that a randomly selected student is someone from northern Texas who has not passed the ELM is ________.

Answer: 0.09 Difficulty: Difficult Keywords: joint probability, multiplication rule 100) Referring to Table 4-6, the probability that a randomly selected student has passed the ELM is ________.

Answer: 0.66 Difficulty: Difficult Keywords: marginal probability, multiplication rule, addition rule 101) Referring to Table 4-6, if a randomly selected student has passed the ELM, the probability the student is from out-of-state is ________.

Answer: 0.136 Difficulty: Difficult Keywords: conditional probability, Bayes' theorem 102) Referring to Table 4-6, if a randomly selected student has not passed the ELM, the probability the student is from southern Texas is ________.

Answer: 0.706 Difficulty: Difficult Keywords: conditional probability, complement, Bayes' theorem 103) Referring to Table 4-6, the probability that a randomly selected student is not from southern Texas and has not passed the ELM is ________.

Answer: 0.10 Difficulty: Difficult Keywords: joint probability, complement, multiplication rule, addition 104) Referring to Table 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 Difficulty: Difficult Keywords: conditional probability, complement, addition rule, multiplication rule, Bayes' theorem 105) Referring to Table 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 Difficulty: Difficult Keywords: conditional probability, complement, addition rule, multiplication rule, Bayes' theorem

4-20 .

106) Referring to Table 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 Difficulty: Difficult Keywords: conditional probability, complement, addition rule, multiplication rule, Bayes' theorem TABLE 4-7 The next state lottery will have the following payoffs possible with their associated probabilities.

Payoff $2.00 $25.00 $100.00 $500.00 $5,000.00 $10,000.00

Probability 0.0500 0.0100 0.0050 0.0010 0.0005 0.0001

You buy a single ticket.

107) Referring to Table 4-7, the probability that you win any money is ________.

Answer: 0.0666 Difficulty: Easy Keywords: addition rule 108) Referring to Table 4-7, the probability that you win at least $100.00 is ________.

Answer: 0.0066 Difficulty: Easy Keywords: addition rule 109) Referring to Table 4-7, if you have a winning ticket, the probability that you win at least $100.00 is ________.

Answer: 0.10 Difficulty: Moderate Keywords: conditional probability, addition rule 110) A new model car from Ford Motor Company offers a keyless entry system that utilizes a four-letter code. How many different possible combinations are there for the code?

Answer: 456,976 Difficulty: Easy Keywords: counting rule 111) 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 Difficulty: Easy Keywords: counting rule

4-21 .

112) 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 Difficulty: Easy Keywords: counting rule, permutation 113) 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 Difficulty: Easy Keywords: counting rule, permutation 114) There are only four 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 four empty rooms be filled with one student per room?

Answer: 7,920 Difficulty: Easy Keywords: counting rule, permutation 115) There are only four 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 four empty rooms be filled with one student per room?

Answer: 330 Difficulty: Easy Keywords: counting rule, combination 116) 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 four freshmen be assigned?

Answer: 330 Difficulty: Easy Keywords: counting rule, combination 117) 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 Difficulty: Easy Keywords: counting rule, permutation 118) Seven passengers are on a waiting list for an overbooked flight. As a result of cancellations, three seats become available. How many different ways can those three available seats be filled regardless of the order?

Answer: 35 Difficulty: Easy Keywords: counting rule, combination

4-22 .

119) 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 Difficulty: Easy Keywords: counting rule, combination 120) 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 Difficulty: Difficult Keywords: counting rule, combination 121) 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 Difficulty: Moderate Keywords: counting rule, combination 122) 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 Difficulty: Moderate Keywords: counting rule, combination 123) 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 Difficulty: Moderate Keywords: counting rule, combination 124) 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 Explanation: ( (12!/(4! 8!)) (8!/(4! 4!)) ) / 3!

Difficulty: Difficult Keywords: counting rule, combination 125) The closing price of a company's stock tomorrow can be lower, higher or the same as today's closing price. 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 Difficulty: Easy Keywords: a priori probability, empirical probability, subjective probability 4-23 .

126) 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, on 25% of the days the closing price was higher than previous day's closing price, on 45% of the days it was lower than previous day's closing price, and on 30% of the days it was the same as previous day's closing price.

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 Difficulty: Easy Keywords: a priori probability, empirical probability, subjective probability 127) 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 Difficulty: Easy Keywords: a priori probability, empirical probability, subjective probability TABLE 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%.

128) Referring to Table 4-8, what is the probability that a randomly selected student is a freshman who lives in a dormitory?

Answer: 0.28 Difficulty: Easy Keywords: joint probability, multiplication rule 129) Referring to Table 4-8, what is the probability that a randomly selected student is a sophomore who does not live in a dormitory?

Answer: 0.1 Difficulty: Easy Keywords: joint probability, multiplication rule, complement 130) Referring to Table 4-8, what is the probability that a randomly selected student is a junior who does not live in a dormitory?

Answer: 0.112 Difficulty: Easy Keywords: joint probability, multiplication rule, complement 4-24 .

131) Referring to Table 4-8, what is the probability that a randomly selected student is a junior or senior who lives in a dormitory?

Answer: 0.096 Difficulty: Moderate Keywords: joint probability, multiplication rule, addition rule 132) Referring to Table 4-8, what percentage of the students live in a dormitory?

Answer: 0.526 Difficulty: Easy Keywords: marginal probability, multiplication rule, addition rule 133) Referring to Table 4-8, what percentage of the students do not live in a dormitory?

Answer: 0.474 Difficulty: Easy Keywords: marginal probability, multiplication rule, addition rule 134) Referring to Table 4-8, if a randomly selected student lives in the dormitory, what is the probability that the student is a freshman?

Answer: 0.532 Difficulty: Moderate Keywords: conditional probability, Bayes' theorem 135) Referring to Table 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 Difficulty: Moderate Keywords: conditional probability, Bayes' theorem, complement, addition rule 136) Referring to Table 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 Difficulty: Moderate Keywords: conditional probability, Bayes' theorem, complement, addition rule 137) Referring to Table 4-8, determine whether "the class status of a student" and "whether the student lives in a dormitory" are independent.

Answer: not independent Difficulty: Easy Keywords: independence

4-25 .

TABLE 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 noncash 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.

138) Referring to Table 4-9, set up a contingency table.

Answer:

Difficulty: Moderate Keywords: contingency table 139) Referring to Table 4-9, if a company is selected at random, what is the probability that the company offers stock options to their board members?

Answer: 83/369 = 0.2249 or 22.49% Difficulty: Easy Keywords: marginal probability 140) Referring to Table 4-9, if a company is selected at random, what is the probability that the company is small to mid-sized and does not offer stock options to their board members?

Answer: 137/369 = 0.3713 or 37.13% Difficulty: Easy Keywords: joint probability 141) Referring to Table 4-9, if a company is selected at random, what is the probability that the company is small to mid-sized or offers stock options to their board members?

Answer: 220/369 = 0.5962 or 59.62% Difficulty: Easy Keywords: addition rule 142) Referring to Table 4-9, if a randomly selected company is a large company, what is the probability that it offers stock options to their board members?

Answer: 40/189 = 0.2116 or 21.16% Difficulty: Easy Keywords: conditional probability 143) Referring to Table 4-9, if a randomly selected company offers stock options to their board members, what is the probability that it is a large company?

Answer: 40/83 = 0.4819 or 48.19% Difficulty: Easy Keywords: conditional probability

4-26 .

144) Referring to Table 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).

Difficulty: Moderate Keywords: conditional probability, independence TABLE 4-10 Are whites more likely to claim bias? It was found that 60% of the workers were white, 30% were black and 10% were 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%.

145) Referring to Table 4-10, what is the probability that a randomly selected worker had not claimed bias?

Answer: 0.7 or 70% Difficulty: Moderate Keywords: complement, marginal probability, multiplication rule 146) Referring to Table 4-10, if a randomly selected worker had claimed bias, what is the probability that the worker is white?

Answer: 0.6 or 60% Difficulty: Moderate Keywords: conditional probability, Bayes' theorem 147) Referring to Table 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% Difficulty: Moderate Keywords: conditional probability, Bayes' theorem 148) Referring to Table 4-10, what is the probability that a randomly selected worker is white and had claimed bias?

Answer: 0.18 or 18% Difficulty: Moderate Keywords: joint probability, multiplication rule 149) Referring to Table 4-10, what is the probability that a randomly selected worker is black and had not claimed bias?

Answer: 0.18 or 18% Difficulty: Moderate Keywords: joint probability, multiplication rule 150) Referring to Table 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% Difficulty: Moderate Keywords: joint probability, multiplication rule, addition rule

4-27 .

151) Referring to Table 4-10, what is the probability that a randomly selected worker is not black and had not claimed bias?

Answer: 0.52 or 52% Difficulty: Moderate Keywords: joint probability, multiplication rule, addition rule 152) Referring to Table 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% Difficulty: Moderate Keywords: conditional probability, multiplication rule, addition rule 153) 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 Difficulty: Easy Keywords: statistical independence 154) 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 Difficulty: Easy Keywords: ethic 155) True or False: An investment consultant is recommending a certain class of mutual funds to clients based on its exceptionally high probability of exceptionally high gain. It is an unethical practice to tell clients the probability of a loss in her recommendations.

Answer: FALSE Difficulty: Easy Keywords: ethic 156) True or False: An investment consultant is recommending a certain class of mutual funds to clients based on its exceptionally high probability of gain. It is an ethical practice to explain to clients what the basis of her probability estimate is.

Answer: TRUE Difficulty: Easy Keywords: ethic

4-28 .

157) True or False: An investment consultant is recommending a certain class of mutual funds to clients based on its exceptionally high probability of gain. It is an ethical practice to explain to clients what the meaning of probability is.

Answer: TRUE Difficulty: Easy Keywords: ethic 158) True or False: An investment consultant is recommending a certain class of mutual funds to clients 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 Difficulty: Easy Keywords: ethic TABLE 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.

159) Referring to Table 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% Difficulty: Easy Keywords: marginal probability 160) Referring to Table 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% Difficulty: Easy Keywords: marginal probability 161) Referring to Table 4-11, if an adult is selected at random, what is the probability that he/she is a registered voter who prefers to get his/her current information from the television?

Answer: 45/300 = 0.15 or 15% Difficulty: Easy Keywords: joint probability 162) Referring to Table 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% Difficulty: Moderate Keywords: joint probability, complement, and addition rule

4-29 .

163) Referring to Table 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% Difficulty: Easy Keywords: addition rule 164) Referring to Table 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% Difficulty: Moderate Keywords: addition rule 165) Referring to Table 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% Difficulty: Easy Keywords: conditional probability 166) Referring to Table 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% Difficulty: Easy Keywords: conditional probability 167) Referring to Table 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).

Difficulty: Moderate Keywords: conditional probability, independence TABLE 4-12 Jake wakes 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.

168) Referring to Table 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% Difficulty: Moderate Keywords: Bayes' theorem 169) Referring to Table 4-12, if Jake, in fact, gets to the test on time, what is the probability that he rode his bike?

Answer: 0.4286 or 42.86% Difficulty: Moderate Keywords: Bayes' theorem

4-30 .

170) Referring to Table 4-12, if Jake is late to the test, what is the probability that he rode his bike?

Answer: 0.6667 or 66.67% Difficulty: Moderate Keywords: Bayes' theorem 171) Referring to Table 4-12, if Jake is late to the test, what is the probability that he took the bus?

Answer: 0.3333 or 33.33% Difficulty: Moderate Keywords: Bayes' theorem

4-31 .

Business Statistics: A First Course, 6e (Levine) Chapter 5 Discrete Probability Distributions 1) Thirty-six of the staff of 80 teachers at a local intermediate school are certified in cardio-pulmonary 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 Difficulty: Moderate Keywords: binomial distribution, mean 2) A campus program evenly enrolls undergraduate and graduate students. If a random sample of four 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 four students selected are undergraduate students?

A) 0.0256 B) 0.0625 C) 0.16 D) 1.00 Answer: B Difficulty: Difficult Keywords: binomial distribution 3) A probability distribution is an equation that A) associates a particular 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 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 Difficulty: Easy Keywords: expected value

5-1 .

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 random variable of interest is continuous.

Answer: D Difficulty: Easy Keywords: binomial distribution, properties 6) In a binomial distribution, A) the random variable X is continuous.

B) the probability of event of interest π 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 Difficulty: Easy Keywords: binomial distribution, properties 7) Whenever π = 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 Difficulty: Moderate Keywords: binomial distribution, properties 8) Whenever π = 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 Difficulty: Moderate Keywords: binomial distribution, properties 9) If n = 10 and π = 0.70, then the mean of the binomial distribution is ________.

A) 0.07 B) 1.45 C) 7.00 D) 14.29 Answer: C Difficulty: Easy Keywords: binomial distribution, mean

5-2 .

10) If n = 10 and π = 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 Difficulty: Easy Keywords: binomial distribution, standard deviation 11) If the outcomes of a random variable follow a Poisson distribution, then their A) mean equals the standard deviation.

B) median equals the standard deviation.

C) mean equals the variance.

D) median equals the variance.

Answer: C 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) all of the above D) none of the above Answer: A Difficulty: Difficult Keywords: binomial distribution, properties 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) all of the above D) none of the above Answer: A Difficulty: Difficult Keywords: binomial distribution, properties

5-3 .

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 average number of blue chocolate chips per bag is 6.0. The manager is interested in analyzing the probability that any particular bag being inspected has fewer than 5.0 blue chocolate chips.

A) binomial distribution B) Poisson distribution C) all of the above D) none of the above Answer: B Difficulty: Moderate Keywords: Poisson distribution, properties 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) all of the above D) none of the above Answer: B 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) all of the above D) none of the above Answer: A Difficulty: Moderate Keywords: binomial distribution, properties 17) On 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) all of the above D) none of the above Answer: B Difficulty: Moderate Keywords: Poisson distribution, properties

5-4 .

18) 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) all of the above D) none of the above Answer: A Difficulty: Moderate Keywords: binomial distribution, properties 19) 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 average 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 Difficulty: Easy Keywords: mean 20) 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: Probability:

$10.00 0.35

$12.50 0.40

$15.00 0.25

How much should the lab budget for next year's rat orders be, assuming this distribution does not change?

A) $520 B) $637 C) $650 D) $780 Answer: B Difficulty: Moderate Keywords: mean, probability distribution 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 Difficulty: Easy Keywords: mean, Poisson distribution 5-5 .

22) True or False: The Poisson distribution can be used to model a continuous random variable.

Answer: FALSE 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 Difficulty: Easy Keywords: mean 24) True or False: The number of customers arriving at a department store in a five-minute period has a binomial distribution.

Answer: FALSE Difficulty: Easy Keywords: Poisson distribution, properties 25) True or False: The number of customers arriving at a department store in a five-minute period has a Poisson distribution.

Answer: TRUE Difficulty: Easy Keywords: Poisson distribution, properties 26) True or False: The diameters of 10 randomly selected bolts have a binomial distribution.

Answer: FALSE Difficulty: Easy Keywords: binomial distribution, properties 27) True or False: The largest value that a Poisson random variable X can have is n.

Answer: FALSE Difficulty: Moderate Keywords: Poisson distribution, properties 28) True or False: In a Poisson distribution, the mean and standard deviation are equal.

Answer: FALSE Difficulty: Moderate Keywords: Poisson distribution, properties 29) True or False: In a Poisson distribution, the mean and variance are equal.

Answer: TRUE Difficulty: Moderate Keywords: Poisson distribution, properties 30) True or False: If π remains constant in a binomial distribution, an increase in n will increase the variance.

Answer: TRUE Difficulty: Moderate Keywords: binomial distribution, properties

5-6 .

31) True or False: If π remains constant in a binomial distribution, an increase in n will not change the mean.

Answer: FALSE Difficulty: Moderate Keywords: binomial distribution, properties 32) 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 Difficulty: Moderate Keywords: binomial distribution, probability 33) True or False: Suppose that the number of airplanes arriving at an airport per minute is a Poisson process. The average number of airplanes arriving per minute is 3. The probability that exactly 6 planes arrive in the next minute is 0.05041.

Answer: TRUE Difficulty: Easy Keywords: Poisson distribution, probability TABLE 5-1 The probability that a particular type of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have two such alarms in your home and they operate independently.

34) Referring to Table 5-1, the probability that both sound an alarm in the presence of smoke is ________.

Answer: 0.64 Difficulty: Moderate Keywords: binomial distribution 35) Referring to Table 5-1, the probability that neither sound an alarm in the presence of smoke is ________.

Answer: 0.04 Difficulty: Moderate Keywords: binomial distribution 36) Referring to Table 5-1, the probability that at least one sounds an alarm in the presence of smoke is ________.

Answer: 0.96 Difficulty: Difficult Keywords: binomial distribution

5-7 .

TABLE 5-2 A certain type of new business succeeds 60% of the time. Suppose that three such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent).

37) Referring to Table 5-2, the probability that all three businesses succeed is ________.

Answer: 0.216 Difficulty: Moderate Keywords: binomial distribution 38) Referring to Table 5-2, the probability that all three businesses fail is ________.

Answer: 0.064 Difficulty: Moderate Keywords: binomial distribution 39) Referring to Table 5-2, the probability that at least one business succeeds is ________.

Answer: 0.936 Difficulty: Moderate Keywords: binomial distribution 40) Referring to Table 5-2, the probability that exactly one business succeeds is ________.

Answer: 0.288 Difficulty: Moderate Keywords: binomial distribution 41) If X has a binomial distribution with n = 4 and p = 0.3, then P(X = 1) = ________.

Answer: 0.4116 Difficulty: Easy Keywords: binomial distribution 42) If X has a binomial distribution with n = 4 and p = 0.3, then P(X > 1) = ________.

Answer: 0.3483 Difficulty: Moderate Keywords: binomial distribution 43) If X has a binomial distribution with n = 5 and p = 0.1, then P(X = 2) = ________.

Answer: 0.0729 Difficulty: Easy Keywords: binomial distribution 44) Suppose that past 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 Difficulty: Easy Keywords: binomial distribution

5-8 .

45) Suppose that past 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 Difficulty: Moderate Keywords: binomial distribution 46) Suppose that past 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 Difficulty: Easy Keywords: binomial distribution 47) Suppose that past 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 Difficulty: Easy Keywords: binomial distribution 48) Suppose that past 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 Difficulty: Moderate Keywords: binomial distribution 49) Suppose that past 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 Difficulty: Moderate Keywords: binomial distribution 50) Suppose that past 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 Difficulty: Moderate Keywords: binomial distribution 51) Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. The average number that you would expect to prefer Brand C is ________.

Answer: 3 Difficulty: Easy Keywords: binomial distribution, mean 52) Suppose that past 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 Difficulty: Easy Keywords: binomial distribution, variance

5-9 .

TABLE 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 double satellite media.

X P(X)

0 0.35

1 0.35

2 0.25

3 0.05

53) Referring to Table 5-3, the probability of no retransmissions is ________.

Answer: 0.35 Difficulty: Easy Keywords: probability distribution 54) Referring to Table 5-3, the probability of at least one retransmission is ________.

Answer: 0.65 Difficulty: Easy Keywords: probability distribution 55) Referring to Table 5-3, the mean or expected value for the number of retransmissions is ________.

Answer: 1.0 Difficulty: Easy Keywords: probability distribution, mean 56) Referring to Table 5-3, the variance for the number of retransmissions is ________.

Answer: 0.80 Difficulty: Easy Keywords: probability distribution, variance 57) Referring to Table 5-3, the standard deviation of the number of retransmissions is ________.

Answer: 0.894 Difficulty: Easy Keywords: probability distribution, standard deviation 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 does not get audited is ________.

Answer: 0.2373 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 once is ________.

Answer: 0.3955 Difficulty: Moderate Keywords: binomial distribution

5-10 .

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 at least once is ________.

Answer: 0.7627 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 probability that she gets audited no more than two times is ________.

Answer: 0.8965 Difficulty: Moderate Keywords: binomial distribution 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 expected number of times she will be audited is ________.

Answer: 1.25 Difficulty: Easy Keywords: binomial distribution, mean 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 variance of the number of times she will be audited is ________.

Answer: 0.9375 Difficulty: Moderate Keywords: binomial distribution, variance 64) 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 Difficulty: Moderate Keywords: binomial distribution, standard deviation

5-11 .

TABLE 5-4 The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Corvallis, Oregon.

X P(X)

0 0.10

1 0.20

2 0.45

3 0.15

4 0.05

5 0.05

65) Referring to Table 5-4, the probability of three accidents is ________.

Answer: 0.15 Difficulty: Easy Keywords: probability distribution 66) Referring to Table 5-4, the probability of at least one accident is ________.

Answer: 0.90 Difficulty: Easy Keywords: probability distribution 67) Referring to Table 5-4, the mean or expected value of the number of accidents is ________.

Answer: 2.0 Difficulty: Easy Keywords: probability distribution, mean, 68) Referring to Table 5-4, the variance of the number of accidents is ________.

Answer: 1.4 Difficulty: Easy Keywords: probability distribution, variance 69) Referring to Table 5-4, the standard deviation of the number of accidents is ________.

Answer: 1.18 Difficulty: Easy Keywords: probability distribution, standard deviation 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 exactly three power outages in a year is ________.

Answer: 0.0892 Difficulty: Easy Keywords: Poisson distribution 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 threepower outages in a year is ________.

Answer: 0.9380 Difficulty: Difficult 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 at least one power outage in a year is ________.

Answer: 0.9975 Difficulty: Moderate Keywords: Poisson distribution 5-12 .

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 no more than one power outage in a year is ________.

Answer: 0.0174 Difficulty: Moderate 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 probability that there will be between 1 and 3 inclusive power outages in a year is ________.

Answer: 0.1487 Difficulty: Difficult Keywords: Poisson distribution 75) 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 Difficulty: Easy Keywords: Poisson distribution 76) The number of 911 calls in Butte, Montana, 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 Difficulty: Easy Keywords: Poisson distribution 77) The number of 911 calls in Butte, Montana, 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 Difficulty: Moderate Keywords: Poisson distribution 78) The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 10 calls a day.

The probability of two or more 911 calls in a day is ________.

Answer: 0.9995 Difficulty: Moderate Keywords: Poisson distribution 79) The number of 911 calls in Butte, Montana, 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 Difficulty: Easy Keywords: Poisson distribution 80) The Department of Commerce in a particular 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 Difficulty: Moderate Keywords: Poisson distribution 5-13 .

81) The Department of Commerce in a particular 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 Difficulty: Easy Keywords: Poisson distribution 82) The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 75% of the home-based computers 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 Difficulty: Moderate Keywords: binomial distribution 83) The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that 75% of the home-based computers 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 Difficulty: Difficult Keywords: binomial distribution 84) A national trend predicts that women will account for half of all business travelers in the next three 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 of the hotels in the sample offered hairdryers in the bathrooms.

Answer: 0.0008 Difficulty: Moderate Keywords: binomial distribution 85) A national trend predicts that women will account for half of all business travelers in the next three 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.

Answer: 0.2264 Difficulty: Moderate Keywords: binomial distribution 86) A national trend predicts that women will account for half of all business travelers in the next three 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 Difficulty: Difficult Keywords: binomial distribution 5-14 .

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 less than 6 tickets are written on a randomly selected day from this population.

Answer: 0.3837 Difficulty: Easy Keywords: Poisson distribution 88) 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 Difficulty: Easy Keywords: Poisson distribution TABLE 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.

89) Referring to Table 5-5, what is the probability that any particular shift being inspected has produced 4.0 bad bulbs.

Answer: 0.1339 Difficulty: Easy Keywords: Poisson distribution 90) Referring to Table 5-5, what is the probability that any particular shift being inspected has produced fewer than 5.0 bad bulbs.

Answer: 0.2851 Difficulty: Moderate Keywords: Poisson distribution 91) Referring to Table 5-5, what is the probability that any particular shift being inspected has produced at least 6.0 bad bulbs.

Answer: 0.5543 Difficulty: Moderate Keywords: Poisson distribution 92) Referring to Table 5-5, what is the probability that any particular shift being inspected has produced between 5.0 and 8.0 inclusive bad bulbs.

Answer: 0.5622 Difficulty: Moderate Keywords: Poisson distribution

5-15 .

93) Referring to Table 5-5, what is the probability that any particular shift being inspected has less than 5.0 or more than 8.0 bad bulbs.

Answer: 0.4378 Difficulty: Difficult Keywords: Poisson distribution TABLE 5-6 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution:

94) Referring to Table 5-6, what is the expected value gain for the house in neighborhood A? Answer: $ 12,550 Difficulty: Easy Keywords: mean 95) Referring to Table 5-6, what is the expected value gain for the house in neighborhood B? Answer: $ 21,300 Difficulty: Easy Keywords: mean 96) Referring to Table 5-6, what is the variance of the gain in value for the house in neighborhood A? Answer: 583,147,500 dollars2 Difficulty: Easy Keywords: variance 97) Referring to Table 5-6, what is the variance of the gain in value for the house in neighborhood B? Answer: 67,460,000 dollars2 Difficulty: Easy Keywords: variance 98) Referring to Table 5-6, what is the standard deviation of the value gain for the house in neighborhood A? Answer: $24,148.45 Difficulty: Easy Keywords: standard deviation 99) Referring to Table 5-6, what is the standard deviation of the value gain for the house in neighborhood B? Answer: $8,213.40 Difficulty: Easy Keywords: standard deviation 5-16 .

TABLE 5-7 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

Probability 0.2 0.5 0.3

Taste more conservative no change more liberal

Design A 180 230 350

Design B 520 310 270

100) Referring to Table 5-7, the table above is called the ________ for the two designs.

Answer: probability distribution Difficulty: Easy Keywords: probability distribution 101) Referring to Table 5-7, what is your expected profit when Design A is chosen?

Answer: $256 thousands or $256,000 Difficulty: Easy Keywords: mean 102) Referring to Table 5-7, what is your expected profit when Design B is chosen?

Answer: $340 thousands or $340,000 Difficulty: Easy Keywords: mean 103) Referring to Table 5-7, what is the variance of your profit when Design A is chosen?

Answer: 4,144 × 1,0002 or 4,144,000,000 Difficulty: Difficult Keywords: variance 104) Referring to Table 5-7, what is the variance of your profit when Design B is chosen?

Answer: 8,400 × 1,0002 or 8,400,000,000 Difficulty: Difficult Keywords: variance 105) Referring to Table 5-7, what is the standard deviation of your profit when Design A is chosen?

Answer: $64.37391 thousands or $64,373.91 Difficulty: Easy Keywords: standard deviation 106) Referring to Table 5-7, what is the standard deviation of your profit when Design B is chosen?

Answer: $91.65151 thousands or $91,651.51 Difficulty: Easy Keywords: standard deviation

5-17 .

TABLE 5-8 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.

107) Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have no mishandled bags?

Answer: 0.0172 Difficulty: Easy Keywords: Poisson distribution 108) Referring to Table 5-8, what is the probability that in the next 1,000 customers, the chain will have at least one mishandled bags?

Answer: 0.9828 Difficulty: Easy Keywords: Poisson distribution 109) Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have at least two mishandled bags?

Answer: 0.9127 Difficulty: Easy Keywords: Poisson distribution 110) Referring to Table 5-8, 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 Difficulty: Easy Keywords: Poisson distribution 111) Referring to Table 5-8, 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 Difficulty: Easy Keywords: Poisson distribution 112) Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have fewer than six mishandled bags?

Answer: 0.7757 Difficulty: Easy Keywords: Poisson distribution 113) Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have fewer than eight mishandled bags?

Answer: 0.9452 Difficulty: Easy Keywords: Poisson distribution

5-18 .

114) Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have more than eight mishandled bags?

Answer: 0.02320 Difficulty: Easy Keywords: Poisson distribution 115) Referring to Table 5-8, what is the probability that in the next 1,000 customers, the hotel chain will have more than ten mishandled bags?

Answer: 0.003172 Difficulty: Easy Keywords: Poisson distribution 116) Referring to Table 5-8, 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 Difficulty: Moderate Keywords: Poisson distribution 117) Referring to Table 5-8, 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 Difficulty: Moderate Keywords: Poisson distribution 118) Referring to Table 5-8, 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 Difficulty: Moderate Keywords: Poisson distribution 119) Referring to Table 5-8, 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 Difficulty: Moderate Keywords: Poisson distribution 120) Referring to Table 5-8, 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 Difficulty: Difficult Keywords: Poisson distribution 121) Referring to Table 5-8, 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 Difficulty: Difficult Keywords: Poisson distribution

5-19 .

122) The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have five such alarms in your home and they operate independently.

Which of the following distributions would you use to determine the probability that all of them will function properly in case of a fire?

A) binomial distribution B) Poisson distribution C) both of the above D) none of the above Answer: A Difficulty: Easy Keywords: choice of distribution 123) A certain type of new business succeeds 60% of the time. Suppose that three such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). Which of the following distributions would you use to determine the probability that all of them will fail?

A) binomial distribution B) Poisson distribution C) both of the above D) none of the above Answer: A Difficulty: Easy Keywords: choice of distribution 124) Suppose that past history shows that 60% of college students prefer Coca-Cola®. A sample of 10 students is to be selected. Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola®?

A) binomial distribution B) Poisson distribution C) both of the above D) none of the above Answer: A Difficulty: Easy Keywords: choice of distribution 125) Suppose the probability of a power outage at a nuclear power plant on a single day is the same every day of the year. Also the probability of having a power outage on a single day does not increase or decrease the probability of a power outage on another day. Which of the following distributions would you use to determine the probability that a power outage will occur next Monday?

A) binomial distribution B) Poisson distribution C) both of the above D) none of the above Answer: B Difficulty: Easy Keywords: choice of distribution

5-20 .

126) The probability of receiving a 911 call on a university campus is the same every day. The probability of having received a 911 call on a single day does not change the probability of receiving a 911 call on any other day. Which of the following distributions would you use to determine the probability that a 911 call will be received next day?

A) binomial distribution B) Poisson distribution C) both of the above D) none of the above Answer: B Difficulty: Easy Keywords: choice of distribution 127) It was believed that the probability of a small business that declared bankruptcy per month was the same in any month. Also the number of small businesses that declared bankruptcy was the same every month. Which of the following distributions would you use to determine the probability that more than three bankruptcies will occur next month?

A) binomial distribution B) Poisson distribution C) both of the above D) none of the above Answer: B Difficulty: Easy Keywords: choice of distribution 128) The probability that a particular brand of smoke alarm will malfunction in the presence of smoke is 0.002. A batch of 100,000 such alarms was produced by independent production lines. Which of the following distributions would you use to figure out the probability that at most 5,000 of them will malfunction in case of a fire?

A) binomial distribution B) Poisson distribution C) both of the above D) none of the above Answer: B Difficulty: Moderate Keywords: choice of distribution 129) Suppose that past history shows that 6% of college students prefer Brand A cola. A sample of 10,000 students is to be selected. Which of the following distributions would you use to figure out the probability that at least half of them will prefer Brand A cola?

A) normal distribution B) Poisson distribution C) both of the above D) none of the above Answer: B Difficulty: Moderate Keywords: choice of distribution

5-21 .

TABLE 5-9 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.

130) Referring to Table 5-9, what is the mean number of transactions per month for this subscriber?

Answer: 5 Difficulty: Easy Keywords: Poisson distribution 131) Referring to Table 5-9, what is the variance of the number of transactions per month for this subscriber?

Answer: 5 Difficulty: Easy Keywords: Poisson distribution 132) Referring to Table 5-9, what is the probability that exactly ten security transactions will be conducted in one month?

Answer: 0.0181 Difficulty: Easy Keywords: Poisson distribution 133) Referring to Table 5-9, what is the probability that at least five security transactions will be conducted in one month?

Answer: 0.5595 Difficulty: Moderate Keywords: Poisson distribution 134) Referring to Table 5-9, what is the probability that no more than five security transactions will be conducted in one month?

Answer: 0.6160 Difficulty: Moderate Keywords: Poisson distribution 135) Referring to Table 5-9, what is the probability that no security transaction will be conducted in one month?

Answer: 0.0067 Difficulty: Moderate Keywords: Poisson distribution 136) Referring to Table 5-9, what is the probability that more than two security transactions will be conducted in one month?

Answer: 0.8753 Difficulty: Moderate Keywords: Poisson distribution

5-22 .

137) Referring to Table 5-9, what is the probability that fewer than two security transactions will be conducted in one month?

Answer: 0.0404 Difficulty: Moderate Keywords: Poisson distribution

5-23 .

Business Statistics: A First Course, 6e (Levine) 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 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, μ, and standard deviation, σ.

Answer: C Difficulty: Easy Keywords: normal distribution, properties 3) If a particular 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 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 Difficulty: Moderate Keywords: standardized normal distribution, value 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 Difficulty: Moderate Keywords: standardized normal distribution, value 6-1 .

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 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 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 Difficulty: Difficult Keywords: normal distribution, value 9) Given that X is a normally distributed random 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 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 Difficulty: Easy Keywords: standardized normal distribution, probability

6-2 .

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 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 Difficulty: Difficult Keywords: standardized normal distribution, value 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 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 Difficulty: Easy Keywords: standardized normal distribution, probability

6-3 .

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 Difficulty: Moderate Keywords: standardized normal distribution, value 16) The owner of a fish market determined that the average 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 Difficulty: Easy Keywords: standardized normal distribution, probability 17) The owner of a fish market determined that the average 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 Difficulty: Easy Keywords: standardized normal distribution, probability 18) The owner of a fish market determined that the average 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 Difficulty: Moderate Keywords: standardized normal distribution, value 19) The owner of a fish market determined that the average 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 Difficulty: Moderate Keywords: standardized normal distribution, value

6-4 .

20) The owner of a fish market determined that the average 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 Difficulty: Easy Keywords: normal distribution, probability 21) The amount of juice that can be squeezed from an orange randomly selected from a box of oranges that are all approximately the same size can most likely be modeled by which of the following distributions?

A) binomial distribution B) Poisson distribution C) normal distribution D) none of the above Answer: C Difficulty: Easy Keywords: normal distribution, properties 22) The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

A) binomial distribution B) Poisson distribution C) normal distribution D) none of the above Answer: C Difficulty: Easy Keywords: normal distribution, properties 23) Suppose that past history shows that 60% of college students prefer Coca-Cola®. A sample of 10,000 students is to be selected. Which of the following distributions would you use to figure out the probability that at least half of them will prefer Coca-Cola®?

A) binomial distribution B) Poisson distribution C) normal distribution D) none of the above Answer: C Difficulty: Moderate Keywords: normal distribution, properties

6-5 .

24) The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. A batch of 100,000 such alarms was produced by independent production lines. Which of the following distributions would you use to figure out the probability that at least 90,000 of them will function properly in case of a fire?

A) binomial distribution B) Poisson distribution C) normal distribution D) none of the above Answer: C Difficulty: Moderate Keywords: normal distribution, properties 25) A quality control manager at a plant that produces o-rings is concerned about whether the diameter of the o-rings that are produced is conformable to the specification. She has calculated that the average diameter of the o-rings is 4.2 centimeters. She also knows that approximately 95% of the o-rings have diameters fall between 3.2 and 5.2 centimeters and almost all of the o-rings have diameters between 2.7 and 5.7 centimeters. When modeling the diameters of the o-rings, which distribution should the quality control manager use?

A) Poisson distribution B) binomial distribution C) normal distribution D) none of the above Answer: C Difficulty: Moderate Keywords: normal distribution, properties 26) 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 Difficulty: Easy Keywords: standardized normal distribution, probability 27) 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 Difficulty: Easy Keywords: normal distribution, probability 28) True or False: The probability that a standard normal random variable, Z, falls between -1.50 and 0.81 is 0.7242.

Answer: TRUE Difficulty: Easy Keywords: standardized normal distribution, probability

6-6 .

29) True or False: The probability that a standard normal random 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 Difficulty: Easy Keywords: standardized normal distribution, probability 30) True or False: The probability that a standard normal random variable, Z, is below 1.96 is 0.4750.

Answer: FALSE Difficulty: Easy Keywords: standardized normal distribution, probability 31) True or False: The probability that a standard normal random variable, Z, is between 1.00 and 3.00 is 0.1574.

Answer: TRUE Difficulty: Easy Keywords: standardized normal distribution, probability 32) True or False: The probability that a standard normal random variable, Z, falls between -2.00 and 0.44 is 0.6472.

Answer: FALSE Difficulty: Easy Keywords: standardized normal distribution, probability 33) True or False: The probability that a standard normal random variable, Z, is less than 5.0 is approximately 0.

Answer: FALSE Difficulty: Easy Keywords: standardized normal distribution, probability 34) 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 average wage for the plant is $7.50 per hour.

Answer: FALSE Difficulty: Moderate Keywords: standardized normal distribution, mean 35) True or False: Theoretically, the mean, median, and mode are all equal for a normal distribution.

Answer: TRUE Difficulty: Easy Keywords: normal distribution, properties 36) True or False: Any set of normally distributed data can be transformed to its standardized form.

Answer: TRUE Difficulty: Easy Keywords: normal distribution, properties

6-7 .

37) True or False: The "middle spread," that is, the middle 50% of the normal distribution, is equal to one standard deviation.

Answer: FALSE Difficulty: Moderate Keywords: normal distribution, probability, value 38) True or False: A normal probability plot may be used to assess the assumption of normality for a particular set of data.

Answer: TRUE Difficulty: Easy Keywords: normal probability plot 39) True or False: If a data set is approximately normally distributed, its normal probability plot would be S-shaped.

Answer: FALSE Difficulty: Moderate Keywords: normal probability plot 40) The probability that a standard normal variable Z is positive is ________.

Answer: 0.50 Difficulty: Easy Keywords: standardized normal distribution 41) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain between 100 and 110 grams of tea leaves?

Answer: 0.1554 Difficulty: Easy Keywords: normal distribution, probability 42) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain between 82 and 100 grams of tea leaves?

Answer: 0.2132 Difficulty: Easy Keywords: normal distribution, probability 43) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain at least 100 grams of tea leaves?

Answer: 0.6554 Difficulty: Easy Keywords: normal distribution, probability 44) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain between 100 and 120 grams of tea leaves?

Answer: 0.3108 Difficulty: Moderate Keywords: normal distribution, probability 6-8 .

45) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain less than 100 grams of tea leaves?

Answer: 0.3446 Difficulty: Easy Keywords: normal distribution, probability 46) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 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 Difficulty: Easy Keywords: normal distribution, probability 47) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 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 Difficulty: Moderate Keywords: normal distribution, value 48) 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 Difficulty: Easy Keywords: normal distribution, probability 49) 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 Difficulty: Easy Keywords: normal distribution, probability 50) 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 Difficulty: Easy Keywords: normal distribution, probability

6-9 .

51) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be longer than 17 seconds?

Answer: 7% or 0.07 Difficulty: Easy Keywords: normal distribution, probability 52) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be between 13 and 14 seconds?

Answer: 13% or 0.13 Difficulty: Easy Keywords: normal distribution, probability 53) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be between 15 and 16 seconds?

Answer: 30% or 0.30 Difficulty: Easy Keywords: normal distribution, probability 54) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be between 14 and 15 seconds?

Answer: 30% or 0.30 Difficulty: Easy Keywords: normal distribution, probability 55) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be between 13 and 16 seconds?

Answer: 73% or 0.73 Difficulty: Moderate Keywords: normal distribution, probability 6-10 .

56) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be between 14 and 17 seconds?

Answer: 73% or 0.73 Difficulty: Moderate Keywords: normal distribution, probability 57) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. The probability is 20% that the time lapsed will be shorter than how many seconds?

Answer: 14 seconds Difficulty: Easy Keywords: normal distribution, probability 58) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. The probability is 80% that the time lapsed will be longer than how many seconds?

Answer: 14 seconds Difficulty: Easy Keywords: normal distribution, probability 59) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. The middle 60% of the time lapsed will fall between which two numbers?

Answer: 14 seconds and 16 seconds Difficulty: Moderate Keywords: normal distribution, probability 60) You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. The middle 86% of the time lapsed will fall between which two numbers?

Answer: 13 seconds and 17 seconds Difficulty: Moderate Keywords: normal distribution, probability

6-11 .

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 90 and 95?

Answer: 4.41% or 0.0441 Difficulty: Easy Keywords: normal distribution, probability 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 greater than 95?

Answer: 2.27% or 0.0227 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 lower than 55?

Answer: 2.27% or 0.0227 Difficulty: Easy 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%. What is the probability of a score between 75 and 90?

Answer: 43.32% or 0.4332 Difficulty: Easy 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%. What is the probability of a score between 60 and 75?

Answer: 43.32% or 0.4332 Difficulty: Easy Keywords: normal distribution, probability 66) 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 Difficulty: Moderate Keywords: normal distribution, probability 67) 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 Difficulty: Moderate Keywords: normal distribution, probability

6-12 .

68) 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 Difficulty: Moderate Keywords: normal distribution, probability 69) 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 Difficulty: Moderate Keywords: normal distribution, probability 70) 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 Difficulty: Moderate Keywords: 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 less than 1.15 is ________.

Answer: 0.8749 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 more than 0.77 is ________.

Answer: 0.2206 Difficulty: Easy Keywords: standardized normal distribution, probability 73) 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 Difficulty: Easy 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 is more than -0.98 is ________.

Answer: 0.8365 Difficulty: Easy Keywords: standardized normal distribution, probability 75) 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 Difficulty: Easy Keywords: standardized normal distribution, probability 6-13 .

76) 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 Difficulty: Easy Keywords: standardized normal distribution, probability 77) 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 Difficulty: Easy Keywords: standardized normal distribution, probability 78) 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 Difficulty: Moderate Keywords: standardized normal distribution, probability 79) 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 Difficulty: Moderate Keywords: standardized normal distribution, probability 80) 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 Difficulty: Moderate Keywords: standardized normal distribution, value 81) 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 Difficulty: Moderate Keywords: standardized normal distribution, value 82) 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 Difficulty: Moderate Keywords: standardized normal distribution, value 83) 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 Difficulty: Moderate Keywords: standardized normal distribution, value 6-14 .

84) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Easy Keywords: normal distribution, probability 85) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Easy Keywords: normal distribution, probability 86) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Easy Keywords: normal distribution, probability 87) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Easy Keywords: normal distribution, probability 88) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Easy Keywords: normal distribution, probability 89) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Easy Keywords: normal distribution, probability 90) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Easy Keywords: normal distribution, probability

6-15 .

91) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Easy Keywords: normal distribution, probability 92) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Moderate Keywords: normal distribution, value 93) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Moderate Keywords: normal distribution, value 94) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Difficult Keywords: normal distribution, value 95) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Moderate Keywords: normal distribution, value 96) The amount of time necessary for assembly line workers to complete a product is a normal random 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 Difficulty: Moderate Keywords: normal distribution, value

6-16 .

TABLE 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.

97) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability 98) Referring to Table 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 Difficulty: Moderate Keywords: normal distribution, probability 99) Referring to Table 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 Difficulty: Moderate Keywords: normal distribution, value 100) Referring to Table 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 Difficulty: Moderate Keywords: normal distribution, probability TABLE 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 $2,000. At night he works 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.

101) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability

6-17 .

102) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability 103) Referring to Table 6-2, for a given month, what is the probability that John's commission from the jewelry store is at least than $12,000?

Answer: 0.1587 Difficulty: Easy Keywords: normal distribution, probability 104) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability 105) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability 106) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability 107) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability 108) Referring to Table 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: $ 11,348.98 Difficulty: Moderate Keywords: normal distribution, value 109) Referring to Table 6-2, the probability is 0.95 that John's commission from the jewelry store is at least how much in a given month?

Answer: $6,710.29 Difficulty: Moderate Keywords: normal distribution, value

6-18 .

110) Referring to Table 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: $7,436.90 and $12,563.10 Difficulty: Difficult Keywords: normal distribution, value 111) Referring to Table 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: $6,710.29 and $13,289.71 Difficulty: Difficult Keywords: normal distribution, value 112) Referring to Table 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: $12,563.10 Difficulty: Moderate Keywords: normal distribution, value 113) Referring to Table 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: $8,951.20 Difficulty: Moderate Keywords: normal distribution, value 114) Referring to Table 6-2, for a given month, what is the probability that John's income as a waiter is between $700 and $1,600?

Answer: 0.8186 Difficulty: Easy Keywords: normal distribution, probability 115) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability 116) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability 117) Referring to Table 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 Difficulty: Easy Keywords: normal distribution, probability

6-19 .

118) Referring to Table 6-2, for a given month, what is the probability that John's income as a waiter is less than $1,300?

Answer: 0.8413 Difficulty: Easy Keywords: normal distribution, probability 119) Referring to Table 6-2, for a given month, what is the probability that John's income as a waiter is at least $1,400?

Answer: 0.0912 Difficulty: Easy Keywords: normal distribution, probability 120) Referring to Table 6-2, for a given month, what is the probability that John's income as a waiter is more than $900?

Answer: 0.6306 Difficulty: Easy Keywords: normal distribution, probability 121) Referring to Table 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 Difficulty: Moderate Keywords: normal distribution, value 122) Referring to Table 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 Difficulty: Moderate Keywords: normal distribution, value 123) Referring to Table 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 Difficulty: Moderate Keywords: normal distribution, value 124) Referring to Table 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 Difficulty: Difficult Keywords: normal distribution, value 125) Referring to Table 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 $1,493.46 Difficulty: Difficult Keywords: normal distribution, value

6-20 .

126) Referring to Table 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 Difficulty: Moderate Keywords: normal distribution, value 127) The owner of a fish market determined that the average 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 Difficulty: Easy Keywords: normal distribution, probability, properties 128) The owner of a fish market determined that the average 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 Difficulty: Easy Keywords: normal distribution, probability, properties TABLE 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.

129) Referring to Table 6-3, what is the probability that a randomly selected orange will contain between 4.5 and 5.2 ounces of juice?

Answer: 0.5859 or 58.59% Difficulty: Easy Keywords: normal distribution, probability, properties 130) Referring to Table 6-3, what is the probability that a randomly selected orange will contain between 4.2 and 4.9 ounces of juice?

Answer: 0.5859 or 58.59% Difficulty: Moderate Keywords: normal distribution, probability, properties 131) Referring to Table 6-3, what is the probability that a randomly selected orange will contain at least 4.9 ounces of juice?

Answer: 0.3085 or 30.85% Difficulty: Easy Keywords: normal distribution, probability, properties

6-21 .

132) Referring to Table 6-3, what is the probability that a randomly selected orange will contain no more than 4.9 ounces of juice?

Answer: 0.6915 or 69.15% Difficulty: Easy Keywords: normal distribution, probability, properties 133) Referring to Table 6-3, what is the probability that a randomly selected orange will contain no more than 4.2 ounces of juice?

Answer: 0.1056 or 10.56% Difficulty: Easy Keywords: normal distribution, probability, properties 134) Referring to Table 6-3, what is the probability that a randomly selected orange will contain more than 4.2 ounces of juice?

Answer: 0.8944 or 89.44% Difficulty: Easy Keywords: normal distribution, probability, properties TABLE 6-4 According to Investment Digest, the arithmetic mean of the annual return for common stocks from 19262010 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.

135) Referring to Table 6-4, find the probability that the annual return of a random year will be less than 11.5%.

Answer: 0.90 or 90% Difficulty: Easy Keywords: normal distribution, probability, properties 136) Referring to Table 6-4, find the probability that the annual return of a random year will be more than 11.5%.

Answer: 0.10 or 10% Difficulty: Easy Keywords: normal distribution, probability, properties 137) Referring to Table 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% Difficulty: Moderate Keywords: normal distribution, probability, properties 138) Referring to Table 6-4, find the probability that the annual return of a random year will be less than 7.5%.

Answer: 0.10 or 10% Difficulty: Easy Keywords: normal distribution, probability, properties 6-22 .

139) Referring to Table 6-4, find the probability that the annual return of a random year will be more than 7.5%.

Answer: 0.90 or 90% Difficulty: Easy Keywords: normal distribution, probability, properties 140) Referring to Table 6-4, what is the value above which will account for the highest 25% of the possible annual returns?

Answer: 11% Difficulty: Moderate Keywords: normal distribution, probability, properties 141) Referring to Table 6-4, 75% of the annual returns will be lower than what value?

Answer: 11% Difficulty: Moderate Keywords: normal distribution, probability, properties 142) Referring to Table 6-4, find the two values that will bound the middle 50% of the annual returns.

Answer: 8% and 11% Difficulty: Moderate Keywords: normal distribution, probability, properties 143) Referring to Table 6-4, find the two values that will bound the middle 80% of the annual returns.

Answer: 7.5% and 11.5% Difficulty: Moderate Keywords: normal distribution, probability, properties 144) Referring to Table 6-4, 10% of the annual returns will be less than what amount?

Answer: 7.5% Difficulty: Moderate Keywords: normal distribution, probability, properties 145) Referring to Table 6-4, 10% of the annual returns will be at least what amount?

Answer: 11.5% Difficulty: Moderate Keywords: normal distribution, probability, properties

6-23 .

Business Statistics: A First Course, 6e (Levine) Chapter 7 Sampling and Sampling Distributions 1) 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 Difficulty: Moderate Keywords: reasons for sampling 2) 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 Difficulty: Easy Keywords: reasons for sampling 3) Which of the following sampling methods is a probability sample?

A) convenience sample B) quota sample C) stratified sample D) judgment sample Answer: C Difficulty: Easy Keywords: probability sample 4) At U.S. 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) population.

B) statistic.

C) parameter.

D) frame.

Answer: D Difficulty: Easy Keywords: frame

7-1 .

5) The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a DVD 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 Difficulty: Easy Keywords: frame 6) A sample of 300 subscribers to a particular 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: B Difficulty: Moderate Keywords: sampling method 7) Which of the following scenarios will yield a nonprobability sample?

A) The subjects of the sample are chosen on the basis of 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 Difficulty: Easy Keywords: sampling method, nonprobability sample 8) 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 Difficulty: Easy Keywords: sampling method, nonprobability sample, convenience sample

7-2 .

9) To demonstrate a sampling method, the instructor in a class picked the first five 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 Difficulty: Easy Keywords: sampling method, nonprobability sample, convenience sample 10) 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 Difficulty: Easy Keywords: sampling method, nonprobability sample, convenience sample 11) 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 Difficulty: Easy Keywords: sampling method, nonprobability sample, judgment sample 12) 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 owners 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 Difficulty: Easy Keywords: sampling method, nonprobability sample, judgment sample

7-3 .

13) 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 first 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 Difficulty: Easy Keywords: sampling method, probability sample, systematic sample 14) 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 first 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 Difficulty: Easy Keywords: sampling method, probability sample, stratified sample 15) 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 first 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 in which they are seated. One of the groups is randomly selected.

Answer: D Difficulty: Easy Keywords: sampling method, probability sample, cluster sample 16) 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 first 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 in which they are seated. One of the groups is randomly selected.

Answer: C Difficulty: Easy Keywords: sampling method, probability sample, simple random sample

7-4 .

17) 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 in which they are seated. One of the groups is randomly selected.

Answer: C Difficulty: Easy Keywords: sampling method, probability sample, simple random sample 18) For a population frame containing N = 1,007 individuals, what code number should you assign to the first person on the list in order to use a table of random numbers?

A) 0 B) 1 C) 01 D) 0001 Answer: D Difficulty: Easy Keywords: random number 19) 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 Difficulty: Easy Keywords: probability sample, sampling method 20) 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 Difficulty: Easy Keywords: simple random sample, probability sample, sampling method

7-5 .

21) 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 Difficulty: Easy Keywords: stratified sample, probability sample, sampling method 22) 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 Difficulty: Easy Keywords: systematic sample, probability sample, sampling method 23) 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 Difficulty: Easy Keywords: convenience sample, nonprobability sample, sampling method 24) 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 Difficulty: Easy Keywords: random number 25) 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 Difficulty: Easy Keywords: random number 7-6 .

26) Which of the following can be reduced by proper interviewer training?

A) sampling error B) measurement error C) both of the above D) none of the above Answer: B Difficulty: Difficult Keywords: measurement error, survey worthiness 27) 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 Difficulty: Easy Keywords: ethical issues, sampling method 28) 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 Difficulty: Easy Keywords: judgment sample, ethical issues, sampling method 29) 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 Difficulty: Easy Keywords: convenience sample, ethical issues, sampling method 30) True or False: As a population becomes large, it is usually better to obtain statistical information from the entire population.

Answer: FALSE Difficulty: Easy Keywords: population, sample, reasons for samplings 31) True or False: If a simple random sample is chosen with replacement, each individual has the same chance of selection on every selection.

Answer: TRUE Difficulty: Easy Keywords: simple random sample, probability sample, sampling method 7-7 .

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

Answer: FALSE Difficulty: Moderate Keywords: sampling with replacement, sampling method, survey worthiness 33) 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 Difficulty: Easy Keywords: nonprobability, probability sample, sampling method 34) True or False: A sample is always a good representation of the target population.

Answer: FALSE Difficulty: Easy Keywords: sample, population, sampling method 35) True or False: There can be only one sample selected from a population.

Answer: FALSE Difficulty: Easy Keywords: sample, sampling method 36) True or False: Using different frames to generate data can lead to totally different conclusions.

Answer: TRUE Difficulty: Easy Keywords: frame, sampling method 37) True or False: Sampling error can be completely eliminated by taking larger sample sizes.

Answer: FALSE Difficulty: Difficult Keywords: sampling error 38) True or False: Sampling error can be reduced by taking larger sample sizes.

Answer: TRUE Difficulty: Easy Keywords: sampling error 39) True or False: A convenience sample is a type of probability sample.

Answer: FALSE Difficulty: Easy Keywords: chunk sample 40) True or False: Items or individuals in a judgment sample are chosen according to their probability of occurrence.

Answer: FALSE Difficulty: Easy Keywords: judgment sample, nonprobability sample

7-8 .

41) True or False: When participants are allowed to self-select into the sample, you have a nonprobability sample.

Answer: TRUE Difficulty: Easy Keywords: nonprobability sample 42) True or False: Systematic samples are less efficient than a stratified sample.

Answer: TRUE Difficulty: Easy Keywords: systematic sample, stratified sample 43) 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 Difficulty: Moderate Keywords: stratified sample 44) 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 200 students. This list is a ________.

Answer: frame Difficulty: Easy Keywords: frame 45) ________ results from the exclusion of certain groups of subjects from a population frame.

Answer: Coverage error Difficulty: Difficult Keywords: coverage error, survey worthiness, frame 46) Coverage error results in a ________.

Answer: selection bias Difficulty: Difficult Keywords: selection bias, survey worthiness 47) ________ results from the failure to collect data on all subjects in the sample.

Answer: Nonresponse error or bias Difficulty: Moderate Keywords: nonresponse error, survey worthiness 48) The sampling process begins by locating appropriate data sources called ________.

Answer: frames Difficulty: Easy Keywords: frames, sampling method

7-9 .

49) 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 Difficulty: Easy Keywords: chunk sample 50) True or False: You stand at the main entrance to a department 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 Difficulty: Easy Keywords: systematic sample 51) 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 Difficulty: Easy Keywords: convenience sample 52) 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 Difficulty: Easy Keywords: judgment sample 53) True or False: In a business statistics class, students sit randomly without particular preferences. A sample is selected by including everybody who sits in the first row. This is an example of a cluster sample.

Answer: TRUE Difficulty: Easy Keywords: cluster sample 54) True or False: The question "How many times have you abused your spouse in the last six months?" will most likely result in nonresponse error.

Answer: TRUE Difficulty: Easy Keywords: nonresponse error, survey worthiness 55) 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 Difficulty: Easy Keywords: coverage error, survey worthiness

7-10 .

56) True or False: The only way one can eliminate sampling error is to take the whole population as the sample.

Answer: TRUE Difficulty: Moderate Keywords: sampling error, survey worthiness 57) True or False: Coverage error can become an ethical issue if a particular group is intentionally excluded from the frame.

Answer: TRUE Difficulty: Easy Keywords: ethical issue, coverage error, survey worthiness, frame 58) 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 Difficulty: Easy Keywords: ethical issue, measurement error, sampling error, survey worthiness 59) True or False: Measurement error can become an ethical issue when a survey sponsor chooses leading questions that guide the responses in a particular direction.

Answer: TRUE Difficulty: Easy Keywords: ethical issue, measurement error, survey worthiness 60) True or False: Measurement error can become an ethical issue when an interviewer purposely guides the responses in a particular direction.

Answer: TRUE Difficulty: Easy Keywords: ethical issue, measurement error, survey worthiness 61) 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 Difficulty: Easy Keywords: ethical issue, sampling error, survey worthiness 62) 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 three 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 Difficulty: Moderate Keywords: cluster sample

7-11 .

63) 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 Difficulty: Moderate Keywords: systematic sample 64) True or False: Selection bias occurs more frequently in systematic samples than in simple random samples.

Answer: TRUE Difficulty: Easy Keywords: simple random sample, systematic sample 65) True or False: The question: "Have you used any form of illicit drugs over the past two months?" will most likely result in measurement error if the question is answered.

Answer: TRUE Difficulty: Moderate Keywords: measurement error, survey worthiness 66) True or False: The question: "How much did you earn last year rounded to the nearest hundred dollars?" will most likely result in measurement error.

Answer: TRUE Difficulty: Moderate Keywords: measurement error, survey worthiness 67) Sampling distributions describe the distribution of A) parameters.

B) statistics.

C) both parameters and statistics.

D) neither parameters nor statistics.

Answer: B Difficulty: Easy Keywords: statistics, sampling distribution 68) 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 of the above Answer: D Difficulty: Easy Keywords: standard error, mean

7-12 .

69) 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 a sample of any size, it says the sampling distribution of the sample mean is approximately normal.

Answer: C Difficulty: Difficult Keywords: central limit theorem 70) 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 Difficulty: Moderate Keywords: unbiased 71) 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 Difficulty: Moderate Keywords: central limit theorem 72) 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 μ.

D) The standard deviation of the sampling distribution of the sample mean is equal to σ.

Answer: D Difficulty: Easy Keywords: sampling distribution, properties

7-13 .

73) Which of the following is true about the sampling distribution of the sample mean?

A) The mean of the sampling distribution is always μ.

B) The standard deviation of the sampling distribution is always σ.

C) The shape of the sampling distribution is always approximately normal.

D) All of the above are true.

Answer: A Difficulty: Moderate Keywords: sampling distribution, properties 74) 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 Difficulty: Moderate Keywords: sampling distribution, central limit theorem 75) 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 Difficulty: Easy Keywords: sampling distribution, central limit theorem 76) 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 Difficulty: Moderate Keywords: central limit theorem 77) 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 Difficulty: Moderate Keywords: unbiased 78) 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 Difficulty: Moderate Keywords: central limit theorem 7-14 .

79) 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 μ = 6 ounces and σ = 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 of the above are correct.

Answer: A Difficulty: Moderate Keywords: sampling distribution, unbiased 80) The average score of all pro golfers for a particular 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 average score of the 36 pro golfers exceeded 71.

Answer: 0.0228 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 81) The distribution of the number of loaves of bread sold per day by a large bakery over the past five years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of n = 40 days has been selected. What is the approximate probability that the mean number of loaves sold in the sampled days exceeds 7,895 loaves?

Answer: approximately 0 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 82) 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 Difficulty: Easy Keywords: sampling distribution, central limit theorem 83) Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. 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 Difficulty: Moderate Keywords: standard error, mean 7-15 .

84) Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 85) Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 86) Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 87) Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem

7-16 .

88) At a computer manufacturing company, the actual size of computer chips 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 Difficulty: Easy Keywords: standard error, mean 89) At a computer manufacturing company, the actual size of computer chips 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 90) At a computer manufacturing company, the actual size of computer chips 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 less than 0.95 centimeters?

Answer: 0.0416 using Excel or 0.0418 using Table E.2 Difficulty: Moderate Keywords: sampling distribution, mean, probability 91) At a computer manufacturing company, the actual size of computer chips 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 Difficulty: Difficult Keywords: sampling distribution, mean, value 92) 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 Difficulty: Easy Keywords: standard error, mean

7-17 .

93) 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 Difficulty: Easy Keywords: sampling distribution, mean 94) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 95) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 96) 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 Difficulty: Moderate Keywords: sampling distribution, mean, central limit theorem

7-18 .

97) The standard error of the mean for a sample of 100 is 30. In order 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 Difficulty: Moderate Keywords: standard error, mean 98) 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 Difficulty: Moderate Keywords: sampling distribution, mean, central limit theorem 99) 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 Difficulty: Easy Keywords: sampling distribution, mean, central limit theorem 100) 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 Difficulty: Moderate Keywords: sampling distribution, mean, central limit theorem 101) The standard error of the population proportion will become larger A) as the population proportion approaches 0.

B) as the population proportion approaches 0.50.

C) as the population proportion approaches 1.00.

D) as the sample size increases.

Answer: B Difficulty: Moderate Keywords: standard error, proportion

7-19 .

102) True or False: As the sample size increases, the standard error of the mean increases.

Answer: FALSE Difficulty: Easy Keywords: standard error, mean 103) 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 Difficulty: Easy Keywords: sampling distribution, mean, central limit theorem 104) 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 Difficulty: Easy Keywords: sampling distribution, mean, central limit theorem 105) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 106) 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 Explanation: The sample is too small for the normal approximation.

Difficulty: Moderate Keywords: sampling distribution, mean, probability 107) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 108) 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 Difficulty: Difficult Keywords: sampling distribution, mean, probability

7-20 .

109) True or False: As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

Answer: TRUE Difficulty: Moderate Keywords: sampling distribution, law of large numbers 110) 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 Difficulty: Easy Keywords: sampling distribution, mean, central limit theorem 111) True or False: A sampling distribution is a distribution for a statistic.

Answer: TRUE Difficulty: Moderate Keywords: sampling distribution 112) True or False: Suppose μ = 50 and σ = 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 113) True or False: Suppose μ= 80 and σ = 20 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall above 76.71.

Answer: TRUE Difficulty: Moderate Keywords: sampling distribution, mean, probability 114) True or False: Suppose μ = 50 and σ = 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 115) 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 Difficulty: Easy Keywords: central limit theorem 116) 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 Difficulty: Easy Keywords: standard error, mean

7-21 .

117) 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 Difficulty: Easy Keywords: sampling distribution 118) 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 Difficulty: Easy Keywords: standard error, properties 119) 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 Difficulty: Moderate Keywords: sampling distribution, mean 120) 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 Difficulty: Easy Keywords: sampling distribution, mean, standard error 121) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 122) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 123) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability

7-22 .

124) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 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 Difficulty: Difficult Keywords: sampling distribution, mean, value 125) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 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 Difficulty: Difficult Keywords: sampling distribution, mean, value 126) 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 Difficulty: Easy Keywords: standard error, mean 127) 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 45 and 52 minutes?

Answer: 0.4974 Difficulty: Moderate Keywords: sampling distribution, mean, probability 128) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 129) 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 Difficulty: Difficult Keywords: sampling distribution, mean, probability 130) 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 Difficulty: Difficult Keywords: sampling distribution, mean, probability

7-23 .

131) 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 Difficulty: Easy Keywords: sampling distribution, mean, unbiased 132) 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 Difficulty: Easy Keywords: sampling distribution, mean, standard error 133) 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 Difficulty: Easy Keywords: sampling distribution, mean, central limit theorem 134) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 135) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 136) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 137) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 7-24 .

138) 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 ________ ounces.

Answer: 35.951 and 36.049 Difficulty: Difficult Keywords: sampling distribution, mean, value, central limit theorem 139) A manufacturer of power tools claims that the mean amount of time required to assemble their topof-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 Difficulty: Easy Keywords: sampling distribution, mean, unbiased 140) A manufacturer of power tools claims that the mean amount of time required to assemble their topof-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 Difficulty: Easy Keywords: sampling distribution, mean, standard error 141) A manufacturer of power tools claims that the mean amount of time required to assemble their topof-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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 142) A manufacturer of power tools claims that the mean amount of time required to assemble their topof-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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem 143) A manufacturer of power tools claims that the mean amount of time required to assemble their topof-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 Difficulty: Moderate Keywords: sampling distribution, mean, probability, central limit theorem

7-25 .

144) A manufacturer of power tools claims that the mean amount of time required to assemble their topof-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 ________ minutes.

Answer: 70.2 and 89.8 Difficulty: Difficult Keywords: sampling distribution, mean, value, central limit theorem 145) To use the normal distribution to approximate the binomial distribution, we need ________ and ________ to be at least 5.

Answer: nπ and n(1-π ) Difficulty: Easy Keywords: sampling distribution, proportion, central limit theorem 146) True or False: The sample mean is an unbiased estimate of the population mean.

Answer: TRUE Difficulty: Easy Keywords: mean, unbiased 147) True or False: The sample proportion is an unbiased estimate of the population proportion.

Answer: TRUE Difficulty: Difficult Keywords: proportion, unbiased 148) True or False: The mean of the sampling distribution of a sample proportion is the population proportion, π.

Answer: TRUE Difficulty: Easy Keywords: sampling distribution, proportion 149) True or False: The standard error of the sampling distribution of a sample proportion is where p is the sample proportion.

Answer: FALSE Difficulty: Easy Keywords: sampling distribution, proportion 150) True or False: The standard deviation of the sampling distribution of a sample proportion is , where π is the population proportion.

Answer: TRUE Difficulty: Easy Keywords: sampling distribution, proportion

7-26 .

,

151) 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 Difficulty: Moderate Keywords: standard error 152) True or False: An unbiased estimator will have a value, on average across samples, equal to the population parameter value.

Answer: TRUE Difficulty: Easy Keywords: unbiased 153) True or False: In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.

Answer: TRUE Difficulty: Easy Keywords: mean, standard error 154) 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability TABLE 7-1 The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a DVD player made by the company over the past 12 months are satisfied with their products.

155) Referring to Table 7-1, the manager decides to ask a sample of customers who have bought a DVD 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) nonprobability sampling.

Answer: C Difficulty: Difficult Keywords: coverage error, survey worthiness

7-27 .

156) Referring to Table 7-1, if there are four different brands of DVD players made by the company, the best sampling strategy would be to use a A) simple random sample.

B) stratified sample.

C) cluster sample.

D) systematic sample.

Answer: B Difficulty: Difficult Keywords: stratified sample, probability sample, sampling method 157) Referring to Table 7-1, 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 DVD player back for service?

D) How many times have you failed to set the time on the DVD player?

Answer: C Difficulty: Difficult Keywords: measurement error, survey worthiness 158) Referring to Table 7-1, if a customer survey questionnaire is included in all the DVD players made and sold by the company over the past 12 months, this method of collecting data will most like suffer from a A) nonresponse error.

B) measurement error.

C) coverage error.

D) nonprobability sampling.

Answer: A Difficulty: Difficult Keywords: nonresponse error, survey worthiness TABLE 7-2 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 in order to estimate the mean study time for the population of all students.

159) Referring to Table 7-2, what is the probability that the sample mean exceeds the population mean by more than 2 hours?

Answer: 0.3085 Difficulty: Moderate Keywords: sampling distribution, mean, probability 160) Referring to Table 7-2, what is the probability that the sample mean is more than 3 hours below the population mean?

Answer: 0.2266 Difficulty: Moderate Keywords: sampling distribution, mean, probability

7-28 .

161) Referring to Table 7-2, 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 162) Referring to Table 7-2, 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability TABLE 7-3 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.

163) Referring to Table 7-3, what is the probability that the sample mean selling price was more than $110,000?

Answer: 0.9772 Difficulty: Easy Keywords: sampling distribution, mean, probability, central limit theorem 164) Referring to Table 7-3, 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 Difficulty: Easy Keywords: sampling distribution, mean, probability, central limit theorem 165) Referring to Table 7-3, what is the probability that the sample mean selling price was between $114,000 and $116,000?

Answer: 0.3108 Difficulty: Easy Keywords: sampling distribution, mean, probability, central limit theorem 166) Referring to Table 7-3, 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 Difficulty: Easy Keywords: sampling distribution, mean, probability, central limit theorem

7-29 .

TABLE 7-4 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.

167) Referring to Table 7-4, what is the probability that the sample mean lifetime is more than 1,550 hours?

Answer: 0.8413 Difficulty: Easy Keywords: sampling distribution, mean, probability 168) Referring to Table 7-4, 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 Difficulty: Moderate Keywords: sampling distribution, mean, probability 169) Referring to Table 7-4, 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 Difficulty: Difficult Keywords: sampling distribution, mean, value TABLE 7-5 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.

170) Referring to Table 7-5, 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% Difficulty: Moderate Keywords: sampling distribution, proportion, mean 171) Referring to Table 7-5, the standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is ________.

Answer: 0.05050 Difficulty: Moderate Keywords: sampling distribution, proportion, standard error 172) True or False: Referring to Table 7-5, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

Answer: TRUE Difficulty: Easy Keywords: sampling distribution, proportion, central limit theorem 173) Referring to Table 7-5, 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 Difficulty: Easy Keywords: sampling distribution, proportion, probability 7-30 .

174) Referring to Table 7-5, 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 Difficulty: Easy Keywords: sampling distribution, proportion, probability 175) Referring to Table 7-5, 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 Difficulty: Easy Keywords: sampling distribution, proportion, probability 176) Referring to Table 7-5, 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% Difficulty: Difficult Keywords: sampling distribution, proportion, value 177) Referring to Table 7-5, 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 Difficulty: Difficult Keywords: sampling distribution, proportion, value 178) A study at a college on 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% Difficulty: Moderate Keywords: sampling distribution, proportion, mean 179) A study at a college on 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 Difficulty: Moderate Keywords: sampling distribution, proportion, standard error 180) A study at a college on 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 Difficulty: Easy Keywords: sampling distribution, proportion, probability 181) A study at a college on 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 Difficulty: Easy Keywords: sampling distribution, proportion, probability 7-31 .

182) A study at a college on 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 Difficulty: Difficult Keywords: sampling distribution, proportion, value 183) A study at a college on 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 Difficulty: Difficult Keywords: sampling distribution, proportion, value TABLE 7-6 According to an article, 19% of the entire population in a developing country have high-speed access to the Internet. Random samples of size 200 are selected from the country's population.

184) Referring to Table 7-6, the population mean of all the sample proportions is ________.

Answer: 19% or 0.19 Difficulty: Easy Keywords: mean, sampling distribution, proportion, central limit theorem 185) Referring to Table 7-6, the standard error of all the sample proportions is ________.

Answer: 0.0277 Difficulty: Easy Keywords: standard error, sampling distribution, proportion, central limit theorem 186) Referring to Table 7-6, 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 Difficulty: Easy Keywords: sampling distribution, proportion, central limit theorem 187) Referring to Table 7-6, 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 Difficulty: Easy Keywords: sampling distribution, proportion, central limit theorem 188) Referring to Table 7-6, 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 Difficulty: Easy Keywords: sampling distribution, proportion, central limit theorem

7-32 .

189) Referring to Table 7-6, 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 Difficulty: Easy Keywords: sampling distribution, proportion, central limit theorem 190) Referring to Table 7-6, among all the random samples of size 200, 90% will have less than ________% who have high-speed access to the Internet.

Answer: 22.56 using Excel or 22.55 using Table E.2 Difficulty: Moderate Keywords: sampling distribution, proportion, central limit theorem 191) Referring to Table 7-6, among all the random samples of size 200, 90% will have more than ________% who have high-speed access to the Internet.

Answer: 15.45 Difficulty: Moderate Keywords: sampling distribution, proportion, central limit theorem TABLE 7-7 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.

192) Referring to Table 7-7, the population mean of all possible sample proportions is ________.

Answer: 0.375 or 37.5% Difficulty: Easy Keywords: mean, sampling distribution, proportion, central limit theorem 193) Referring to Table 7-7, the standard error of all possible sample proportions is ________.

Answer: 0.0342 Difficulty: Easy Keywords: standard error, sampling distribution, proportion, central limit theorem 194) Referring to Table 7-7, ________% 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 Difficulty: Easy Keywords: sampling distribution, proportion, central limit theorem 195) Referring to Table 7-7, ________% of the samples are likely to have less than 37.5% who take advantage of online customer service.

Answer: 50 Difficulty: Easy Keywords: sampling distribution, proportion, central limit theorem

7-33 .

196) Referring to Table 7-7, 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 Difficulty: Moderate Keywords: sampling distribution, proportion, central limit theorem 197) Referring to Table 7-7, 95% of the samples proportions 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 Difficulty: Moderate Keywords: sampling distribution, proportion, central limit theorem

7-34 .

Business Statistics: A First Course, 6e (Levine) 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 Difficulty: Easy Keywords: point estimate 2) True or False: The sample mean is a point estimate of the population mean.

Answer: TRUE 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 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 Difficulty: Easy Keywords: point estimate, mean 5) True or False: A population parameter is used to estimate a confidence interval.

Answer: FALSE Difficulty: Easy Keywords: point estimate, confidence interval

8-1 .

6) True or False: For a given data set, the confidence interval will be wider for 95% confidence than for 90% confidence.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, properties, width 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 Difficulty: Easy Keywords: confidence interval, properties, width, trade-off 8) True or False: Holding the level of confidence fixed, increasing the sample size will lead to a wider confidence interval.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, properties, width, trade-off 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 Difficulty: Easy Keywords: confidence interval, properties, width, trade-off 10) Suppose a 95% confidence interval for μ 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 Difficulty: Moderate Keywords: confidence interval, properties, width 11) Suppose a 95% confidence interval for μ 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: B Difficulty: Moderate Keywords: confidence interval, properties, width

8-2 .

12) In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a ________ interval.

A) narrower B) wider C) less significant D) biased Answer: A Difficulty: Easy Keywords: confidence interval, properties, width 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 Difficulty: Easy Keywords: confidence interval, properties 14) True or False: The confidence interval obtained will always correctly estimate the population parameter.

Answer: FALSE 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 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 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 Difficulty: Moderate Keywords: sampling error 18) True or False: Sampling error equals half the width of a confidence interval.

Answer: TRUE Difficulty: Moderate Keywords: sampling error 19) True or False: The width of a confidence interval equals twice the sampling error.

Answer: TRUE Difficulty: Moderate Keywords: sampling error 8-3 .

20) True or False: The sampling error can either be positive or negative.

Answer: TRUE 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 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 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 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 Difficulty: Easy Keywords: confidence interval, mean 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 of the above D) none of the above Answer: C Difficulty: Moderate Keywords: confidence interval, interpretation

8-4 .

26) An economist is interested in studying the incomes of consumers in a particular 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 point in a 99% confidence interval for the average income?

A) $15,052 B) $15,141 C) $15,330 D) $15,364 Answer: D Difficulty: Easy Keywords: confidence interval, mean, standardized normal distribution 27) An economist is interested in studying the incomes of consumers in a particular 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 Difficulty: Moderate Keywords: width, confidence interval, mean, 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 Difficulty: Moderate Keywords: confidence interval, mean, standardized normal distribution 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 Difficulty: Moderate Keywords: confidence interval, mean, standardized normal distribution 30) True or False: The t distribution approaches the standardized normal distribution when the number of degrees of freedom increases.

Answer: TRUE Difficulty: Easy Keywords: t distribution, standardized normal distribution 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 Difficulty: Easy Keywords: confidence interval, mean, t distribution

8-5 .

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 Difficulty: Moderate Keywords: t distribution 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 Difficulty: Easy Keywords: critical value, t distribution 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 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 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 of the above Answer: D Difficulty: Easy Keywords: t distribution, properties

8-6 .

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 Difficulty: Difficult Keywords: confidence interval, interpretation 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 Difficulty: Difficult Keywords: confidence interval, interpretation 39) Suppose a 95% confidence interval for μ 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 Difficulty: Moderate Keywords: confidence interval, 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: = $50.50 and S = 20. Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ?

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 Difficulty: Easy Keywords: confidence interval, mean, t distribution 8-7 .

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: =$50.50 and S = 20. 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 assuming that 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 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 = $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 Difficulty: Moderate Keywords: confidence interval, mean, t distribution 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, = 19.8 and S = 5. Which of the following assumptions is necessary in order 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 Difficulty: Moderate Keywords: confidence interval, mean, t distribution

8-8 .

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, = 19.8 and S2 = 25. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval.

Answer: 19.8 ± 1.249 or 18.55 ≤ μ ≤ 21.049 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 Difficulty: Easy Keywords: confidence interval, mean, t distribution 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 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 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 Difficulty: Moderate Keywords: confidence interval, mean, t distribution 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 Difficulty: Easy Keywords: confidence interval, mean, t distribution 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 Difficulty: Easy Keywords: confidence interval, mean, t distribution

8-9 .

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 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 ≤ π ≤ 0.647 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 π 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 Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 54) The county clerk wants to estimate the proportion of voters who will need special election facilities.

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 Difficulty: Easy Keywords: proportion, sample size determination 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 an 90% confidence interval for the population proportion.

Answer: 0.3352 to 0.4148 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 Difficulty: Moderate Keywords: confidence interval, proportion 8-10 .

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 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 Difficulty: Moderate Keywords: confidence interval, proportion 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 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 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 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 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 Difficulty: Easy Keywords: confidence interval, proportion, standardized normal distribution

8-11 .

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 Difficulty: Moderate Keywords: confidence interval, proportion, properties, width 65) When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that π 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 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 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 Difficulty: Easy Keywords: mean, sample size determination

8-12 .

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 Difficulty: Difficult Keywords: mean, sample size determination 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 Difficulty: Difficult Keywords: mean, sample size determination 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 Difficulty: Difficult Keywords: mean, sample size determination 71) An economist is interested in studying the incomes of consumers in a particular 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 Difficulty: Easy Keywords: mean, sample size determination 8-13 .

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, = 19.8 and S2 = 25. 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 Explanation: The answer is computed using Z = 2.575 from Table E.2 or Z = 2.5758293 using PHStat.

Difficulty: Moderate Keywords: mean, sample size determination 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 Difficulty: Easy Keywords: mean, sample size determination 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 Explanation: B) The answer is computed using Z = 2.575 from Table E.2 or Z = 2.5758293 using PHStat.

Difficulty: Moderate Keywords: proportion, sample size determination 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 Difficulty: Moderate Keywords: proportion, sample size determination

8-14 .

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 = 2,033 Difficulty: Easy Keywords: mean, sample size determination TABLE 8-1 The managers of a company are worried about the morale of their employees. In order 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 Table 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 Difficulty: Easy Keywords: mean, sample size determination 78) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, mean, standardized normal distribution 79) True or False: Referring to Table 8-1, this confidence interval is only valid if the scores on the Fortunato test are normally distributed.

Answer: FALSE Difficulty: Difficult Keywords: confidence interval, mean, standardized normal distribution, central limit theorem

8-15 .

TABLE 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 Table 8-2, the critical value to use in obtaining the confidence interval is ________.

Answer: 2.58 Difficulty: Easy Keywords: confidence interval, mean, standardized normal distribution 81) Referring to Table 8-2, the confidence interval goes from ________ to ________.

Answer: 12.09 to 12.19 Difficulty: Moderate Keywords: confidence interval, mean, standardized normal distribution 82) True or False: Referring to Table 8-2, the confidence interval indicates that the machine is not working properly.

Answer: TRUE Difficulty: Moderate Keywords: confidence interval, mean, standardized normal distribution, interpretation 83) True or False: Referring to Table 8-2, the confidence interval is valid only if the lengths cut are normally distributed.

Answer: FALSE 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.

Difficulty: Moderate Keywords: confidence interval, mean, standardized normal distribution, central limit theorem 84) Referring to Table 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 Explanation: The answer is computed using Z = 2.575 from Table E.2 or Z = 2.5758293 using PHStat.

Difficulty: Moderate Keywords: mean, sample size determination

8-16 .

TABLE 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 Table 8-3, the mean of the sample is ________, while the standard deviation of the sample is ________.

Answer: 6.0; 2.0 Difficulty: Moderate Keywords: confidence interval 86) Referring to Table 8-3, the confidence interval will be based on ________ degrees of freedom.

Answer: 7 Difficulty: Easy Keywords: confidence interval, mean, t distribution 87) Referring to Table 8-3, the critical value used in constructing a 90% confidence interval is ________.

Answer: 1.8946 Difficulty: Easy Keywords: confidence interval, mean, t distribution 88) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, mean, t distribution 89) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, mean, t distribution 90) True or False: Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, mean, interpretation 91) True or False: Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, mean, properties, width 8-17 .

TABLE 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 Table 8-4, a confidence interval for this sample would be based on the t distribution with ________ degrees of freedom.

Answer: 6 Difficulty: Easy Keywords: confidence interval, mean, t distribution 93) Referring to Table 8-4, the critical value for a 99% confidence interval for this sample is ________.

Answer: 3.7074 Difficulty: Easy Keywords: confidence interval, mean, t distribution 94) Referring to Table 8-4, a 99% confidence interval for the mean voltage of the power packs is from ________ to ________.

Answer: 11.6367 to 12.0891 Difficulty: Moderate Keywords: confidence interval, mean, t distribution 95) True or False: Referring to Table 8-4, a 95% confidence interval for the mean voltage of the power pack is wider than a 99% confidence interval.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, mean, properties, width 96) True or False: Referring to Table 8-4, a 99% confidence interval will contain 99% of the voltages for all such power packs.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, mean, interpretation 97) True or False: Referring to Table 8-4, a confidence interval estimate of the population mean would only be valid if the distribution of voltages is normal.

Answer: TRUE Difficulty: Moderate Keywords: confidence interval, mean, t distribution 98) True or False: Referring to Table 8-4, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, mean, properties, width 99) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, mean, interpretation 8-18 .

100) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, mean, interpretation TABLE 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 Table 8-5, 95% of the time, the sample mean salary offer to management majors will fall between 47.19 and 52.61.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, mean, interpretation 102) True or False: Referring to Table 8-5, 95% of the salary offers are between 47.19 and 52.61.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, mean, interpretation 103) True or False: Referring to Table 8-5, it is possible that the mean of the population is between 47.19 and 52.61.

Answer: TRUE Difficulty: Moderate Keywords: confidence interval, mean, interpretation 104) True or False: Referring to Table 8-5, it is possible that the mean of the population is not between 47.19 and 52.61.

Answer: TRUE Difficulty: Moderate Keywords: confidence interval, mean, interpretation 105) True or False: Referring to Table 8-5, 95% of the sample means will fall between 47.19 and 52.61.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, mean, interpretation 106) True or False: Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, mean, interpretation

8-19 .

107) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, mean, properties, width 108) True or False: Referring to Table 8-5, the confidence interval obtained is valid only if the distribution of the population of salary offers is normal.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, mean, t distribution TABLE 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 Table 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 Difficulty: Easy Keywords: confidence interval, proportion, parameter 110) True or False: Referring to Table 8-6, the parameter of interest is 54/120 = 0.45.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, proportion, parameter 111) True or False: Referring to Table 8-6, this interval requires the use of the t distribution to obtain the confidence coefficient.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, proportion, t distribution 112) True or False: Referring to Table 8-6, this interval requires the assumption that the distribution of the number of people recognizing the product has a normal distribution.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, proportion 113) True or False: Referring to Table 8-6, 95% of the time, the proportion of people that recognize the product will fall between 0.36 and 0.54.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, proportion, interpretation

8-20 .

114) True or False: Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 115) True or False: Referring to Table 8-6, 95% of the people will recognize the product between 36% and 54% of the time.

Answer: FALSE Difficulty: Difficult Keywords: confidence interval, proportion, interpretation 116) True or False: Referring to Table 8-6, it is possible that the true proportion of people that recognize the product is between 0.36 and 0.54.

Answer: TRUE Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 117) True or False: Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 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 Difficulty: Moderate Keywords: proportion, sample size determination 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: 73 Difficulty: Easy Keywords: proportion, sample size determination

8-21 .

TABLE 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 24 rooms. During February, a sample of 25 days has a sample mean of 37 rooms.

120) True or False: Referring to Table 8-7, the parameter of interest is the mean number of rooms rented daily in a given month.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, mean, parameter 121) True or False: Referring to Table 8-7, the parameter of interest is the proportion of the rooms rented daily in a given month.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, mean, parameter 122) Referring to Table 8-7, the critical value for a 99% confidence interval for this sample is ________.

Answer: 2.5758 or 2.58 Difficulty: Easy Keywords: confidence interval, mean 123) Referring to Table 8-7, a 99% confidence interval for the mean number of rooms rented daily in a given month is from ________ to ________.

Answer: 24.64 to 49.36 Difficulty: Moderate Keywords: confidence interval, mean 124) Referring to Table 8-7, the sampling error of a 99% confidence interval for the mean number of rooms rented daily in a given month is ________.

Answer: 12.36 Difficulty: Moderate Keywords: confidence interval, mean, sampling error 125) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, mean, properties, width 126) True or False: Referring to Table 8-7, a 99% confidence interval will contain 99% of the sample mean number of rooms rented daily in a given month.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, mean, interpretation

8-22 .

127) True or False: Referring to Table 8-7, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, mean, properties, width 128) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, mean, interpretation 129) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, mean, interpretation 130) True or False: Referring to Table 8-7, we are 99% confident that between 24.64% and 49.36% of the rooms will be rented daily in a given month.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, mean, interpretation 131) True or False: Referring to Table 8-7, we are 99% confident that the average number of rooms rented daily in a given month is somewhere between 24.64 and 49.36.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, mean, interpretation TABLE 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 Table 8-8, the parameter of interest is the mean number of students in the population who own a personal computer.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, proportion, parameter 133) True or False: Referring to Table 8-8, the parameter of interest is the proportion of the student population who own a personal computer.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, proportion, parameter 134) Referring to Table 8-8, the critical value for a 99% confidence interval for this sample is ________.

Answer: 2.5758 Difficulty: Easy Keywords: confidence interval, proportion 8-23 .

135) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, proportion 136) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, proportion, sampling error 137) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, proportion, properties, width 138) True or False: Referring to Table 8-8, a 99% confidence interval will contain 99% of the student population who own a personal computer.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 139) True or False: Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, proportion 140) True or False: Referring to Table 8-8, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, proportion, properties, width 141) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, proportion, interpretation 142) True or False: Referring to Table 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 Difficulty: Easy Keywords: confidence interval, proportion, interpretation 8-24 .

143) True or False: Referring to Table 8-8, we are 99% confident that the mean number of the student population who own a personal computer is between 0.7911 and 0.8769.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, proportion, interpretation 144) True or False: Referring to Table 8-8, we are 99% confident that between 79.11% and 87.69% of the student population own a personal computer.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, proportion, interpretation TABLE 8-9 The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year. A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year.

145) Referring to Table 8-9, what is the critical value for the 95% one-sided confidence interval for the proportion of students who skipped more than 10 days of school last year?

Answer: 1.6449 (using PHStat) or 1.645 (using Table E.2) Difficulty: Easy Keywords: confidence interval, proportion, one-sided, critical value 146) True or False: Referring to Table 8-9, the superintendent can conclude with 95% level of confidence that no more than 5% of the students in the unified school district skipped more than 10 days of school last year.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, proportion, one-sided, interpretation TABLE 8-10 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".

147) True or False: Referring to Table 8-10, the parameter of interest is the total number of students in the population who feel comfortable reporting cheating by their fellow students.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, proportion, parameter 148) True or False: Referring to Table 8-10, the parameter of interest is the proportion of the student population who feel comfortable reporting cheating by their fellow students.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, proportion, parameter

8-25 .

149) Referring to Table 8-10, the critical value for a 99% confidence interval for this sample is ________.

Answer: 2.5758 Difficulty: Easy Keywords: confidence interval, proportion 150) Referring to Table 8-10, 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 Difficulty: Moderate Keywords: confidence interval, proportion 151) Referring to Table 8-10, 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 Difficulty: Moderate Keywords: confidence interval, proportion, sampling error 152) True or False: Referring to Table 8-10, 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 Difficulty: Easy Keywords: confidence interval, proportion, properties, width 153) True or False: Referring to Table 8-10, a 99% confidence interval will contain 99% of the student population who feel comfortable reporting cheating by their fellow students.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 154) True or False: Referring to Table 8-10, 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 Difficulty: Moderate Keywords: confidence interval, proportion 155) True or False: Referring to Table 8-10, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, proportion, properties, width

8-26 .

156) True or False: Referring to Table 8-10, 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 Explanation: The confidence interval always contains the sample proportion.

Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 157) True or False: Referring to Table 8-10, it is possible that the 99% confidence interval calculated from the data will not contain the proportion of student population who feel comfortable reporting cheating by their fellow students.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, proportion, interpretation 158) True or False: Referring to Table 8-10, we are 99% confident that the total numbers of the student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

Answer: FALSE Difficulty: Difficult Keywords: confidence interval, proportion, interpretation 159) True or False: Referring to Table 8-10, 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 Difficulty: Easy Keywords: confidence interval, proportion, interpretation TABLE 8-11 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.

160) Referring to Table 8-11, 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 Difficulty: Moderate Keywords: confidence interval, proportion 161) Referring to Table 8-11, 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 Difficulty: Easy Keywords: confidence interval, proportion

8-27 .

162) Referring to Table 8-11, 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 Difficulty: Moderate Keywords: confidence interval, proportion, sampling error 163) True or False: Referring to Table 8-11, a 95% confidence interval will contain 95% of the population proportion of managers who have caught salespeople cheating on an expense report.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 164) True or False: Referring to Table 8-11, 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 Explanation: The confidence interval always contains the sample proportion.

Difficulty: Moderate Keywords: confidence interval, proportion, interpretation 165) True or False: Referring to Table 8-11, 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 Difficulty: Easy Keywords: confidence interval, proportion, interpretation 166) True or False: Referring to Table 8-11, 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 Difficulty: Difficult Keywords: confidence interval, proportion, interpretation 167) True or False: Referring to Table 8-11, 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 Difficulty: Easy Keywords: confidence interval, proportion, interpretation 168) Referring to Table 8-11, 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 Difficulty: Moderate Keywords: confidence interval, proportion

8-28 .

169) Referring to Table 8-11, 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 Difficulty: Moderate Keywords: confidence interval, proportion, sampling error 170) Referring to Table 8-11, 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 Difficulty: Moderate Keywords: confidence interval, proportion 171) Referring to Table 8-11, 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 Difficulty: Moderate Keywords: confidence interval, proportion, sampling error 172) Referring to Table 8-11, 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 Difficulty: Moderate Keywords: confidence interval, proportion 173) Referring to Table 8-11, 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 Difficulty: Moderate Keywords: confidence interval, proportion, sampling error 174) Referring to Table 8-11, 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: 2,401 Difficulty: Moderate Keywords: confidence interval, proportion, sample size determination

8-29 .

TABLE 8-12 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.

175) True or False: Referring to Table 8-12, the report contains all the essential components for an ethical reporting of poll results.

Answer: FALSE Explanation: The level of confidence is missing.

Difficulty: Easy Keywords: confidence interval, ethical issues 176) True or False: Referring to Table 8-12, the size of the population is 1,500.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, proportion 177) Referring to Table 8-12, 1,500 is the size of the A) population.

B) sample.

C) frame.

D) proportion.

Answer: B Difficulty: Easy Keywords: confidence interval, proportion 178) True or False: Referring to Table 8-12, 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 Difficulty: Moderate Keywords: confidence interval, interpretation 179) True or False: Referring to Table 8-12, the standard error is 3%.

Answer: FALSE Difficulty: Easy Keywords: confidence interval, sampling error 180) True or False: Referring to Table 8-12, the sampling error is 3%.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, sampling error 181) Referring to Table 8-12, 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: 1,067 Difficulty: Moderate Keywords: confidence interval, sample size determination, proportion 8-30 .

182) Referring to Table 8-12, 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 Difficulty: Moderate Keywords: confidence interval, sample size determination, proportion 183) Referring to Table 8-12, 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 Difficulty: Moderate Keywords: confidence interval, sample size determination, proportion 184) Referring to Table 8-12, 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 Difficulty: Moderate Keywords: confidence interval, sample size determination, proportion 185) Referring to Table 8-12, 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 Difficulty: Moderate Keywords: confidence interval, sample size determination, proportion

8-31 .

Business Statistics: A First Course, 6e (Levine) 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 Difficulty: Easy Keywords: 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 Difficulty: Easy Keywords: 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 Difficulty: Easy Keywords: 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 Difficulty: Easy Keywords: form of hypothesis 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 Difficulty: Easy Keywords: Type II error

9-1 .

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 Difficulty: Easy Keywords: 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 Difficulty: Easy Keywords: 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 Difficulty: Easy Keywords: one-tail test 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 Difficulty: Easy Keywords: two-tail test 10) If the p-value is less than α 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 Difficulty: Easy Keywords: p-value, level of significance

9-2 .

11) If a test of hypothesis has a Type I error probability (α) 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 Difficulty: Moderate Keywords: Type I error, level of significance 12) If the Type I error (α) for a given test is to be decreased, then for a fixed sample size n A) the Type II error (β) will also decrease.

B) the Type II error (β) will increase.

C) the power of the test will increase.

D) a one-tail test must be utilized.

Answer: B Difficulty: Moderate Keywords: Type I error, Type II error, sample size 13) For a given sample size n, if the level of significance (α) is decreased, the power of the test A) will increase.

B) will decrease.

C) will remain the same.

D) cannot be determined.

Answer: B Difficulty: Moderate Keywords: level of significance, power, sample size 14) For a given level of significance (α), if the sample size n is increased, the probability of a Type II error (β) A) will decrease.

B) will increase.

C) will remain the same.

D) cannot be determined.

Answer: A Difficulty: Moderate Keywords: level of significance, beta-risk, sample size 15) If you know that the level of significance (α) of a test is 5%, you can tell that the probability of committing a Type II error (β) is A) 2.5%.

B) 95%.

C) 97.5%.

D) unknown.

Answer: D Difficulty: Moderate Keywords: level of significance, beta-risk

9-3 .

16) If you know that the probability of committing a Type II error (β) is 5%, you can tell that the power of the test is A) 2.5%.

B) 95%.

C) 97.5%.

D) unknown.

Answer: B Difficulty: Easy Keywords: level of significance, beta-risk, power 17) If a researcher rejects a true null hypothesis, she has made a ________ error.

Answer: Type I Difficulty: Easy Keywords: Type I error 18) If a researcher does not reject a true null hypothesis, she has made a ________ decision.

Answer: correct Difficulty: Easy Keywords: decision 19) If a researcher rejects a false null hypothesis, she has made a ________ decision.

Answer: correct Difficulty: Easy Keywords: decision 20) If a researcher does not reject a false null hypothesis, she has made a ________ error.

Answer: Type II Difficulty: Easy Keywords: Type II error 21) 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 μ is used.

B) a one-tail test for μ is used.

C) Both of the previous statements are true.

D) None of the previous statements is true.

Answer: A Difficulty: Moderate Keywords: confidence interval, two-tail test 22) 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 Difficulty: Moderate Keywords: power 9-4 .

23) The symbol for the power of a statistical test is A) α.

B) 1 - α.

C) β.

D) 1 - β.

Answer: D Difficulty: Easy Keywords: power 24) The symbol for the probability of committing a Type I error of a statistical test is A) α.

B) 1 - α.

C) β.

D) 1 - β.

Answer: A Difficulty: Easy Keywords: level of significance, probability, Type I error 25) The symbol for the level of significance of a statistical test is A) α.

B) 1 - α.

C) β.

D) 1 - β.

Answer: A Difficulty: Easy Keywords: level of significance, probability, Type I error 26) The symbol for the probability of committing a Type II error of a statistical test is A) α.

B) 1 - α.

C) β.

D) 1 - β.

Answer: C Difficulty: Easy Keywords: probability, Type II error 27) The symbol for the confidence coefficient of a statistical test is A) α.

B) 1 - α.

C) β.

D) 1 - β.

Answer: B Difficulty: Easy Keywords: confidence coefficient

9-5 .

28) Suppose we wish to test H0: μ ≤ 47 versus H1: μ > 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 Difficulty: Moderate Keywords: one-tail test, conclusion 29) 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: = 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: μ ≤ 60 and H1: μ > 60.

B) H0: μ ≥ 60 and H1: μ < 60.

C) H0:

≥ 60 and H1:

< 60.

D) H0: = 52 and H1: ≠ 52.

Answer: B Difficulty: Moderate Keywords: one-tail test, form of hypothesis, form of hypothesis, mean, t test 30) 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: = 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 = (52 - 60) / (22/1002) D) t = (52 - 60) / (22/10) Answer: D Difficulty: Easy Keywords: one-tail test, mean, t test

9-6 .

31) 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: = 52, S = 22. Suppose the alternative you wanted to test was H1: μ < 60. State the correct rejection region for α = 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, rejection region 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: = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decisions is correct?

A) At α = 0.05, you do not reject H0.

B) At α = 0.05, you reject H0.

C) At α = 0.10 you reject H0.

D) At α = 0.10, you do not reject H0.

Answer: B Difficulty: Easy Keywords: one-tail test, mean, t test, decision 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: = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following conclusions is correct?

A) At α = 0.05, there is not sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues.

B) At α = 0.05, there is sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues.

C) At α = 0.05, there is insufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.

D) At α = 0.10, there is sufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.

Answer: D Difficulty: Moderate Keywords: two-tail test, mean, t test, conclusion

9-7 .

34) You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if you test H0: μ =16 versus H1: μ ≠ 16 at α = 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 Difficulty: Easy Keywords: two-tail test, confidence interval, mean, t test, decision 35) You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if we test H0: μ =16 versus H1: μ ≠ 16 at α = 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 Explanation: A) The 90% confidence interval is narrower than (10, 15), which still does not contain 16.

Difficulty: Moderate Keywords: two-tail test, confidence interval, mean, t test, decision 36) You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if we test H0: μ =16 versus H1: μ ≠ 16 at α = 0.01?

A) Reject Ho in favor of H1.

B) Do not reject Ho in favor of H1.

C) Fail to reject Ho in favor of H1.

D) You cannot tell what our decision will be from the information given.

Answer: D Explanation: D) The 99% confidence interval is wider than (10, 15), which could have contained 16 or not have contained 16.

Difficulty: Moderate Keywords: two-tail test, confidence interval, mean, t test, decision 37) Suppose you want to test H0: μ ≥ 30 versus H1: μ < 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) B)

= 28, S = 6 = 27, S = 4

C) = 32, S = 2 D) = 26, S = 9 Answer: B Difficulty: Moderate Keywords: one-tail test, rejection region

9-8 .

38) 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 α level.

D) The significance level is another name for Type II error.

Answer: D Difficulty: Moderate Keywords: level of significance 39) 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 Difficulty: Moderate Keywords: decision, Type I error, Type II error 40) The value that separates a rejection region from a non-rejection region is called the ________.

Answer: critical value Difficulty: Easy Keywords: critical value, rejection region 41) 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 Difficulty: Easy Keywords: test statistic 42) 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: μ ≥ 30 versus H1: μ < 30.

B) H0: μ ≤ 30 versus H1: μ > 30.

C) H0: ≥ 30 versus H1: < 30.

D) H0: ≤ 30 versus H1: > 30.

Answer: B Difficulty: Easy Keywords: one-tail test, form of hypothesis, form of hypothesis, mean

9-9 .

43) 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 Difficulty: Moderate Keywords: one-tail test, mean, Z test, t test, rejection region 44) 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, decision 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. 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, conclusion

9-10 .

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. 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, p-value 47) An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past five 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 Difficulty: Moderate Keywords: two-tail test, mean, Z test 48) An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past five 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 Difficulty: Moderate Keywords: two-tail test, mean, Z test, conclusion 49) 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 Difficulty: Easy Keywords: two-tail test, mean, t test 9-11 .

50) 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 Difficulty: Moderate Keywords: two-tail test, mean, t test, conclusion 51) 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 Difficulty: Easy Keywords: one-tail test, proportion, test statistic 52) 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) α = 0.10, (b) α = 0.05, and (c) α = 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 Difficulty: Moderate Keywords: one-tail test, proportion, decision

9-12 .

53) 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 Difficulty: Moderate Keywords: one-tail test, proportion, conclusion 54) A major DVD rental 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 are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. State the test of hypothesis that is of interest to the rental chain.

A) H0: π ≤ 0.32 versus H1: π > 0.32 B) H0: π ≤ 0.25 versus H1: π > 0.25 C) H0: π ≤ 5,000 versus H1: μ > 5,000 D) H0: μ ≤ 5,000 versus H1: μ > 5,000 Answer: B Difficulty: Easy Keywords: one-tail test, proportion, form of hypothesis, form of hypothesis 55) A major DVD rental 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 are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, test statistic

9-13 .

56) A major DVD rental 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 are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, p-value 57) A major DVD rental 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 are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, decision 58) A major DVD rental 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 are equipped with DVD players. It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have DVD players. The rental 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, conclusion

9-14 .

59) The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a side curtain air bag 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 side curtain air bags. 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 Difficulty: Easy Keywords: two-tail test, proportion 60) The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a knee airbag 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 knee airbag. 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 Difficulty: Easy Keywords: two-tail test, proportion, conclusion TABLE 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:

61) Referring to Table 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 Difficulty: Easy Keywords: mean, t test, parameter 9-15 .

62) Referring to Table 9-1, state the alternative hypothesis for this study.

Answer: H1: μ > 20 Difficulty: Easy Keywords: one-tail test, mean, t test, form of hypothesis 63) Referring to Table 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 Difficulty: Easy Keywords: one-tail test, mean, t test, critical value 64) True or False: Referring to Table 9-1, the null hypothesis would be rejected.

Answer: TRUE Difficulty: Easy Keywords: one-tail test, mean, t test, decision 65) True or False: Referring to Table 9-1, the null hypothesis would be rejected if a 5% probability of committing a Type I error is allowed.

Answer: TRUE Difficulty: Easy Keywords: one-tail test, mean, t test, decision 66) True or False: Referring to Table 9-1, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

Answer: FALSE Difficulty: Easy Keywords: one-tail test, mean, t test, decision 67) Referring to Table 9-1, the lowest level of significance at which the null hypothesis can be rejected is ________.

Answer: 0.021 Difficulty: Moderate Keywords: one-tail test, mean, t test, p-value 68) True or False: Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, conclusion 69) True or False: Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, conclusion 9-16 .

70) True or False: Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, decision 71) True or False: Referring to Table 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 Difficulty: Easy Keywords: one-tail test, mean, t test, decision 72) True or False: Referring to Table 9-1, if these data were used to perform a two-tail test, the p-value would be 0.042.

Answer: TRUE Difficulty: Moderate Keywords: one-tail test, mean, t test, p-value 73) 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 Difficulty: Easy Keywords: mean, t test, p-value, level of significance, decision 74) 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 Difficulty: Easy Keywords: p-value, level of significance, decision 75) 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 Difficulty: Easy Keywords: proportion, Z test, test statistic, critical value, decision 76) True or False: In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.

Answer: FALSE Difficulty: Easy Keywords: pitfalls, testing 77) True or False: The test statistic measures how close the computed sample statistic has come to the hypothesized population parameter.

Answer: TRUE Difficulty: Moderate Keywords: test statistic 9-17 .

78) True or False: The statement of the null hypothesis always contains an equality.

Answer: TRUE Difficulty: Easy Keywords: form of null hypothesis 79) True or False: The larger the p-value, the more likely you are to reject the null hypothesis.

Answer: FALSE Difficulty: Easy Keywords: p-value 80) True or False: The smaller the p-value, the stronger is the evidence against the null hypothesis.

Answer: TRUE Difficulty: Easy Keywords: p-value 81) 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 Difficulty: Easy Keywords: confidence interval, two-tail test, decision 82) 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 Difficulty: Moderate Keywords: confidence interval, two-tail test, decision 83) 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 Difficulty: Moderate Keywords: confidence interval, two-tail test, decision 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 0.02.

Answer: FALSE Explanation: We are not sure if 20 will be in the wider confidence interval.

Difficulty: Moderate Keywords: confidence interval, two-tail test, decision

9-18 .

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 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 Explanation: We are not sure if 20 will be in the wider confidence interval.

Difficulty: Moderate Keywords: confidence interval, two-tail test, decision 86) True or False: In testing a hypothesis, you should always raise the question concerning the purpose of the study, survey, or experiment.

Answer: TRUE Difficulty: Easy Keywords: pitfalls, testing 87) 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 Difficulty: Easy Keywords: pitfalls, testing 88) 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 Difficulty: Easy Keywords: pitfalls, testing 89) 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 Difficulty: Easy Keywords: pitfalls, testing 90) 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 Difficulty: Easy Keywords: pitfalls, testing 91) 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 Difficulty: Moderate Keywords: pitfalls, testing 92) True or False: In conducting research, you should document both good and bad results.

Answer: TRUE Difficulty: Easy Keywords: pitfalls, testing 9-19 .

93) 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 Difficulty: Easy Keywords: pitfalls, testing TABLE 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, the student 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), the student 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.

94) Referring to Table 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 Difficulty: Difficult Keywords: form of hypothesis, form of hypothesis 95) Referring to Table 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 Difficulty: Difficult Keywords: Type II error 96) Referring to Table 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 Difficulty: Difficult Keywords: level of significance 97) Referring to Table 9-2, what is the "actual confidence coefficient"?

A) 0.13 B) 0.16 C) 0.84 D) 0.87 Answer: D Difficulty: Difficult Keywords: confidence coefficient 9-20 .

98) Referring to Table 9-2, what is the value of α?

A) 0.13 B) 0.16 C) 0.84 D) 0.87 Answer: A Difficulty: Difficult Keywords: level of significance 99) Referring to Table 9-2, what is the value of β?

A) 0.13 B) 0.16 C) 0.84 D) 0.87 Answer: B Difficulty: Difficult Keywords: beta-risk TABLE 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 an mean of 257.3 W. 100) Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, Z test 101) Referring to Table 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 Difficulty: Easy Keywords: one-tail test, mean, Z test, parameter

9-21 .

102) Referring to Table 9-3, the appropriate hypotheses to determine if the manufacturer's claim appears reasonable are: A) H0: μ = 250 versus H1: μ ≠ 250.

B) H0: μ ≥ 250 versus H1: μ < 250.

C) H0: μ ≤ 250 versus H1: μ > 250.

D) H0: μ ≥ 257.3 versus H1: μ < 257.3.

Answer: C Difficulty: Moderate Keywords: one-tail test, mean, Z test, form of hypothesis, form of hypothesis 103) Referring to Table 9-3, for a test with a level of significance of 0.05, the critical value would be ________.

Answer: Z = 1.645 Difficulty: Moderate Keywords: one-tail test, mean, Z test, critical value 104) Referring to Table 9.3, the value of the test statistic is ________.

Answer: 2.18 Difficulty: Easy Keywords: one-tail test, mean, Z test, test statistic 105) Referring to Table 9-3, the p-value of the test is ________.

Answer: 0.0148 using Excel or 0.0146 using Table E.2 Difficulty: Moderate Keywords: one-tail test, mean, Z test, p-value 106) True or False: Referring to Table 9-3, for this test to be valid, it is necessary that the power consumption for microwave ovens has a normal distribution.

Answer: TRUE Difficulty: Easy Keywords: one-tail test, mean, Z test, assumptions 107) True or False: Referring to Table 9-3, the null hypothesis will be rejected at 5% level of significance.

Answer: TRUE Difficulty: Moderate Keywords: one-tail test, mean, Z test, decision 108) True or False: Referring to Table 9-3, the null hypothesis will be rejected at 1% level of significance.

Answer: FALSE Difficulty: Moderate Keywords: one-tail test, mean, Z test, decision

9-22 .

109) True or False: Referring to Table 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 Difficulty: Difficult Keywords: one-tail test, mean, Z test, conclusion TABLE 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 an 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, it will continue to produce the older drug. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision.

110) Referring to Table 9-4, the appropriate hypotheses are: A) H0: μ = 7.4 versus H1: μ ≠ 7.4.

B) H0: μ ≤ 7.4 versus H1: μ > 7.4.

C) H0: μ ≥ 7.4 versus H1: μ < 7.4.

D) H0: μ > 7.4 versus H1: μ ≤ 7.4.

Answer: C Difficulty: Easy Keywords: one-tail test, mean, Z test, form of hypothesis, form of hypothesis 111) Referring to Table 9-4, for a test with a level of significance of 0.10, the critical value would be ________.

Answer: -1.28 Difficulty: Easy Keywords: one-tail test, mean, Z test, critical value 112) Referring to Table 9-4, the value of the test statistic is ________.

Answer: -1.50 Difficulty: Easy Keywords: one-tail test, mean, Z test, test statistic 113) Referring to Table 9-4, the p-value of the test is ________.

Answer: 0.0668 Difficulty: Moderate Keywords: one-tail test, mean, Z test, p-value 114) True or False: Referring to Table 9-4, the null hypothesis will be rejected with a level of significance of 0.10.

Answer: TRUE Difficulty: Moderate Keywords: one-tail test, mean, Z test, decision

9-23 .

115) True or False: Referring to Table 9-4, if the level of significance had been chosen as 0.05, the null hypothesis would be rejected.

Answer: FALSE Difficulty: Moderate Keywords: one-tail test, mean, Z test, decision 116) True or False: Referring to Table 9-4, if the level of significance had been chosen as 0.05, the company would market the new anesthetic.

Answer: FALSE Difficulty: Moderate Keywords: one-tail test, mean, Z test, conclusion TABLE 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.

117) True or False: Referring to Table 9-5, the null hypothesis would be rejected at a significance level of α = 0.05.

Answer: TRUE Difficulty: Easy Keywords: one-tail test, mean, decision 118) True or False: Referring to Table 9-5, the null hypothesis would be rejected at a significance level of α = 0.01.

Answer: FALSE Difficulty: Easy Keywords: one-tail test, mean, decision 119) True or False: Referring to Table 9-5, the bank can conclude that the mean age is greater than 45 at a significance level of α = 0.01.

Answer: FALSE Difficulty: Moderate Keywords: one-tail test, mean, conclude 120) Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, p-value

9-24 .

TABLE 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. The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test.

121) True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.

Answer: TRUE Difficulty: Easy Keywords: one-tail test, mean, Z test, decision 122) True or False: Referring to Table 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.

Answer: FALSE Difficulty: Moderate Keywords: one-tail test, mean, Z test, conclusion 123) True or False: Referring to Table 9-6, if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

Answer: FALSE Difficulty: Easy Keywords: one-tail test, mean, Z test, decision 124) True or False: Referring to Table 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 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.

Difficulty: Moderate Keywords: one-tail test, mean, Z test, conclusion 125) True or False: Referring to Table 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 Difficulty: Easy Keywords: one-tail test, mean, Z test, decision

9-25 .

126) Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater 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: A Difficulty: Moderate Keywords: one-tail test, mean, Z test, p-value 127) Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, Z test, p-value 128) True or False: Referring to Table 9-6, suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. Then if the test is performed with a level of significance of 0.05, the null hypothesis would be rejected.

Answer: FALSE Difficulty: Moderate Keywords: one-tail test, mean, Z test, decision TABLE 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.

129) Referring to Table 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 Difficulty: Easy Keywords: proportion, Z test, parameter

9-26 .

130) Referring to Table 9-7, state the null hypothesis for this study.

Answer: H0: π ≥ 0.22 Difficulty: Easy Keywords: one-tail test, proportion, Z test, form of hypothesis 131) Referring to Table 9-7, state the alternative hypothesis for this study.

Answer: H1: π < 0.22 Difficulty: Easy Keywords: one-tail test, proportion, Z test, form of hypothesis 132) Referring to Table 9-7, what critical value should the company officials use to determine the rejection region?

Answer: −2.3263 Difficulty: Easy Keywords: one-tail test, proportion, Z test, critical value 133) Referring to Table 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, rejection region 134) True or False: Referring to Table 9-7, the null hypothesis would be rejected.

Answer: FALSE Difficulty: Easy Keywords: one-tail test, proportion, Z test, decision 135) Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, proportion, Z test, p-value 136) Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, proportion, Z test, p-value 137) True or False: Referring to Table 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, conclusion

9-27 .

138) True or False: Referring to Table 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, decision 139) True or False: Referring to Table 9-7, the value of β is 0.90.

Answer: FALSE Difficulty: Moderate Keywords: one-tail test, mean, Z test, beta-risk 140) Referring to Table 9-7, what will be the p-value if these data were used to perform a two-tail test?

Answer: 0.027 Difficulty: Moderate Keywords: one-tail test, proportion, Z test, p-value TABLE 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 samples 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.

141) Referring to Table 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 Difficulty: Easy Keywords: proportion, Z test, parameter 142) Referring to Table 9-8, state the null hypothesis for this study.

Answer: H0: π ≤ 0.101 Difficulty: Easy Keywords: one-tail test, proportion, Z test, form of hypothesis 143) Referring to Table 9-8, state the alternative hypothesis for this study.

Answer: H1: π > 0.101 Difficulty: Easy Keywords: one-tail test, proportion, Z test, form of hypothesis 144) Referring to Table 9-8, what critical value should the company officials use to determine the rejection region?

Answer: 1.645 Difficulty: Easy Keywords: one-tail test, proportion, Z test, critical value 9-28 .

145) Referring to Table 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, rejection region 146) True or False: Referring to Table 9-8, the null hypothesis would be rejected.

Answer: FALSE Difficulty: Easy Keywords: one-tail test, proportion, Z test, decision 147) Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, proportion, Z test, p-value 148) Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, proportion, Z test, p-value 149) True or False: Referring to Table 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 Difficulty: Easy Keywords: one-tail test, proportion, Z test, conclusion 150) True or False: Referring to Table 9-8, the value of the probability of committing a Type II error β is 0.95.

Answer: FALSE Difficulty: Moderate Keywords: one-tail test, mean, Z test, beta-risk 151) Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, proportion, Z test, p-value

9-29 .

TABLE 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.

152) Referring to Table 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 Difficulty: Easy Keywords: mean, t test, parameter 153) Referring to Table 9-9, the population the president is interested in is: A) all entering students to all universities in the United States this year.

B) all entering students to his university this year.

C) all SAT test centers in the United States this year.

D) the SAT scores of all students entering universities in the United States this year.

Answer: B Difficulty: Easy Keywords: mean, t test, population 154) Referring to Table 9-9, state the null hypothesis for this study.

Answer: H0: μ ≥ 1520 Difficulty: Easy Keywords: one-tail test, mean, t test, form of hypothesis 155) Referring to Table 9-9, state the alternative hypothesis for this study.

Answer: H1: μ < 1520 Difficulty: Easy Keywords: one-tail test, mean, t test, form of hypothesis 156) Referring to Table 9-9, what critical value should the president use to determine the rejection region?

Answer: -1.7291 Difficulty: Easy Keywords: one-tail test, mean, t test, critical value 157) True or False: Referring to Table 9-9, the null hypothesis would be rejected.

Answer: FALSE Difficulty: Easy Keywords: one-tail test, mean, t test, decision

9-30 .

158) True or False: Referring to Table 9-9, the null hypothesis would be rejected if a 10% probability of committing a Type I error is allowed.

Answer: TRUE Difficulty: Easy Keywords: one-tail test, mean, t test, decision 159) True or False: Referring to Table 9-9, the null hypothesis would be rejected if a 1% probability of committing a Type I error is allowed.

Answer: FALSE Difficulty: Easy Keywords: one-tail test, mean, t test, decision 160) Referring to Table 9-9, the lowest level of significance at which the null hypothesis can still be rejected is ________.

Answer: 0.0627 Difficulty: Moderate Keywords: one-tail test, mean, t test, p-value 161) Referring to Table 9-9, the highest level of significance at which the null hypothesis cannot be rejected is ________.

Answer: 0.0627 Difficulty: Moderate Keywords: one-tail test, mean, t test, p-value 162) True or False: Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, conclusion 163) True or False: Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, conclusion 164) True or False: Referring to Table 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 Difficulty: Moderate Keywords: one-tail test, mean, t test, decision 165) True or False: Referring to Table 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 Difficulty: Easy Keywords: one-tail test, mean, t test, decision 9-31 .

166) True or False: Referring to Table 9-9, if these data were used to perform a two-tail test, the p-value would be 0.1254.

Answer: TRUE Difficulty: Moderate Keywords: one-tail test, mean, t test, p-value 167) Referring to Table 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 Difficulty: Easy Keywords: mean, t test, Type I error 168) Referring to Table 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 Difficulty: Easy Keywords: mean, t test, Type II error

9-32 .

Business Statistics: A First Course, 6e (Levine) Chapter 10 Two-Sample Tests and One-Way ANOVA 1) True or False: For all two-sample tests, the sample sizes must be equal in the two groups.

Answer: FALSE 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 two sample variances.

Answer: TRUE Difficulty: Easy Keywords: pooled variance, t test, sample size 3) The t test for the difference between the means of two independent populations assumes that the respective A) sample sizes are equal.

B) sample variances are equal.

C) populations are approximately normal.

D) all of the above Answer: C Difficulty: Moderate Keywords: pooled variance, t test, assumption 4) If we are testing for the difference between the means of two 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 Difficulty: Easy Keywords: pooled variance, t test, degrees of freedom 5) In testing for the differences between the means of two 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 Difficulty: Easy Keywords: pooled variance, t test, degrees of freedom

10-1 .

6) In testing for differences between the means of two independent populations, the null hypothesis is: A) H0: μ1 - μ2 = 2.

B) H0: μ1 - μ2 = 0.

C) H0: μ1 - μ2 > 0.

D) H0: μ1 - μ2 < 2.

Answer: B 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 two populations each follow a ________ distribution.

Answer: normal Difficulty: Easy Keywords: pooled variance, t test, assumption 8) Given the following information, calculate the degrees of freedom that should be used in the pooledvariance t test.

S12 = 4 S22 = 6 n1 = 16 n2 = 25 A) df = 41 B) df = 39 C) df = 16 D) df = 25 Answer: B 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 Difficulty: Easy Keywords: pooled variance, t test

10-2 .

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 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 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 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 Difficulty: Easy Keywords: pooled variance, t test TABLE 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.

American Sample Size 211 Sample Mean SSATL Score 65.75 Sample Std. Dev. 11.07

Japanese 100 79.83 6.41

14) Referring to Table 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) test for the ratio of two variances D) Z test for the difference between two proportions Answer: B Difficulty: Easy Keywords: pooled variance, t test, difference between two means

10-3 .

15) Referring to Table 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) H0: μA - μJ ≥ 0 versus H1: μA - μJ < 0 B) H0: μA - μJ ≤ 0 versus H1: μA - μJ > 0 C) H0: μA - μJ = 0 versus H1: μA - μJ ≠ 0 D) H0: = 0 versus H1: ≠0 Answer: C Difficulty: Easy Keywords: pooled variance, t test, mean differences, form of hypothesis 16) Referring to Table 10-1, what is the value of the test statistic?

A) -14.08 B) -11.8092 C) -1.9677 D) 96.4471 Answer: B Difficulty: Moderate Keywords: pooled variance, t test, mean differences, test statistic 17) Referring to Table 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 Difficulty: Moderate Keywords: pooled variance, t test, mean differences, p-value

10-4 .

TABLE 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.

18) Referring to Table 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: μfemales > μmales B) H1: μfemales < μmales C) H1: μfemales ≠ μmales D) H1: μfemales =μmales Answer: B Difficulty: Moderate Keywords: pooled variance, t test, form of hypothesis 19) Referring to Table 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 Table 10-2, the correct test statistic is ________.

A) -6610 B) -1.3763 C) -1.7011 D) 0.0898 Answer: B Difficulty: Easy Keywords: pooled variance, t test, test statistic

10-5 .

20) Referring to Table 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 α = 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 α = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates.

C) At the α = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates.

D) At the α = 0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.

Answer: B Difficulty: Moderate Keywords: pooled variance, t test, conclusion 21) Referring to Table 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 Difficulty: Moderate Keywords: pooled variance, t test, assumption 22) Referring to Table 10-2, what is the 99% confidence interval estimate for the difference between two means?

Answer: -$ 1,9881.07 to $6,661.07 Difficulty: Moderate Keywords: confidence interval, difference between two means 23) Referring to Table 10-2, what is the 95% confidence interval estimate for the difference between two means?

Answer: -$16,447.85 to $3,227.85 Difficulty: Moderate Keywords: confidence interval, difference between two means 24) Referring to Table 10-2, what is the 90% confidence interval estimate for the difference between two means?

Answer: -$14,779.99 to $1,559.99 Difficulty: Moderate Keywords: confidence interval, difference between two means

10-6 .

TABLE 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: G = 35 months, SG2 = 900 Metropolis: M = 50 months, SM2 = 1,050 25) Referring to Table 10-3, which of the following represents the relevant hypotheses tested by the real estate company?

A) H0: μG - μM ≥ 0 versus H1: μG - μM < 0 B) H0: μG - μM ≤ 0 versus H1: μG - μM > 0 C) H0: μG - μM = 0 versus H1: μG - μM ≠ 0 D) H0: G - M ≥ 0 versus H1: G - M < 0 Answer: A Difficulty: Easy Keywords: pooled variance, t test, form of hypothesis 26) Referring to Table 10-3, what is the estimated standard error of the difference between the two sample means?

A) 4.06 B) 5.61 C) 8.01 D) 16.00 Answer: A Difficulty: Moderate Keywords: pooled variance, t test, standard error 27) Referring to Table 10-3, what is a point estimate for the mean of the sampling distribution of the difference between the two sample means?

A) -22 B) -10 C) -15 D) 0 Answer: C Difficulty: Easy Keywords: pooled variance, t test, unbiased, point estimate 28) Referring to Table 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 Difficulty: Easy Keywords: pooled variance, t test, critical value

10-7 .

29) Referring to Table 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 Difficulty: Easy Keywords: pooled variance, t test, critical value 30) Referring to Table 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 Difficulty: Moderate Keywords: pooled variance, t test, test statistic 31) Referring to Table 10-3, suppose α = 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 make a decision.

Answer: B Difficulty: Easy Keywords: pooled variance, t test, decision 32) Referring to Table 10-3, suppose α = 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 make a decision.

Answer: B Difficulty: Easy Keywords: pooled variance, t test, decision 33) Referring to Table 10-3, suppose α = 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 make a decision.

Answer: B Difficulty: Easy Keywords: pooled variance, t test, decision 34) Referring to Table 10-3, suppose α = 0.10. Which of the following represents the correct 10-8 .

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 Difficulty: Easy Keywords: pooled variance, t test, conclusion 35) Referring to Table 10-3, suppose α = 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 Difficulty: Easy Keywords: pooled variance, t test, conclusion 36) Referring to Table 10-3, suppose α = 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 Difficulty: Easy Keywords: pooled variance, t test, conclusion 37) Referring to Table 10-3, what is the 99% confidence interval estimate for the difference in the two means?

Answer: -25.54 to -4.46 months Difficulty: Moderate Keywords: confidence interval, difference between two means

10-9 .

38) Referring to Table 10-3, what is the 95% confidence interval estimate for the difference in the two means?

Answer: -23.00 to -7.00 months Difficulty: Moderate Keywords: confidence interval, difference between two means TABLE 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 Table 10-4, the pooled (i.e., combined) variance is ________.

Answer: 12.5 Difficulty: Easy Keywords: pooled variance, t test 40) Referring to Table 10-4, the computed t statistic is ________.

Answer: 2.50 Difficulty: Easy Keywords: pooled variance, t test, test statistic 41) Referring to Table 10-4, there are ________ degrees of freedom for this test.

Answer: 48 Difficulty: Easy Keywords: pooled variance, t test, degrees of freedom 42) Referring to Table 10-4, the critical values for a two-tail test of the null hypothesis of no difference in the population means at the α = 0.05 level of significance are ________.

Answer: ±2.0106 Difficulty: Easy Keywords: pooled variance, t test, critical value 43) Referring to Table 10-4, a two-tail test of the null hypothesis of no difference would ________ (be rejected/not be rejected) at the α = 0.05 level of significance.

Answer: be rejected Difficulty: Easy Keywords: pooled variance, t test, decision 44) Referring to Table 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 Difficulty: Moderate Keywords: pooled variance, t test, p-value 45) Referring to Table 10-4, if you were interested in testing against the one-tail alternative that μ1 > μ2 at the α = 0.01 level of significance, the null hypothesis would ________ (be rejected/not be rejected).

Answer: be rejected Difficulty: Easy Keywords: pooled variance, t test, decision

10-10 .

46) Referring to Table 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 Difficulty: Moderate Keywords: pooled variance, t test, p-value 47) Referring to Table 10-4, what is the 99% confidence interval estimate for the difference in the two means?

Answer: -0.1822 to 5.1822 Difficulty: Moderate Keywords: confidence interval, difference between two means 48) Referring to Table 10-4, what is the 95% confidence interval estimate for the difference in the two means?

Answer: 0.4894 to 4.5106 Difficulty: Moderate Keywords: confidence interval, difference between two means 49) Referring to Table 10-4, what is the 90% confidence interval estimate for the difference in the two means?

Answer: 0.8228 to 4.1772 Difficulty: Moderate Keywords: confidence interval, difference between two means 50) The t test for the mean difference between two 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 Difficulty: Moderate Keywords: t test, mean difference, assumption 51) If we are testing for the difference between the means of two 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 Difficulty: Easy Keywords: t test, mean difference, degrees of freedom

10-11 .

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 two independent populations B) a test for the difference between the means of two related populations C) a test for the difference between the means of two independent populations D) all of the above Answer: B Difficulty: Moderate Keywords: t test, mean difference 53) In testing for differences between the means of two 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 Difficulty: Easy Keywords: t test, mean difference, degrees of freedom 54) In testing for differences between the means of two related populations, the null hypothesis is A) H0: μD = 2.

B) H0: μD = 0.

C) H0: μD < 2.

D) H0: μD > 2.

Answer: B Difficulty: Easy Keywords: t test, mean difference, form of hypothesis 55) In testing for the differences between the means of two related populations, the ________ hypothesis is the hypothesis of "no differences."

Answer: null or H0 Difficulty: Easy Keywords: 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 Difficulty: Easy Keywords: t test, mean difference, assumption 57) True or False: When testing for differences between the means of two related populations, you can use either a one-tail or two-tail test.

Answer: TRUE Difficulty: Easy Keywords: t test, mean difference, rejection region

10-12 .

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 of sleep and one after eight hours of sleep. The test the researcher should use would be a related samples test.

Answer: TRUE Difficulty: Easy Keywords: 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 Difficulty: Easy Keywords: 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 Difficulty: Moderate Keywords: t test, mean difference, degrees of freedom 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 Difficulty: Moderate Keywords: t test, mean difference, degrees of freedom TABLE 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.

Student 1 2 3 4 5 6 7 8

Exam Score Before Course (1) 530 690 910 700 450 820 820 630

Exam Score After Course (2) 670 770 1,000 710 550 870 770 610

62) Referring to Table 10-5, the number of degrees of freedom is A) 14.

B) 13.

C) 8.

D) 7.

Answer: D Difficulty: Easy Keywords: t test, mean difference, degrees of freedom 10-13 .

63) Referring to Table 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 Difficulty: Easy Keywords: t test, mean difference, test statistic 64) Referring to Table 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 Difficulty: Easy Keywords: t test, mean difference, standard error 65) Referring to Table 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 Difficulty: Easy Keywords: t test, mean difference, critical value 66) Referring to Table 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 Difficulty: Easy Keywords: t test, mean difference, decision 67) Referring to Table 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 Difficulty: Easy Keywords: t test, mean difference, conclusion 10-14 .

68) True or False: Referring to Table 10-5, you must assume that the population of difference scores is normally distributed.

Answer: TRUE Difficulty: Easy Keywords: t test, mean difference, assumption 69) Referring to Table 10-5, the calculated value of the test statistic is ________.

Answer: 2.175 Difficulty: Easy Keywords: t test, mean difference, test statistic 70) Referring to Table 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) Explanation: p-value obtained from Excel Difficulty: Moderate Keywords: t test, mean difference, p-value 71) True or False: Referring to Table 10-5, in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."

Answer: TRUE Difficulty: Easy Keywords: t test, mean difference, sampling distribution TABLE 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 four 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 Table 10-6, the t test should be ________-tail.

Answer: one Difficulty: Easy Keywords: t test, mean difference, rejection region 73) Referring to Table 10-6, the computed t statistic is ________.

Answer: 2.00 Difficulty: Easy Keywords: t test, mean difference, test statistic 74) Referring to Table 10-6, there are ________ degrees of freedom for this test.

Answer: 15 Difficulty: Easy Keywords: t test, mean difference, degrees of freedom

10-15 .

75) Referring to Table 10-6, the critical value for a one-tail test of the null hypothesis of no difference at the α = 0.05 level of significance is ________.

Answer: 1.7531 Difficulty: Easy Keywords: t test, mean difference, critical value 76) Referring to Table 10-6, a one-tail test of the null hypothesis of no difference would ________ (be rejected/not be rejected) at the α = 0.05 level of significance.

Answer: be rejected Difficulty: Easy Keywords: t test, mean difference, decision 77) Referring to Table 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 Difficulty: Moderate Keywords: t test, mean difference, p-value 78) Referring to Table 10-6, if we were interested in testing against the two-tail alternative that μ is not equal to zero at the α = 0.05 level of significance, the null hypothesis would ________ (be rejected/not be rejected).

Answer: not be rejected Difficulty: Easy Keywords: t test, mean difference, decision 79) Referring to Table 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 Difficulty: Moderate Keywords: t test, mean difference, p-value 80) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, mean difference 81) Referring to Table 10-6, what is the 99% confidence interval estimate for the mean difference in weight before and after the diet?

Answer: -1.42 to 7.42 Difficulty: Moderate Keywords: confidence interval, mean difference 82) Referring to Table 10-6, what is the 90% confidence interval estimate for the mean difference in weight before and after the diet?

Answer: 0.37 to 5.63 Difficulty: Moderate Keywords: confidence interval, mean difference

10-16 .

TABLE 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 Material Supplier 1 $55 2 $48 3 $31 4 $83 5 $37 6 $55 Sum: $309 Sum of Squares: $17,573

Secondary Supplier $45 $47 $32 $77 $37 $54 $292 $15,472

Difference $10 $1 -$1 $6 $0 $1 $17 $139

83) Referring to Table 10-7, the hypotheses that the buyer should test are a null hypothesis that ________ versus an alternative hypothesis that ________.

Answer: H0: μD ≤ 0, H1: μD > 0 Difficulty: Moderate Keywords: t test, mean difference, form of hypothesis 84) Referring to Table 10-7, the test to perform is a A) pooled-variance t test for differences between two means.

B) one-way ANOVA F test for differences among more than two means.

C) Z test for the difference between two proportions.

D) paired t test for the mean difference.

Answer: D Difficulty: Easy Keywords: t test, mean difference 85) Referring to Table 10-7, the decision rule is to reject the null hypothesis if ________.

Answer: t > 3.3649 Difficulty: Easy Keywords: t test, mean difference, decision 86) Referring to Table 10-7, the calculated value of the test statistic is ________.

Answer: 1.628 Difficulty: Easy Keywords: t test, mean difference, test statistic 87) Referring to Table 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 Difficulty: Moderate Keywords: t test, mean difference, p-value 10-17 .

88) True or False: Referring to Table 10-7, the null hypothesis should be rejected.

Answer: FALSE Difficulty: Easy Keywords: t test, mean difference, decision 89) Referring to Table 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 Difficulty: Moderate Keywords: t test, mean difference, conclusion 90) Referring to Table 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 Difficulty: Moderate Keywords: t test, mean difference, p-value 91) Referring to Table 10-7, what is the 99% confidence interval estimate for the mean difference in prices?

Answer: -$4.18 to $9.85 Difficulty: Moderate Keywords: confidence interval, mean difference 92) Referring to Table 10-7, what is the 95% confidence interval estimate for the mean difference in prices?

Answer: -$1.64 to $7.31 Difficulty: Moderate Keywords: confidence interval, mean difference 93) Referring to Table 10-7, what is the 90% confidence interval estimate for the mean difference in prices?

Answer: -$0.67 to $6.34 Difficulty: Moderate Keywords: confidence interval, mean difference 94) When testing H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 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 Difficulty: Easy Keywords: Z test, difference between two proportions, p-value

10-18 .

95) When testing H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, p-value 96) When testing H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 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 Difficulty: Easy Keywords: Z test, difference between two proportions, p-value 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-theMove, each decide to estimate this figure by sampling their records, and they report the data shown in the following table.

Total shipments sampled Number of shipments with a claim ≥ $50

Econo-Move 900 162

On-the-Move 750 60

The owner of On-the-Move is hoping to use these data to show that the company is superior to EconoMove with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment?

A) pooled-variance t test for the difference between two means B) test for the difference between two variances C) one-way ANOVA F test for differences among more than two means D) Z test for the difference between two proportions Answer: D Difficulty: Moderate Keywords: Z test, difference between two proportions

10-19 .

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: πW - πM ≥ 0 versus H1: πW - πM < 0 B) H0: πW - πM ≤ 0 versus H1: πW - πM > 0 C) H0: πW - πM = 0 versus H1: πW - πM ≠ 0 D) H0: πW - πM ≠ 0 versus H1: πW - πM = 0 Answer: B Difficulty: Easy Keywords: Z test, difference between two proportions, form of hypothesis 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?" 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 Difficulty: Moderate Keywords: Z test, difference between two 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?" 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, test statistic

10-20 .

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?" 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 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?" 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 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?" 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 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?" 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, decision, conclusion

10-21 .

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: πM - πW ≤ 0 versus H1: πM - πW > 0 B) H0: πM - πW ≥ 0 versus H1: πM - πW < 0 C) H0: πM - πW = 0 versus H1: πM - πW ≠ 0 D) H0: πM - πW ≠ 0 versus H1: πM - πW = 0 Answer: C Difficulty: Moderate Keywords: Z test, difference between two 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 Difficulty: Moderate Keywords: Z test, difference between two 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 α = 0.05, you should fail to reject H0.

B) at α = 0.04, you should reject H0.

C) at α = 0.03, you should reject H0.

D) None of the above would be correct statements.

Answer: B Difficulty: Moderate Keywords: Z test, difference between two proportions, decision, conclusion 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 10-22 .

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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 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 difference between two 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 Difficulty: Easy Keywords: Z test for the difference between two proportions 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 Difficulty: Easy Keywords: Z test, difference between two 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 Difficulty: Moderate Keywords: Z test, difference between two 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, p-value 10-23 .

TABLE 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 Table 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: μM - μF ≠ 0 B) H1: μM - μF > 0 C) H1: πM - πF ≠ 0 D) H1: πM - πF = 0 Answer: C Difficulty: Easy Keywords: Z test, difference between two proportions, form of hypothesis 116) Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, p-value 117) Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, p-value

10-24 .

118) Referring to Table 10-8, suppose that the two-tail p-value was really 0.0734. State the proper conclusion.

A) At α = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.

B) At α = 0.10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.

C) At α = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi.

D) At α = 0.08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.

Answer: B Difficulty: Moderate Keywords: Z test, difference between two proportions, decision, conclusion 119) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 120) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 121) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions

10-25 .

TABLE 10-9 The following Microsoft® Excel output contains the results of a test to determine whether the proportions of satisfied customers at two resorts are the same or different.

122) Referring to Table 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 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 Difficulty: Easy Keywords: Z test, difference between two proportions, decision, conclusion 123) Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, p-value 10-26 .

124) Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions 125) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 126) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 127) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions TABLE 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 π1 and π2 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 Table 10-10, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

A) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0 B) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0 C) H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0 D) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0 Answer: A Difficulty: Easy Keywords: Z test, difference between two proportions, form of hypothesis

10-27 .

129) Referring to Table 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: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0 B) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0 C) H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0 D) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0 Answer: C Difficulty: Easy Keywords: Z test, difference between two proportions, form of hypothesis 130) Referring to Table 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 Difficulty: Easy Keywords: point estimate 131) Referring to Table 10-10, what is/are the critical value(s) when performing a Z test on whether population proportions are different if α = 0.05?

A) ±1.645 B) ±1.96 C) -1.96 D) ±2.08 Answer: B Difficulty: Easy Keywords: Z test, difference between two proportions, critical value 132) Referring to Table 10-10, what is/are the critical value(s) when testing whether population proportions are different if α = 0.10?

A) ±1.645 B) ±1.96 C) -1.96 D) ±2.08 Answer: A Difficulty: Easy Keywords: Z test, difference between two proportions, critical value

10-28 .

133) Referring to Table 10-10, what is/are the critical value(s) when testing whether the current population proportion is higher than before if α = 0.05?

A) ±1.645 B) +1.645 C) ±1.96 D) +1.96 Answer: B Difficulty: Easy Keywords: Z test for the difference between two proportions, critical value 134) Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, standard error 135) Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, test statistic 136) Referring to Table 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 selfimprovement 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 selfimprovement 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, decision, conclusion

10-29 .

137) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 138) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 139) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions TABLE 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 Table 10-11, the hypotheses the dean should use are: A) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0.

B) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0.

C) H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0.

D) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0.

Answer: A Difficulty: Easy Keywords: Z test, difference between two proportions, form of hypothesis 141) Referring to Table 10-11, the null hypothesis will be rejected if the test statistic is ________.

Answer: Z > 1.96 or < -1.96 Difficulty: Easy Keywords: Z test, difference between two proportions, critical value 142) Referring to Table 10-11, the value of the test statistic is ________.

Answer: Z = 1.866 Difficulty: Moderate Keywords: Z test, difference between two proportions, test statistic

10-30 .

143) Referring to Table 10-11, the p-value of the test is ________.

Answer: 0.0621 Difficulty: Moderate Keywords: Z test, difference between two proportions, p-value 144) True or False: Referring to Table 10-11, the null hypothesis should be rejected.

Answer: FALSE Difficulty: Easy Keywords: Z test, difference between two proportions, decision 145) True or False: Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, decision 146) True or False: Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, decision 147) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 148) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 149) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, difference between two proportions

10-31 .

TABLE 10-12 A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. 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 disks 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 Table 10-12, the hypotheses that should be tested are: A) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0.

B) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0.

C) H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0.

D) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0.

Answer: C Difficulty: Easy Keywords: Z test, difference between two proportions, form of hypothesis 151) Referring to Table 10-12, the null hypothesis will be rejected if the test statistic is ________.

Answer: Z > 2.33 Difficulty: Easy Keywords: Z test, difference between two proportions, critical value 152) Referring to Table 10-12, the value of the test statistic is ________.

Answer: 2.49 Difficulty: Moderate Keywords: Z test, difference between two proportions, test statistic 153) Referring to Table 10-12, the p-value of the test is ________.

Answer: 0.0064 Difficulty: Moderate Keywords: Z test, difference between two proportions, p-value 154) True or False: Referring to Table 10-12, the null hypothesis should be rejected.

Answer: TRUE Difficulty: Moderate Keywords: Z test, difference between two proportions, decision 155) True or False: Referring to Table 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 Difficulty: Moderate Keywords: Z test, difference between two proportions, decision 156) True or False: Referring to Table 10-12, the same decision would be made if this had been a twotail test at a level of significance of 0.01.

Answer: FALSE Difficulty: Moderate Keywords: Z test, difference between two proportions, decision

10-32 .

157) Referring to Table 10-12, construct a 90% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

Answer: 0.03 to 0.15 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 158) Referring to Table 10-12, construct a 95% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

Answer: 0.02 to 0.16 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 159) Referring to Table 10-12, construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.

Answer: -0.01 to 0.19 Difficulty: Moderate Keywords: confidence interval, difference between two proportions 160) When testing for the difference between two 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 Difficulty: Easy Keywords: F test, difference between two 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 Difficulty: Easy Keywords: F test, difference between two variances, degrees of freedom 162) The test for the equality of two population variances is based on A) the difference between the two sample variances.

B) the ratio of the two sample variances.

C) the difference between the two population variances.

D) the difference between the sample variances divided by the difference between the sample means.

Answer: B Difficulty: Easy Keywords: F test, difference between two variances

10-33 .

163) True or False: The F test used for testing the difference in two population variances is always a one-tail test.

Answer: FALSE Difficulty: Easy Keywords: F test, difference between two variances, rejection region 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 Difficulty: Easy Keywords: F test, difference between two variances, assumption 165) True or False: The F distribution is symmetric.

Answer: FALSE Difficulty: Easy Keywords: F distribution, properties 166) True or False: The F distribution can only have positive values.

Answer: TRUE Difficulty: Easy Keywords: F distribution, properties 167) True or False: F tests are one-tail tests.

Answer: FALSE Difficulty: Easy Keywords: F distribution, properties

10-34 .

TABLE 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Microsoft® 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.

168) Referring to Table 10-13, which of the following represents the relevant hypotheses to test whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels?

A) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0 B) H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0 C) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0 D) H0: π1 - π2 ≠ 0 versus H1: πI - π2 = 0 Answer: C Difficulty: Easy Keywords: pooled-variance, t test, form of hypothesis 169) Referring to Table 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 ≤ μ1 - μ2 ≤ 1.3593 Difficulty: Moderate Keywords: confidence interval, difference between two means 170) Referring to Table 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) H0: σ12 - σ22 ≥ 0 versus H1: σ12 - σ22 < 0 B) H0: σ12 - σ22 ≤ 0 versus H1: σ12 - σ22 > 0 C) H0: σ12 - σ22 = 0 versus H1: σ12 - σ22 ≠ 0 D) H0: σ12 - σ22 ≠ 0 versus H1: σ12 - σ22 = 0 Answer: C Difficulty: Moderate Keywords: F test, difference between two variances, form of hypothesis

10-35 .

171) Referring to Table 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 Difficulty: Easy Keywords: F test, difference between two variances, test statistic 172) Referring to Table 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 Difficulty: Easy Keywords: F test, difference between two variances, assumption 173) Referring to Table 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) Difficulty: Easy Keywords: F test, difference between two variances, critical value 174) Referring to Table 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) Difficulty: Difficult Keywords: F test, difference between two variances, p-value 175) Referring to Table 10-13, suppose α = 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 make a decision.

Answer: C Difficulty: Easy Keywords: F test, difference between two variances, decision

10-36 .

176) Referring to Table 10-13, suppose α = 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 Difficulty: Easy Keywords: F test, difference between two variances, conclusion TABLE 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 I = 106.4 hours SI = 10.3 hours

Preservative II II = 96.54 hours SII = 13.4 hours

177) Referring to Table 10-14, state the null and alternative hypotheses for testing if the population variances differ for preservatives I and II. A) H0: σI2 - σII2 ≥ 0 versus H1: σI2 - σII2 < 0 B) H0: σI2 - σII2 ≤ 0 versus H1: σI2 - σII2 > 0 C) H0: σI2 - σII2 = 0 versus H1: σI2 - σII2 ≠ 0 D) H0: σI2 - σII2 ≠ 0 versus H1: σI2 - σII2 = 0 Answer: C Difficulty: Moderate Keywords: F test, difference between two variances, form of hypothesis 178) Referring to Table 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 Difficulty: Easy Keywords: F test, difference between two variances, test statistic

10-37 .

179) Referring to Table 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 Difficulty: Easy Keywords: F test, difference between two variances, assumption 180) Referring to Table 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) Difficulty: Easy Keywords: F test, difference between two variances, critical value 181) Referring to Table 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) Difficulty: Moderate Keywords: F test, difference between two variances, p-value 182) Referring to Table 10-14, suppose α = 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 make a decision.

Answer: C Difficulty: Easy Keywords: F test, difference between two variances, decision 183) Referring to Table 10-14, suppose α = 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 Difficulty: Easy Keywords: F test, difference between two variances, conclusion

10-38 .

TABLE 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 1 (public accounting): Sample 2 (financial planning):

1 = 60.35, S1 = 3.25, n1 = 12 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.

184) Referring to Table 10-15, which of the following represents the relevant hypotheses tested?

A) H0: μ1 - μ2 ≥ 0 versus H1: μ1 - μ2 < 0 B) H0: μ1 - μ2 ≤ 0 versus H1: μ1 - μ2 > 0 C) H0: μ1 - μ2 = 0 versus H1: μ1 - μ2 ≠ 0 D) H0: μ1 - μ2 ≠ 0 versus H1: μ1 - μ2 = 0 Answer: B Difficulty: Easy Keywords: pooled variance, t test, form of hypothesis 185) Referring to Table 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 Difficulty: Easy Keywords: pooled variance, t test, critical value 186) Referring to Table 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 Difficulty: Moderate Keywords: pooled variance, t test, critical value 187) Referring to Table 10-15, what is the value of the test statistic?

Answer: 1.9117 Difficulty: Easy Keywords: pooled variance, t test, test statistic 188) Referring to Table 10-15, what is the smallest level of significance at which the null hypothesis will still not be rejected?

Answer: 0.0340 Difficulty: Moderate Keywords: pooled variance, t test, p-value

10-39 .

189) Referring to Table 10-15, suppose α = 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 make a decision.

Answer: B Difficulty: Easy Keywords: pooled variance, t test, decision 190) Referring to Table 10-15, suppose α = 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 make a decision.

Answer: C Difficulty: Easy Keywords: pooled variance, t test, decision 191) Referring to Table 10-15, suppose α = 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 Difficulty: Easy Keywords: pooled variance, t test, conclusion 192) Referring to Table 10-15, suppose α = 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: D Difficulty: Easy Keywords: pooled variance, t test, conclusion

10-40 .

193) Referring to Table 10-15, what is the 95% confidence interval estimate for the difference in the two means?

Answer: -0.1711 ≤ μ1 - μ2 ≤ 4.4711 Difficulty: Moderate Keywords: confidence interval, difference between two means 194) Referring to Table 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 Difficulty: Easy Keywords: pooled variance, t test, assumption 195) Referring to Table 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) H0: σ12 - σ22 ≥ 0 versus H1: σ12 - σ22 < 0 B) H0: σ12 - σ22 ≤ 0 versus H1: σ12 - σ22 > 0 C) H0: σ12 - σ22 = 0 versus H1: σ12 - σ22 ≠ 0 D) H0: σ12 - σ22 ≠ 0 versus H1: σ12 - σ22 = 0 Answer: C Difficulty: Moderate Keywords: F test, difference between two variances, form of hypothesis 196) Referring to Table 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 Difficulty: Easy Keywords: F test, difference between two variances, test statistic 197) Referring to Table 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 Difficulty: Easy Keywords: F test, difference between two variances, assumption 198) Referring to Table 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) or between 3.15 and 3.25 (using Table E.5 with 10 or 12 and 13 degrees of freedom) Difficulty: Easy Keywords: F test, difference between two variances, critical value

10-41 .

199) Referring to Table 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) Difficulty: Difficult Keywords: F test, difference between two variances, p-value 200) Referring to Table 10-15, suppose α = 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 make a decision.

Answer: C Difficulty: Easy Keywords: F test, difference between two variances, decision 201) Referring to Table 10-15, suppose α = 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 Difficulty: Easy Keywords: F test, difference between two variances, conclusion 202) 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 that not all the means are 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 Difficulty: Easy Keywords: one-way analysis of variance, decision 203) 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 Difficulty: Easy Keywords: one-way analysis of variance, sum of squares, properties

10-42 .

204) 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 Difficulty: Easy Keywords: Tukey-Kramer procedure 205) 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 Difficulty: Moderate Keywords: completely randomized design 206) The F test statistic in a one-way ANOVA is A) MSW/MSA. B) SSW/SSA. C) MSA/MSW. D) SSA/SSW. Answer: C Difficulty: Easy Keywords: one-way analysis of variance, F test for factor 207) 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 Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, degrees of freedom 208) 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 Difficulty: Easy Keywords: one-way analysis of variance, form of hypothesis

10-43 .

209) 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 Difficulty: Moderate Keywords: one-way analysis of variance, properties, interaction 210) 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) F test for differences in variances B) one-way ANOVA F test C) t test for the differences in means D) t test for the mean difference Answer: B Difficulty: Easy Keywords: one-way analysis of variance, F test for factor 211) True or False: The analysis of variance (ANOVA) tests hypotheses about the population variance.

Answer: FALSE Difficulty: Easy Keywords: one-way analysis of variance 212) True or False: When the F test is used for ANOVA, the rejection region is always in the right tail.

Answer: TRUE Difficulty: Easy Keywords: F test for factor, rejection region 213) True or False: If you are comparing the mean sales among three different brands you are dealing with a three-way ANOVA design.

Answer: FALSE Difficulty: Easy Keywords: one-way analysis of variance, properties 214) True or False: The MSE must always be positive.

Answer: TRUE Difficulty: Easy Keywords: mean squares, properties

10-44 .

215) 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 Difficulty: Easy Keywords: one-way analysis of variance, sum of squares, properties TABLE 10-16 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 Microsoft® Excel output:

216) Referring to Table 10-16, the within groups degrees of freedom is A) 3.

B) 4.

C) 16.

D) 19.

Answer: C Difficulty: Easy Keywords: one-way analysis of variance, degrees of freedom 217) Referring to Table 10-16, the total degrees of freedom is A) 3.

B) 4.

C) 16.

D) 19.

Answer: D Difficulty: Easy Keywords: one-way analysis of variance, degrees of freedom 218) Referring to Table 10-16, the among-group (between-group) mean squares is ________.

A) 8.525 B) 70.8 C) 212.4 D) 637.2 Answer: B Difficulty: Easy Keywords: one-way analysis of variance, mean squares

10-45 .

219) Referring to Table 10-16, at a significance level of 1%, A) there is insufficient evidence to conclude that the mean number of customers bumped by the four packages are not all the same.

B) there is insufficient evidence to conclude that the mean number of customers bumped by the four packages are all the same.

C) there is sufficient evidence to conclude that the mean number of customers bumped by the four packages are not all the same.

D) there is sufficient evidence to conclude that the mean number of customers bumped by the four packages are all the same.

Answer: C Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, decision, conclusion TABLE 10-17 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:

220) Referring to Table 10-17, the among group degrees of freedom is A) 3.

B) 4.

C) 12.

D) 16.

Answer: A Difficulty: Easy Keywords: one-way analysis of variance, degrees of freedom 221) Referring to Table 10-17, the within group sum of squares is ________.

A) 1.0606 B) 1.1825 C) 3.1819 D) 4.3644 Answer: B Difficulty: Easy Keywords: one-way analysis of variance, sum of squares

10-46 .

222) Referring to Table 10-17, the within group mean squares is ________.

A) 0.0985 B) 0.2910 C) 1.0606 D) 1.1825 Answer: A Difficulty: Easy Keywords: one-way analysis of variance, mean squares 223) Referring to Table 10-17, A) at the 0.05 level of significance, the mean ratios for the four neighborhoods are not all the same.

B) at the 0.01 level of significance, the mean ratios for the four neighborhoods are all the same.

C) at the 0.10 level of significance, the mean ratios for the four neighborhoods are not significantly different.

D) at the 0.05 level of significance, the mean ratios for the four neighborhoods are not significantly different from 0.

Answer: A Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, decision, conclusion 224) Referring to Table 10-17, the null hypothesis for Levene's test for homogeneity of variances is A) H0: μA = μB = μC = μD. B) H0: MA = MB = MC = MD. C) H0: σA2 = σB2 = σC2 = σD2.

D) H0: πA = πB = πC = πD. Answer: C Difficulty: Easy Keywords: Levene's test, form of hypothesis 225) Referring to Table 10-17, 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 Explanation: A) This question will be easier for students if Excel or Minitab is available.

Difficulty: Difficult Keywords: Levene's test, test statistic 226) Referring to Table 10-17, 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 Difficulty: Moderate Keywords: Levene's test, degrees of freedom 10-47 .

227) Referring to Table 10-17, 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 Difficulty: Moderate Keywords: Levene's test, critical value 228) Referring to Table 10-17, 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 Explanation: C) This question requires PHStat/Excel.Minitab Difficulty: Difficult Keywords: Levene's test, p-value 229) Referring to Table 10-17, 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 Difficulty: Moderate Keywords: Levene's test, decision 230) Referring to Table 10-17, 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 Difficulty: Easy Keywords: Levene's test, conclusion

10-48 .

TABLE 10-18 As part of an evaluation program, a sporting goods retailer wanted to compare the downhill coasting speeds of four brands of bicycles. She took three of each brand and determined their maximum downhill speeds. The results are presented in miles per hour in the table below.

Trial 1 2 3

Barth 43 46 43

Tornado 37 38 39

Reiser 41 45 42

Shaw 43 45 46

231) Referring to Table 10-18, the sporting goods retailer decided to perform an ANOVA F test. The amount of total variation or SST is ________.

Answer: 102.67 Difficulty: Moderate Keywords: one-way analysis of variance, sum of squares, interpretation 232) Referring to Table 10-18, the among group variation or SSA is ________.

Answer: 81.33 Difficulty: Moderate Keywords: one-way analysis of variance, sum of squares 233) Referring to Table 10-18, the within group variation or SSW is ________.

Answer: 21.33 Difficulty: Moderate Keywords: one-way analysis of variance, sum of squares 234) Referring to Table 10-18, the value of MSA is ________, while MSW is ________.

Answer: 27.11; 2.67 Difficulty: Moderate Keywords: one-way analysis of variance, mean squares 235) Referring to Table 10-18, the null hypothesis that the mean downhill coasting speeds of the four 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 Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, decision 236) Referring to Table 10-18, in testing the null hypothesis that the mean downhill coasting speeds of the four brands of bicycles are equal, the value of the test statistic is ________.

Answer: 10.17 Difficulty: Moderate Keywords: one-way analysis of variance, F test for factor, test statistic

10-49 .

237) Referring to Table 10-18, construct the ANOVA table from the sample data.

Answer:

Difficulty: Moderate Keywords: one-way analysis of variance, properties 238) True or False: Referring to Table 10-18, the null hypothesis should be rejected at a 5% level of significance.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, decision 239) True or False: Referring to Table 10-18, the decision made implies that all four means are significantly different.

Answer: FALSE Difficulty: Moderate Keywords: one-way analysis of variance, conclusion, interpretation 240) True or False: Referring to Table 10-18, the test is valid only if the population of speeds has the same variance for the four brands.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, assumption 241) True or False: Referring to Table 10-18, the test is less sensitive to the assumption that the population of speeds has the same variance for the four brands because the sample sizes of the four brands are equal.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, assumption 242) True or False: Referring to Table 10-18, the test is valid only if the population of speeds is normally distributed.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, assumption 243) True or False: Referring to Table 10-18, the test is robust to the violation of the assumption that the population of speeds is normally distributed.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, assumption

10-50 .

244) Referring to Table 10-18, the sporting goods retailer decided to compare the four 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure 245) Referring to Table 10-18, 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, critical value 246) Referring to Table 10-18, using an overall level of significance of 0.05, the critical range for the Tukey-Kramer procedure is ________.

Answer: 4.27 Difficulty: Easy Keywords: one-way analysis of variance,, Tukey-Kramer procedure, critical value 247) True or False: Referring to Table 10-18, 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 248) True or False: Referring to Table 10-18, 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 249) True or False: Referring to Table 10-18, 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 250) True or False: Referring to Table 10-18, based on the Tukey-Kramer procedure with an overall level of significance of 0.05, the retailer would decide that the three means other than the mean for Tornado are not significantly different from each other.

Answer: TRUE Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion

10-51 .

251) Referring to Table 10-18, the null hypothesis for Levene's test for homogeneity of variances is A) H0: μA = μB = μC = μD. B) H0: MA = MB = MC = MD. C) H0: σA2 = σB2 = σC2 = σD2.

D) H0: πA = πB = πC = πD. Answer: C Difficulty: Easy Keywords: Levene's test, form of hypothesis 252) Referring to Table 10-18, what is the value of the test statistic for Levene's test for homogeneity of variances?

Answer: 0.1333 Explanation: NOTE: This question will be easier for students if Excel is available.

Difficulty: Difficult Keywords: Levene's test, test statistic 253) Referring to Table 10-18, what are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

Answer: 3, 8 Difficulty: Moderate Keywords: Levene's test, degrees of freedom 254) Referring to Table 10-18, what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

Answer: 4.07 Difficulty: Moderate Keywords: Levene's test, critical value 255) Referring to Table 10-18, what is the p-value of the test statistic for Levene's test for homogeneity of variances?

Answer: 0.94 Explanation: The answer is obtained with the help of PHStat/Excel/Minitab.

Difficulty: Moderate Keywords: Levene's test, p-value 256) Referring to Table 10-18, 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 Difficulty: Easy Keywords: Levene's test, decision

10-52 .

257) Referring to Table 10-18, 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 Difficulty: Easy Keywords: Levene's test, conclusion TABLE 10-19 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 1 2 3 4 5

Smith 11.1 13.5 15.3 14.6 9.8

Walsh 19.0 18.0 19.8 19.6 16.6

Trevor 14.6 15.7 16.8 16.7 15.2

258) Referring to Table 10-19, the agronomist decided to perform an ANOVA F test. The amount of total variation or SST is ________.

Answer: 114.82 Difficulty: Moderate Keywords: one-way analysis of variance, sum of squares 259) Referring to Table 10-19, the among-group variation or SSA is ________.

Answer: 82.39 Difficulty: Moderate Keywords: one-way analysis of variance, sum of squares 260) Referring to Table 10-19, the within-group variation or SSW is ________.

Answer: 32.43 Difficulty: Moderate Keywords: one-way analysis of variance, sum of squares 261) Referring to Table 10-19, the value of MSA is ________, while MSW is ________.

Answer: 41.19; 2.70 Difficulty: Moderate Keywords: one-way analysis of variance, mean squares 262) Referring to Table 10-19, 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 Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, critical value

10-53 .

263) Referring to Table 10-19, the value of the test statistic is ________.

Answer: 15.24 Difficulty: Moderate Keywords: one-way analysis of variance, F test for factor, test statistic 264) Referring to Table 10-19, construct the ANOVA table from the sample data.

Answer:

Difficulty: Moderate Keywords: one-way analysis of variance, F test for factor, properties 265) Referring to Table 10-19, state the null hypothesis that can be tested.

Answer: H0: μSmith =μWalsh = μTrevor Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, form of hypothesis 266) True or False: Referring to Table 10-19, the null hypothesis should be rejected at 0.005 level of significance.

Answer: TRUE Difficulty: Moderate Keywords: one-way analysis of variance, F test for factor, decision 267) True or False: Referring to Table 10-19, the decision made at 0.005 level of significance implies that all three means are significantly different.

Answer: FALSE Difficulty: Moderate Keywords: one-way analysis of variance, F test for factor, conclusion 268) True or False: Referring to Table 10-19, the test is valid only if the population of crop yields has the same variance for the three varieties.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, assumption 269) True or False: Referring to Table 10-19, the test is valid only if the population of crop yields is normally distributed for the three varieties.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, assumption

10-54 .

270) Referring to Table 10-19, the agronomist decided to compare the three 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, properties 271) Referring to Table 10-19, 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 Difficulty: Easy Keywords: one-way analysis of variance, Tukey-Kramer procedure, critical value 272) Referring to Table 10-19, using an overall level of significance of 0.01, the critical range for the Tukey-Kramer procedure is ________.

Answer: 3.70 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, critical value 273) True or False: Referring to Table 10-19, 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 274) True or False: Referring to Table 10-19, 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion 275) True or False: Referring to Table 10-19, 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 Difficulty: Moderate Keywords: one-way analysis of variance, Tukey-Kramer procedure, decision, conclusion

10-55 .

TABLE 10-20 A hotel chain has identically sized resorts in five locations. The data that follow resulted from analyzing the hotel occupancies on randomly selected days in the five locations.

ROW 1 2 3

Caymen 28 33 41

Pennkamp 40 35 33

California 21 21 27

Mayaguez 37 47 45

Maui 22 19 25

276) Referring to Table 10-20, if a level of significance of 0.05 is chosen, the null hypothesis should be rejected.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, decision 277) True or False: Referring to Table 10-20, if a level of significance of 0.05 is chosen, the decision made indicates that all 5five locations have different mean occupancy rates.

Answer: FALSE Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, conclusion 278) True or False: Referring to Table 10-20, if a level of significance of 0.05 is chosen, the decision made indicates that at least two of the five locations have different mean occupancy rates.

Answer: TRUE Difficulty: Easy Keywords: one-way analysis of variance, F test for factor, conclusion 279) Referring to Table 10-20, the among-group variation or SSA is ________.

Answer: 963.6 Difficulty: Easy Keywords: one-way analysis of variance, sum of squares 280) Referring to Table 10-20, the within-group variation or SSW is ________.

Answer: 210.0 Difficulty: Easy Keywords: one-way analysis of variance, sum of squares 281) Referring to Table 10-20, the total variation or SST is ________.

Answer: 1,173.6 Difficulty: Easy Keywords: one-way analysis of variance, sum of squares

10-56 .

282) Referring to Table 10-20, the value of MSA is ________ while MSW is ________.

Answer: 240.9; 21.0 Difficulty: Easy Keywords: one-way analysis of variance, mean squares 283) Referring to Table 10-20, the numerator and denominator degrees of freedom of the test ratio are ________ and ________, respectively.

Answer: 4 and 10 Difficulty: Easy Keywords: one-way analysis of variance, degrees of freedom 284) True or False: Referring to Table 10-20, the total mean squares is 261.90.

Answer: FALSE Difficulty: Easy Keywords: one-way analysis of variance, sum of squares 285) Referring to Table 10-20, the null hypothesis for Levene's test for homogeneity of variances is A) H0: μA = μB = μC = μD. B) H0: MA = MB = MC = MD. C) H0: σA2 = σB2 = σC2 = σD2.

D) H0: πA = πB = πC = πD. Answer: C Difficulty: Easy Keywords: Levene's test, form of hypothesis 286) Referring to Table 10-20, what is the value of the test statistic for Levene's test for homogeneity of variances?

Answer: 0.28 Explanation: This question will be easier for students if Excel or PHStat or Minitab is available.

Difficulty: Difficult Keywords: Levene's test, test statistic 287) Referring to Table 10-20, what are the numerator and denominator degrees of freedom for Levene's test for homogeneity of variances respectively?

Answer: 4, 10 Difficulty: Moderate Keywords: Levene's test, degrees of freedom 288) Referring to Table 10-20, what is the critical value of Levene's test for homogeneity of variances at a 5% level of significance?

Answer: 3.48 Difficulty: Moderate Keywords: Levene's test, critical value

10-57 .

289) Referring to Table 10-20, what is the p-value of the test statistic for Levene's test for homogeneity of variances?

Answer: 0.88 Explanation: The answer is obtained with the help of PHStat/Excel/Minitab.

Difficulty: Moderate Keywords: Levene's test, p-value 290) Referring to Table 10-20, 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 Difficulty: Easy Keywords: Levene's test, decision 291) Referring to Table 10-20, 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 Difficulty: Easy Keywords: Levene's test, conclusion 292) True or False: The F test in a completely randomized model is just an expansion of the t test for independent samples.

Answer: TRUE Difficulty: Easy Keywords: completely randomized design, F test for factor 293) True or False: A completely randomized design with four groups would have six possible pairwise comparisons.

Answer: TRUE Difficulty: Moderate Keywords: completely randomized design, properties

10-58 .

Business Statistics: A First Course, 6e (Levine) Chapter 11 Chi-Square Tests 1) If we use the χ2 analysis to test for the differences among 4 proportions, the degrees of freedom are equal to ________.

A) 3 B) 4 C) 5 D) 1 Answer: A 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.

B) the χ2 test.

C) both A and B D) neither A nor B. Answer: C Difficulty: Easy Keywords: Chi-square test for difference in proportions 3) In testing a hypothesis using the χ2 test, the theoretical frequencies are based on the A) null hypothesis.

B) alternative hypothesis.

C) normal distribution.

D) none of the above Answer: A Difficulty: Easy Keywords: Chi-square test for difference in proportions, Chi-square test of independence, properties TABLE 11-1 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 π1 and π2 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 Table 11-1, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

A) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0 B) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0 C) H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0 D) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0 Answer: A Difficulty: Easy Keywords: Chi-square test for difference in two proportions 11-1 .

5) Referring to Table 11-1, what is the critical value when performing a chi-square test on whether the population proportions are different if α = 0.05?

A) ±1.645 B) ±1.96 C) 3.841 D) 2.706 Answer: C Difficulty: Easy Keywords: Chi-square test for difference in two proportions, critical value 6) Referring to Table 11-1, what is the critical value when testing whether the population proportions are different if α = 0.10?

A) ±1.645 B) ±1.96 C) 3.842 D) 2.706 Answer: D Difficulty: Easy Keywords: Chi-square test for difference in two proportions, critical value 7) Referring to Table 11-1, 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 α = 0.10?

A) 4.335 B) 2.706 C) 1.194 D) 0.274 Answer: C Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, test statistic 8) Referring to Table 11-1, 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 selfimprovement 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 selfimprovement 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 Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, decision, conclusion

11-2 .

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 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 Difficulty: Easy Keywords: Chi-square test for difference in two proportions, properties 11) True or False: A test for the difference between two proportions can be performed using the chisquare distribution.

Answer: TRUE 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 Difficulty: Easy Keywords: Chi-square test for difference in two proportions TABLE 11-2 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 Table 11-2 , the hypotheses the dean should use are: A) H0: π1 - π2 = 0 versus H1: π1 - π2 ≠ 0.

B) H0: π1 - π2 ≠ 0 versus H1: π1 - π2 = 0.

C) H0: π1 - π2 ≤ 0 versus H1: π1 - π2 > 0.

D) H0: π1 - π2 ≥ 0 versus H1: π1 - π2 < 0.

Answer: A Difficulty: Easy Keywords: Chi-square test for difference in two proportions, form of hypothesis 14) Referring to Table 11-2 , the null hypothesis will be rejected if the test statistic is ________.

Answer: χ2 > 3.841 Difficulty: Easy Keywords: Chi-square test for difference in two proportions, critical value

11-3 .

15) Referring to Table 11-2 , the value of the test statistic is ________.

Answer: χ2 = 3.4806 Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, test statistic 16) Referring to Table 11-2, the p-value of the test is ________.

Answer: 0.0621 Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, p-value 17) True or False: Referring to Table 11-2, the null hypothesis should be rejected.

Answer: FALSE Difficulty: Easy Keywords: Chi-square test for difference in two proportions, decision 18) True or False: Referring to Table 11-2, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

Answer: TRUE Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, decision 19) True or False: Referring to Table 11-2, the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

Answer: FALSE Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, decision TABLE 11-3 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:

She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

20) Referring to Table 11-3, the test will involve ________ degree(s) of freedom.

Answer: 1 Difficulty: Easy Keywords: Chi-square test for difference in two proportions, degrees of freedom

11-4 .

21) Referring to Table 11-3, the overall or mean proportion of local riders is ________.

Answer: 0.5504 Difficulty: Easy Keywords: Chi-square test for difference in two proportions, properties 22) Referring to Table 11-3, the expected cell frequency in the Male/Local cell is ________.

Answer: 33.02 Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, contingency table, properties 23) Referring to Table 11-3, the expected cell frequency in the Female/Non-Local cell is ________.

Answer: 31.02 Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, contingency table, properties 24) Referring to Table 11-3, the critical value of the test is ________.

Answer: 3.841 Difficulty: Easy Keywords: Chi-square test for difference in two proportions, critical value 25) Referring to Table 11-3, the value of the test statistic is ________.

Answer: 4.568 Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, test statistic 26) True or False: Referring to Table 11-3, the null hypothesis will be rejected.

Answer: TRUE Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, decision 27) True or False: Referring to Table 11-3, 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 Difficulty: Moderate Keywords: Chi-square test for difference in two proportions, conclusion

11-5 .

TABLE 11-4 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 Table 11-4, which test would be used to properly analyze the data in this experiment?

A) χ2 test of independence B) χ2 test for difference among more than two proportions C) χ2 test for difference between two proportions D) none of the above Answer: B Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions 29) Referring to Table 11-4, the degrees of freedom of the test statistic is ________.

A) 4 B) 8 C) 10 D) 448 Answer: A Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, degrees of freedom 30) Referring to Table 11-4, 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 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, critical value 31) Referring to Table 11-4, the calculated value of the test statistic is ________.

A) -0.1777 B) -0.0185 C) 1.4999 D) 1.5190 Answer: C Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, test statistic 11-6 .

32) Referring to Table 11-4, 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 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, decision, conclusion TABLE 11-5 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 four procedures, and collects the following numbers of patients from their own records:

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 Table 11-5, the test will involve ________ degrees of freedom.

Answer: 3 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, degrees of freedom 34) Referring to Table 11-5, the overall or mean proportion of clear operations is ________.

Answer: 0.676 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, properties 35) Referring to Table 11-5, the expected cell frequency for the Procedure A/Clear cell is ________.

Answer: 25.69 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, contingency table, properties 36) Referring to Table 11-5, the expected cell frequency for the Procedure D/Return cell is ________.

Answer: 5.83 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, contingency table, properties

11-7 .

37) Referring to Table 11-5, the critical value of the test is ________.

Answer: 7.815 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, critical value 38) Referring to Table 11-5, the value of the test statistic is ________.

Answer: 7.867 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, test statistic 39) True or False: Referring to Table 11-5, the null hypothesis will be rejected.

Answer: TRUE Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, decision 40) True or False: Referring to Table 11-5, the decision made suggests that the four procedures all have different proportions of clear operations.

Answer: FALSE Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, conclusion 41) True or False: Referring to Table 11-5, the decision made suggests that the four procedures do not all have the same proportion of clear operations.

Answer: TRUE Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, conclusion TABLE 11-6 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.

42) Referring to Table 11-6, 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 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, properties 43) Referring to Table 11-6, 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 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, properties 11-8 .

44) Referring to Table 11-6, what is the form of the null hypothesis?

A) H0: π1 = π2 = π3 B) H0: π1 = π2 ≠ π3 C) H0: π1 ≠ π2 = π3 D) H0: π1 ≠ π2 ≠ π3 Answer: A Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, forms of hypothesis 45) Referring to Table 11-6, what is the form of the alternative hypothesis?

A) H0: π1 ≠ π2 ≠ π3 B) H0: π1 ≠ π2 = π3 C) H0: π1 = π2 ≠ π3 D) H1: not all πj are the same Answer: D Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, forms of hypothesis 46) True or False: Referring to Table 11-6, the assumptions needed to perform the test are satisfied.

Answer: TRUE Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, assumption 47) Referring to Table 11-6, what are the degrees of freedom of the test statistic?

Answer: 2 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, degrees of freedom 48) Referring to Table 11-6, what is the value of the test statistic?

Answer: 43.96 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, test statistic 49) Referring to Table 11-6, what is the critical value?

Answer: 5.991 Difficulty: Easy Keywords: Chi-square test for difference in proportions, critical value 50) Referring to Table 11-6, what is the p-value of the test statistic?

Answer: 2.9E-10 or smaller than 0.005 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, p-value 51) True or False: Referring to Table 11-6, the null hypothesis cannot be rejected.

Answer: FALSE Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, decision

11-9 .

52) Referring to Table 11-6, what is the correct conclusion?

A) There is enough evidence that the proportions are all different in the three years.

B) There is not enough evidence that the proportions are all different in the three 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 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, conclusion TABLE 11-7 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 65% 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.

53) Referring to Table 11-7, the test will involve ________ degrees of freedom.

Answer: 2 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, degrees of freedom 54) Referring to Table 11-7, the expected cell frequency for the Hong Kong/Yes cell is ________.

Answer: 160 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, contingency table, properties 55) Referring to Table 11-7, the expected cell frequency for the Paris/No cell is ________.

Answer: 40 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, contingency table, properties 56) Referring to Table 11-7, the critical value of the test is ________.

Answer: 5.9915 Difficulty: Easy Keywords: Chi-square test for difference in more than two proportions, critical value 57) Referring to Table 11-7, the value of the test statistic is ________.

Answer: 7.00 Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, test statistic 58) True or False: Referring to Table 11-7, the null hypothesis will be rejected.

Answer: TRUE Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, decision 11-10 .

59) True or False: Referring to Table 11-7, the decision made suggests that the three cities all have different proportions of hotels that correctly post minibar charges.

Answer: FALSE Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, conclusion 60) True or False: Referring to Table 11-7, the decision made suggests that the three cities do not all have the same proportion of hotels that correctly post minibar charges.

Answer: TRUE Difficulty: Moderate Keywords: Chi-square test for difference in more than two proportions, conclusion 61) True or False: When using the χ2 test for independence, you should be aware that expected frequencies that are too small will lead to a large Type I error.

Answer: TRUE Difficulty: Difficult Keywords: Chi-square test of independence, properties, assumption 62) 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 Difficulty: Moderate Keywords: Chi-square test of independence, properties, assumption 63) 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 Difficulty: Easy Keywords: Chi-square test of independence, degrees of freedom

11-11 .

TABLE 11-8 A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles in San Diego County depends on ethnic status. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) 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 worn Seat belts not worn

Hispanic 31 283

Non-Hispanic 148 330

64) Referring to Table 11-8, which test would be used to properly analyze the data in this experiment?

A) χ2 test for independence B) χ2 test for differences among more than two proportions C) χ2 test for variance D) none of the above Answer: A Difficulty: Moderate Keywords: Chi-square test of independence 65) Referring to Table 11-8, the calculated test statistic is ________.

A) -0.9991 B) -0.1368 C) 48.1849 D) 72.8063 Answer: C Difficulty: Easy Keywords: Chi-square test of independence, test statistic 66) Referring to Table 11-8, 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 Difficulty: Easy Keywords: Chi-square test of independence, critical value 67) Referring to Table 11-8, at 5% level of significance, there is sufficient evidence to conclude that A) use of seat belts in motor vehicles is related to ethnic status in San Diego County.

B) use of seat belts in motor vehicles depends on ethnic status in San Diego County.

C) use of seat belts in motor vehicles is associated with ethnic status in San Diego County.

D) all of the above Answer: D Difficulty: Moderate Keywords: Chi-square test of independence, decision, conclusion

11-12 .

TABLE 11-9 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

68) Referring to Table 11-9, which test would be used to properly analyze the data in this experiment?

A) χ2 test for independence B) χ2 test for differences among more than two proportions C) χ2 test for variance D) none of the above Answer: A Difficulty: Moderate Keywords: Chi-square test of independence 69) Referring to Table 11-9, the calculated test statistic is ________.

A) -0.1006 B) 0.00 C) 5.9418 D) 6.1194 Answer: C Difficulty: Easy Keywords: Chi-square test of independence, test statistic 70) Referring to Table 11-9, 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 Difficulty: Easy Keywords: Chi-square test of independence, critical value 71) Referring to Table 11-9, the degrees of freedom of the test statistic are ________.

A) 1 B) 2 C) 4 D) 299 Answer: A Difficulty: Easy Keywords: Chi-square test of independence, degrees of freedom

11-13 .

72) Referring to Table 11-9, 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 Difficulty: Moderate Keywords: Chi-square test of independence, decision, conclusion TABLE 11-10 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.

73) Referring to Table 11-10, 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?

A) χ2 test for independence B) χ2 test for differences among more than two proportions C) χ2 test for variance D) none of the above Answer: A Difficulty: Moderate Keywords: Chi-square test of independence 74) Referring to Table 11-10, 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.

A) Reject H0 if χ2 > 16.919.

B) Reject H0 if χ2 > 15.507.

C) Reject H0 if χ2 > 11.143.

D) Reject H0 if χ2 > 9.488.

Answer: D Difficulty: Easy Keywords: Chi-square test of independence, critical value

11-14 .

75) Referring to Table 11-10, 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 Difficulty: Moderate Keywords: Chi-square test of independence, contingency table, properties 76) Referring to Table 11-10, 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 Difficulty: Moderate Keywords: Chi-square test of independence, contingency table, properties 77) Referring to Table 11-10, for the cell with 1 to 4 years of training time and a high defect rate, what is the contribution to the overall χ2 statistic for the independence test?

A) 0.36 B) 0.1296 C) 0.015 D) 0.0144 Answer: C Difficulty: Moderate Keywords: Chi-square test of independence, contingency table, properties 78) Referring to Table 11-10, 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 α = 0.05.

A) 0.045 B) 0.055 C) 0.074 D) 0.080 Answer: A Difficulty: Easy Keywords: Chi-square test of independence, p-value, decision

11-15 .

TABLE 11-11 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.

79) Referring to Table 11-11, the test will involve ________ degrees of freedom.

Answer: 4 Difficulty: Easy Keywords: Chi-square test of independence, degrees of freedom 80) Referring to Table 11-11, the critical value of the test is ________.

Answer: 13.277 Difficulty: Easy Keywords: Chi-square test of independence, critical value 81) Referring to Table 11-11, the expected cell frequency for the Admitted/Urban cell is ________.

Answer: 39.06 Difficulty: Moderate Keywords: Chi-square test of independence, contingency table, properties 82) Referring to Table 11-11, the value of the test statistic is ________.

Answer: 12.624 Difficulty: Moderate Keywords: Chi-square test of independence, test statistic 83) True or False: Referring to Table 11-11, the null hypothesis will be rejected.

Answer: FALSE Difficulty: Moderate Keywords: Chi-square test of independence, decision 84) True or False: Referring to Table 11-11, the p-value of this test is greater than 0.01.

Answer: TRUE Difficulty: Moderate Keywords: Chi-square test of independence, p-value 85) True or False: Referring to Table 11-11, the decision made suggests that admissions status at the college is independent of the type of community in which an applicant resides.

Answer: TRUE Difficulty: Easy Keywords: Chi-square test of independence, conclusion

11-16 .

86) True or False: Referring to Table 11-11, the same decision would be made with this test if the level of significance had been 0.005.

Answer: TRUE Difficulty: Easy Keywords: Chi-square test of independence, decision 87) True or False: Referring to Table 11-11, the same decision would be made with this test if the level of significance had been 0.05.

Answer: FALSE Difficulty: Easy Keywords: Chi-square test of independence, decision 88) True or False: Referring to Table 11-11, 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 Difficulty: Easy Keywords: Chi-square test of independence, form of hypothesis, conclusion 89) True or False: Referring to Table 11-11, 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 Difficulty: Easy Keywords: Chi-square test of independence, form of hypothesis, conclusion 90) True or False: The chi-square test of independence requires that the expected frequency in each cell to be at least 5.

Answer: FALSE Difficulty: Easy Keywords: Chi-square test of independence, assumption 91) True or False: The chi-square test of independence requires that the expected frequency in each cell to be at least 1.

Answer: TRUE Difficulty: Easy Keywords: Chi-square test of independence, assumption

11-17 .

TABLE 11-12 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.

92) Referring to Table 11-12, 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 Difficulty: Easy Keywords: contingency table, properties 93) Referring to Table 11-12, 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 Difficulty: Easy Keywords: contingency table, properties 94) Referring to Table 11-12, 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 Difficulty: Difficult Keywords: Chi-square test of independence, contingency table, properties

11-18 .

95) Referring to Table 11-12, 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 Difficulty: Moderate Keywords: Chi-square test of independence, contingency table, properties 96) Referring to Table 11-12, 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 Difficulty: Moderate Keywords: Chi-square test of independence, test statistic 97) Referring to Table 11-12, 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 Difficulty: Easy Keywords: Chi-square test of independence, critical value 98) Referring to Table 11-12, 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 Difficulty: Moderate Keywords: Chi-square test of independence, decision, conclusion

11-19 .

TABLE 11-13 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-year-olds revealed the following with regard 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.

99) Referring to Table 11-13, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to spend 3-6 hours on average watching TV and be more than 10 lbs. underweight?

A) 5 B) 5.8 C) 6.2 D) 8 Answer: B Difficulty: Easy Keywords: Chi-square test of independence, contingency table, properties 100) Referring to Table 11-13, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to spend no more than 6 hours on average watching TV and be more than 10 lbs. underweight?

A) 5.8 B) 6.2 C) 8 D) 12 Answer: D Difficulty: Moderate Keywords: Chi-square test of independence, contingency table, properties 101) Referring to Table 11-13, 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 Difficulty: Easy Keywords: Chi-square test of independence, contingency table, properties

11-20 .

102) Referring to Table 11-13, 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 Difficulty: Easy Keywords: Chi-square test of independence, contingency table, properties 103) Referring to Table 11-13, the value of the test statistic is ________.

A) 8.532 B) 15.483 C) 18.889 D) 69.744 Answer: C Difficulty: Moderate Keywords: Chi-square test of independence, test statistic 104) Referring to Table 11-13, the critical value of the test will be ________.

A) 6.635 B) 13.277 C) 14.860 D) 21.666 Answer: B Difficulty: Easy Keywords: Chi-square test of independence, critical value 105) Referring to Table 11-13, 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 Difficulty: Moderate Keywords: Chi-square test of independence, decision, conclusion

11-21 .

106) Referring to Table 11-13, 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 Difficulty: Difficult Keywords: Chi-square test of independence, decision 107) Referring to Table 11-13, the degrees of freedom of the test statistic are A) 1.

B) 2.

C) 4.

D) 9.

Answer: C Difficulty: Easy Keywords: Chi-square test of independence, degrees of freedom 108) True or False: Referring to Table 11-13, the test is always a one-tail test.

Answer: TRUE Difficulty: Easy Keywords: Chi-square test of independence, properties

11-22 .

Business Statistics: A First Course, 6e (Levine) 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 Difficulty: Easy Keywords: intercept, interpretation 2) The Y-intercept (b0) represents the A) estimated average Y when X = 0.

B) change in estimated average Y per unit change in X. C) predicted value of Y. D) variation around the sample regression line.

Answer: A Difficulty: Easy Keywords: intercept, interpretation 3) 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 Difficulty: Easy Keywords: slope, interpretation 4) The least squares method minimizes which of the following?

A) SSR B) SSE C) SST D) all of the above Answer: B Difficulty: Difficult Keywords: least squares, properties

12-1 .

TABLE 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: Y1 - β0 + β1X1 + εi 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 β1) 5) Referring to Table 12-1, interpret the estimate of β0, 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 Difficulty: Moderate Keywords: intercept, interpretation 6) Referring to Table 12-1, interpret the estimate of σ, 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 Difficulty: Difficult Keywords: standard error of the estimate, interpretation 7) Referring to Table 12-1, interpret the p-value for testing whether β1 exceeds 0.

A) There is sufficient evidence (at the α = 0.05) to conclude that sales revenue (X) is a useful linear predictor of service charge (Y).

B) There is insufficient evidence (at the α = 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 Difficulty: Moderate Keywords: p-value, interpretation

12-2 .

8) Referring to Table 12-1, a 95% confidence interval for β1 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 α = 0.05 level, there is no evidence of a linear relationship between service charge (Y) and sales revenue (X).

Answer: C Difficulty: Moderate Keywords: confidence interval, interpretation TABLE 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 six 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 ($) River Falls 1.30 Hudson 1.60 Ellsworth 1.80 Prescott 2.00 Rock Elm 2.40 Stillwater 2.90

Sales 100 90 90 40 38 32

9) Referring to Table 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 Difficulty: Moderate Keywords: slope, estimation 10) Referring to Table 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 Difficulty: Moderate Keywords: slope, interpretation

12-3 .

11) Referring to Table 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 Difficulty: Moderate Keywords: coefficient of correlation, estimation 12) Referring to Table 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 Difficulty: Moderate Keywords: coefficient of determination, interpretation 13) Referring to Table 12-2, what percentage of the total variation in candy bar sales is explained by the prices?

A) 100% B) 88.54% C) 78.39% D) 48.19% Answer: C Difficulty: Moderate Keywords: coefficient of determination, interpretation 14) Referring to Table 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 Difficulty: Moderate Keywords: standard error of the estimate, estimation 15) Referring to Table 12-2, what is the standard error of the regression slope estimate, A) 0.784 B) 0.885 C) 12.650 D) 16.299 Answer: C Difficulty: Moderate Keywords: standard error, slope

12-4 .

?

16) Referring to Table 12-2, what is ∑ (X - )2 for these data?

A) 0 B) 1.66 C) 2.54 D) 25.66 Answer: B Difficulty: Moderate Keywords: sum of squares 17) Referring to Table 12-2, to test that the regression coefficient, β1, is not equal to 0, what would be the critical values? Use α = 0.05.

A) ± 2.5706 B) ± 2.7764 C) ± 3.1634 D) ± 3.4954 Answer: B Difficulty: Difficult Keywords: t test on slope, critical value 18) Referring to Table 12-2, to test whether a change in price will have any impact on sales, what would be the critical values? Use α = 0.05.

A) ± 2.5706 B) ± 2.7765 C) ± 3.1634 D) ± 3.4954 Answer: B Explanation: B) This is a test for β1 is not equal to 0.

Difficulty: Difficult Keywords: t test on slope, critical value 19) Referring to Table 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 Difficulty: Moderate Keywords: estimation of mean values 20) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values

12-5 .

21) True of 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 Difficulty: Moderate Keywords: t test on slope 22) The residual represents the discrepancy between the observed dependent variable and its ________ value.

Answer: predicted or estimated mean Difficulty: Moderate Keywords: estimation of mean values, prediction of individual values TABLE 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 four students. For these four, 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 Co-op Jobs Job Offer 1 1 4 2 2 6 3 1 3 4 0 1 23) Referring to Table 12-3, set up a scatter plot.

Answer:

12-6 .

Difficulty: Moderate Keywords: scatter plot 24) Referring to Table 12-3, the least squares estimate of the slope is ________.

Answer: 2.50 Difficulty: Moderate Keywords: slope, estimation, least squares 25) Referring to Table 12-3, the least squares estimate of the Y-intercept is ________.

Answer: 1.00 Difficulty: Moderate Keywords: intercept, estimation, least squares 26) Referring to Table 12-3, the prediction for the number of job offers for a person with two cooperative education jobs is ________.

Answer: 6 Difficulty: Moderate Keywords: prediction of individual values 27) Referring to Table 12-3, the total sum of squares (SST) is ________.

Answer: 13.0 Difficulty: Moderate Keywords: sum of squares 28) Referring to Table 12-3, the regression sum of squares (SSR) is ________.

Answer: 12.5 Difficulty: Moderate Keywords: sum of squares 29) Referring to Table 12-3, the error or residual sum of squares (SSE) is ________.

Answer: 0.50 Difficulty: Moderate Keywords: sum of squares 30) Referring to Table 12-3, the coefficient of determination is ________.

Answer: 0.962 Difficulty: Moderate Keywords: coefficient of determination 31) Referring to Table 12-3, the standard error of estimate is ________.

Answer: 0.50 Difficulty: Moderate Keywords: standard error of estimate 32) Referring to Table 12-3, the coefficient of correlation is ________.

Answer: 0.981 Difficulty: Moderate Keywords: coefficient of correlation

12-7 .

33) Referring to Table 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 Difficulty: Easy Keywords: confidence interval, estimation of mean values, critical value 34) Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, estimation of mean values, critical value 35) Referring to Table 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 Difficulty: Moderate Keywords: prediction interval, prediction of individual values 36) True or False: Referring to Table 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 people 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 Difficulty: Moderate Keywords: confidence interval, estimation of mean values 37) Referring to Table 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 Difficulty: Moderate Keywords: prediction interval, prediction of individual values, critical value 38) Referring to Table 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 Difficulty: Moderate Keywords: prediction interval, prediction of individual values

12-8 .

39) True or False: Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, prediction interval, estimation of mean values, prediction of individual values, properties 40) Referring to Table 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 . The value of in this sample is ________.

Answer: 0.3536 Difficulty: Moderate Keywords: t test on slope, standard error, slope 41) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, test statistic, slope 42) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, test statistic, slope 43) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, critical value, slope, decision 44) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, critical value, slope, decision 45) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, p-value, slope

12-9 .

46) Referring to Table 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 Explanation: The t test statistic is t =

=

= -1.4142

Difficulty: Difficult Keywords: t test on slope, p-value, slope

12-10 .

TABLE 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 47) Referring to Table 12-4, set up a scatter plot.

Answer:

Difficulty: Moderate Keywords: scatter plot

12-11 .

48) Referring to Table 12-4, the least squares estimate of the slope is ________.

Answer: 1.12 Difficulty: Moderate Keywords: slope, estimation, least squares 49) Referring to Table 12-4, the least squares estimate of the Y-intercept is ________.

Answer: 17.7 Difficulty: Moderate Keywords: intercept, estimation, least squares 50) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values 51) Referring to Table 12-4, the total sum of squares (SST) is ________.

Answer: 1,564.2 Difficulty: Moderate Keywords: sum of squares 52) Referring to Table 12-4, the regression sum of squares (SSR) is ________.

Answer: 1,227.4 Difficulty: Moderate Keywords: sum of squares 53) Referring to Table 12-4, the error or residual sum of squares (SSE) is ________.

Answer: 336.9 Difficulty: Moderate Keywords: sum of squares 54) Referring to Table 12-4, the coefficient of determination is ________.

Answer: 0.785 Difficulty: Moderate Keywords: coefficient of determination 55) Referring to Table 12-4, ________% of the total variation in sales generated can be explained by the number of new clients brought in.

Answer: 78.5 Difficulty: Moderate Keywords: coefficient of determination, interpretation 56) Referring to Table 12-4, the standard error of the estimated slope coefficient is ________.

Answer: 0.185 Difficulty: Moderate Keywords: slope, standard error

12-12 .

57) Referring to Table 12-4, the standard error of estimate is ________.

Answer: 5.804 Difficulty: Moderate Keywords: standard error of estimate 58) Referring to Table 12-4, the coefficient of correlation is ________.

Answer: 0.886 Difficulty: Moderate Keywords: coefficient of correlation 59) Referring to Table 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 Difficulty: Easy Keywords: estimation of mean values, confidence interval, critical value 60) Referring to Table 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 Difficulty: Moderate Keywords: estimation of mean values, confidence interval 61) Referring to Table 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 t critical value they would use is ________.

Answer: 3.1693 Difficulty: Moderate Keywords: prediction of individual values, prediction interval, critical value 62) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values, prediction interval 63) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values, prediction interval, estimation of mean values, confidence interval, properties

12-13 .

64) Referring to Table 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 . The value of in this sample is ________.

Answer: 0.1853 Difficulty: Moderate Keywords: t test on slope, slope, standard error 65) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, test statistic 66) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, test statistic 67) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, critical value, decision 68) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, p-value 69) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, decision 70) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, conclusion

12-14 .

71) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, test statistic 72) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, critical value, decision 73) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, p-value 74) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, decision 75) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, conclusion

12-15 .

TABLE 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 four years of quarterly data (i.e., n = 16) with the following results:

76) Referring to Table 12-5, the value of the quantity that the least squares regression line minimizes is ________.

Answer: 11.912 Difficulty: Moderate Keywords: least squares, properties, sum of squares 77) Referring to Table 12-5, the estimates of the Y-intercept and slope are ________ and ________, respectively.

Answer: 3.962 and 0.040451 Difficulty: Easy Keywords: intercept, slope, estimation 78) Referring to Table 12-5, the prediction for a quarter in which X = 120 is Y = ________.

Answer: 8.816 Difficulty: Moderate Keywords: prediction of individual values 79) Referring to Table 12-5, the standard error of the estimate is ________.

Answer: 0.9224 Difficulty: Easy Keywords: standard error of estimate

12-16 .

80) Referring to Table 12-5, the coefficient of determination is ________.

Answer: 0.643 Difficulty: Easy Keywords: coefficient of determination 81) Referring to Table 12-5, the standard error of the estimated slope coefficient is ________.

Answer: 0.008 Difficulty: Easy Keywords: slope, standard error 82) Referring to Table 12-5, the correlation coefficient is ________.

Answer: 0.802 Difficulty: Easy Keywords: coefficient of correlation 83) Referring to Table 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 Difficulty: Easy Keywords: Durbin-Watson statistic, critical value, autocorrelation 84) Referring to Table 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 Difficulty: Moderate Keywords: Durbin-Watson statistic, decision, autocorrelation 85) 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 Difficulty: Easy Keywords: Durbin-Watson statistic, autocorrelation, assumption 86) 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 Difficulty: Easy Keywords: Durbin-Watson statistic, assumption, autocorrelation 12-17 .

87) 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 Difficulty: Easy Keywords: standard error of estimate, interpretation 88) 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: B Difficulty: Easy Keywords: coefficient of determination, interpretation TABLE 12-6 The following Microsoft® 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.

89) Referring to Table 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 Difficulty: Easy Keywords: coefficient of determination, interpretation

12-18 .

90) Referring to Table 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 Difficulty: Easy Keywords: slope, interpretation 91) True or False: The Regression Sum of Squares (SSR) can never be greater than the Total Sum of Squares (SST).

Answer: TRUE Difficulty: Easy Keywords: sum of squares, properties 92) True or False: The coefficient of determination represents the ratio of SSR to SST. Answer: TRUE Difficulty: Easy Keywords: coefficient of determination, properties 93) 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 Difficulty: Easy Keywords: coefficient of correlation, slope, interpretation 94) True or False: The value of r is always positive.

Answer: FALSE Difficulty: Easy Keywords: coefficient of correlation, properties 95) 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 Difficulty: Moderate Keywords: assumption

12-19 .

96) 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 Difficulty: Moderate Keywords: assumption 97) Based on the residual plot below, you will conclude that there might be a violation of which of the following assumptions?

A) linearity of the relationship B) normality of errors C) homoscedasticity D) independence of errors Answer: C Difficulty: Moderate Keywords: assumption, homoscedasticity 98) True or False: Data that exhibit an autocorrelation effect violate the regression assumption of independence.

Answer: TRUE Difficulty: Easy Keywords: assumption, autocorrelation 99) True or False: The Durbin-Watson D statistic is used to check the assumption of normality.

Answer: FALSE Difficulty: Easy Keywords: Durbin-Watson statistic, assumption, autocorrelation

12-20 .

100) 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 Difficulty: Moderate Keywords: Durbin-Watson statistic, autocorrelation, properties 101) 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 Difficulty: Easy Keywords: residual, properties 102) 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 Difficulty: Moderate Keywords: residual plot, homoscedasticity 103) 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, .

Answer: D Difficulty: Difficult Keywords: slope, interpretation 104) 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 Difficulty: Moderate Keywords: coefficient of correlation, properties, interpretation

12-21 .

105) 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 Difficulty: Moderate Keywords: coefficient of correlation, properties 106) 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 Difficulty: Moderate Keywords: coefficient of correlation, properties, interpretation 107) Testing for the existence of correlation is equivalent to A) testing for the existence of the slope (β1).

B) testing for the existence of the Y-intercept (β0).

C) the confidence interval estimate for predicting Y. D) none of the above Answer: A Difficulty: Moderate Keywords: coefficient of correlation, t test for correlation coefficient, t test on slope 108) 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation 109) 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 Difficulty: Easy Keywords: coefficient of correlation, slope, properties

12-22 .

110) The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 0. To test H0: ρ = 0 against the one-sided alternative H1: ρ < 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 Difficulty: Difficult Keywords: coefficient of correlation, t test for correlation coefficient, p-value 111) The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 0. To test H0: ρ = 0 against the one-sided alternative H1: ρ > 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 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 p-value is 0.256 when testing H0: ρ = 0 against the one-sided alternative H1: ρ > 0. To test H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 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 Difficulty: Difficult Keywords: coefficient of correlation, t test for correlation coefficient, p-value 113) The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.744 when testing H0: ρ = 0 against the one-sided alternative H1: ρ < 0. To test H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 0 at a significance level of 0.1, the p-value is ________.

A) 0744/2 B) (0.744)(2) C) 1 - 0.744 D) (1 - 0.744)/(2) Answer: D Difficulty: Difficult Keywords: coefficient of correlation, t test for correlation coefficient, p-value

12-23 .

114) If you wanted to find out if alcohol consumption (measured in fluid oz.) and grade point average on a four-point scale are linearly related, you would perform a A) χ2 test for the difference in two proportions.

B) χ2 test for independence.

C) Z test for the difference in two proportions.

D) t test for a correlation coefficient.

Answer: D Difficulty: Difficult Keywords: coefficient of correlation, t test for correlation coefficient 115) True or False: When r = -1, it indicates a perfect relationship between X and Y. Answer: TRUE Difficulty: Easy Keywords: coefficient of correlation, properties TABLE 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 Microsoft® Excel output.

Note: 2.94942E-07 = 2.94942 * 10-7 116) Referring to Table 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: ρ ≥ 0 vs. H1: ρ < 0.

B) H0: ρ ≤ 0 vs. H1: ρ > 0.

C) H0: r ≥ 0 vs. H1: r < 0.

D) H0: r ≤ 0 vs. H1: r > 0.

Answer: A Difficulty: Easy Keywords: coefficient of correlation, t test for correlation coefficient, form of hypothesis

12-24 .

117) Referring to Table 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 Difficulty: Easy Keywords: coefficient of correlation, t test for correlation coefficient, test statistic 118) Referring to Table 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 ________.

A) 2.94942E-07 B) 2.94942E-07 / 2 C) (2.94942E-07)2 D) 8.7932E-13 Answer: B Difficulty: Easy Keywords: coefficient of correlation, t test for correlation coefficient, p-value 119) Referring to Table 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 prison stocks 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 prison stocks 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 prison stocks 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 prison stocks portfolio and S&P 500 Index are negatively related.

Answer: B Difficulty: Easy Keywords: coefficient of correlation, t test for correlation coefficient, decision, conclusion

12-25 .

TABLE 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 Microsoft® Excel output for predicting GPA using ACT scores based a data set of eight randomly chosen students from a Big Ten university.

120) Referring to Table 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 Difficulty: Easy Keywords: coefficient of determination, interpretation 121) Referring to Table 12-8, the value of the measured test statistic to test whether there is any linear relationship between GPA and ACT scores is _______.

A) 0.0356 B) 0.1021 C) 0.7598 D) 2.8633 Answer: D Difficulty: Easy Keywords: coefficient of correlation, t test for correlation coefficient, test statistic 122) Referring to Table 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 Difficulty: Easy Keywords: prediction of individual values 12-26 .

123) Referring to Table 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 Difficulty: Easy Keywords: coefficient of correlation, t test for correlation coefficient, decision, conclusion 124) Referring to Table 12-8, the value of the measured (observed) test statistic of the F test for H0: β1 = 0 vs. H1: β1 = 0 A) may be negative.

B) is always positive.

C) is always negative.

D) has the same sign as the corresponding t test statistic.

Answer: B Difficulty: Easy Keywords: F test on slope, test statistic

12-27 .

TABLE 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 Microsoft® 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.

Note: 2.051E-05 = 2.051 * 10-0.5 and 5.944E-18 = 5.944 * 10-18.

125) Referring to Table 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 Difficulty: Moderate Keywords: slope, interpretation 126) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, test statistic

12-28 .

127) Referring to Table 12-9, the p-value of the measured F test statistic to test whether HOURS affects SALARY is ________.

A) (5.944E-18)/2 B) 5.944E-18 C) (2.051E-05)/2 D) 2.051E-05 Answer: B Explanation: B) 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.

Difficulty: Difficult Keywords: F test on slope, slope, test statistic 128) Referring to Table 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 Difficulty: Moderate Keywords: F test on slope, slope, degrees of freedom 129) Referring to Table 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 Difficulty: Moderate Keywords: sum of squares 130) Referring to Table 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 Difficulty: Moderate Keywords: slope, interpretation, confidence interval

12-29 .

131) Referring to Table 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 ________.

A) (5.944E-18)/2 B) 5.944E-18 C) (2.051E-05)/2 D) 2.051E-05 Answer: A Difficulty: Moderate Keywords: t test on slope, slope, p-value 132) 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 Difficulty: Easy Keywords: coefficient of correlation, interpretation 133) 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 Difficulty: Moderate Keywords: coefficient of correlation, t test for correlation coefficient 134) 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 Difficulty: Moderate Keywords: prediction of individual values, prediction interval, properties 135) 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 Difficulty: Moderate Keywords: estimation of mean values, confidence interval, prediction of individual values, prediction interval, properties

12-30 .

TABLE 12-10 The management of a chain electronic store would like to develop a model for predicting the weekly sales (in thousand 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 907 926 713 741 780 898 510 529 460 872 650 603

Sales (Thousands of Dollars) 11.20 11.05 8.21 9.21 9.42 10.08 6.73 7.02 6.12 9.52 7.53 7.25

136) Referring to Table 12-10, generate the scatter plot.

Answer:

Difficulty: Moderate Keywords: scatter plot 137) Referring to Table 12-10, what are the values of the estimated intercept and slope?

Answer: 1.4464, 0.0100 Difficulty: Moderate Keywords: intercept, slope, estimation 138) Referring to Table 12-10, what is the value of the coefficient of determination?

Answer: 0.9453 Difficulty: Moderate Keywords: coefficient of determination

12-31 .

139) Referring to Table 12-10, what is the value of the coefficient of correlation?

Answer: 0.9723 Difficulty: Moderate Keywords: coefficient of correlation 140) Referring to Table 12-10, what is the value of the standard error of the estimate?

Answer: 0.4191 Difficulty: Moderate Keywords: standard error of estimate 141) Referring to Table 12-10, which is the correct null hypothesis for testing whether the number of customers who make a purchase affects weekly sales?

A) H0: β0 = 0 B) H0: β1 = 0 C) H0: μ = 0 D) H0: π = 0 Answer: B Difficulty: Easy Keywords: t test on slope, slope, form of hypothesis 142) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, test statistic 143) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, slope, degrees of freedom 144) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, p-value 145) True or False: Referring to Table 12-10, the null hypothesis for testing whether the number of customers who make a purchase effects weekly sales cannot be rejected if a 1% probability of committing a Type I error is desired.

Answer: FALSE Difficulty: Moderate Keywords: t test on slope, slope, decision

12-32 .

146) True or False: Referring to Table 12-10, the mean weekly sales will increase by an estimated $0.01 for each additional purchasing customer.

Answer: FALSE Difficulty: Moderate Keywords: t test on slope, slope, interpretation 147) True or False: Referring to Table 12-10, the mean weekly sales will increase by an estimated $10 for each additional purchasing customer.

Answer: TRUE Difficulty: Moderate Keywords: t test on slope, slope, interpretation 148) True or False: Referring to Table 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 Difficulty: Moderate Keywords: coefficient of determination, interpretation 149) Referring to Table 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 Difficulty: Easy Keywords: F test on slope, slope, test statistic 150) Referring to Table 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 Difficulty: Moderate Keywords: F test on slope, slope, test statistic 151) Referring to Table 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 Difficulty: Moderate Keywords: F test on slope, slope, p-value 152) True or False: Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, F test on slope, p-value 153) True or False: Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, F test on slope, test statistic 12-33 .

154) True or False: Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, F test on slope, test statistic 155) Referring to Table 12-10, generate the residual plot.

Answer:

Difficulty: Moderate Keywords: residual plot 156) Referring to Table 12-10, the residual plot indicates possible violation of which assumptions?

A) linearity of the relationship B) homoscedasticity C) autocorrelation D) normality Answer: B Difficulty: Moderate Keywords: homoscedasticity, residual plot, assumption 157) True or False: Referring to Table 12-10, it is inappropriate to compute the Durbin-Watson statistic and test for autocorrelation in this case.

Answer: TRUE Difficulty: Moderate Keywords: Durbin-Watson statistic, autocorrelation 158) Referring to Table 12-10, construct a 95% confidence interval for the change in mean weekly sales when the number of customers who make purchases increases by 1.

Answer: 0.0083 thousands of dollars to 0.0117 thousands of dollars Difficulty: Difficult Keywords: slope, confidence interval, interpretation

12-34 .

159) Referring to Table 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 Difficulty: Difficult Keywords: estimate of mean values, confidence interval 160) Referring to Table 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 Difficulty: Difficult Keywords: prediction of individual values, prediction interval TABLE 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:

12-35 .

161) Referring to Table 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 Difficulty: Easy Keywords: slope, interpretation 162) Referring to Table 12-11, predict the revenue when the number of downloads is 30 thousands.

Answer: $16.8296 thousands Difficulty: Easy Keywords: prediction of individual values 163) Referring to Table 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 Explanation: B) Even though (A) is the correct interpretation for the adjusted r-square, only (B) is the correct interpretation of r-square.

Difficulty: Moderate Keywords: interpretation, coefficient of determination

12-36 .

164) Referring to Table 12-11, what is the standard error of estimate?

Answer: $44.4765 thousands Difficulty: Moderate Keywords: standard error of estimate 165) Referring to Table 12-11, what is the standard deviation around the regression line?

Answer: $44.4765 thousands Difficulty: Difficult Keywords: interpretation, standard error of estimate 166) Referring to Table 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 Difficulty: Moderate Keywords: interpretation, assumption, residual plot, homoscedasticity 167) True or False: Referring to Table 12-11, the normality of error assumption appears to have been violated.

Answer: FALSE Difficulty: Easy Keywords: interpretation, assumption 168) True or False: Referring to Table 12-11, the homoscedasticity of error assumption appears to have been violated.

Answer: FALSE Difficulty: Easy Keywords: interpretation, assumption, homoscedasticity 169) True or False: Referring to Table 12-11, there appears to be autocorrelation in the residuals.

Answer: FALSE Difficulty: Moderate Keywords: interpretation, autocorrelation 170) True or False: Referring to Table 12-11, the Durbin-Watson statistic is inappropriate for this data set.

Answer: TRUE Difficulty: Moderate Keywords: Durbin-Watson statistic, assumption 171) True or False: Referring to Table 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 Difficulty: Moderate Keywords: slope, t test for slope, form of hypothesis

12-37 .

172) Referring to Table 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: β1 = 0 D) H0: β1 ≠ 0 Answer: C Difficulty: Easy Keywords: slope, t test for slope, form of hypothesis 173) Referring to Table 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) H1: b1 = 0 B) H1: b1 ≠ 0 C) H1: β1 = 0 D) H1: β1 ≠ 0 Answer: D Difficulty: Easy Keywords: slope, t test for slope, form of hypothesis 174) Referring to Table 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 Difficulty: Easy Keywords: test statistic, slope, t test for slope 175) Referring to Table 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 Difficulty: Easy Keywords: critical value, slope, t test for slope 176) Referring to Table 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 Difficulty: Easy Keywords: p-value, slope, t test for slope 177) True or False: Referring to Table 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 Difficulty: Easy Keywords: decision, slope, t test for slope 178) True or False: Referring to Table 12-11, there is sufficient evidence that revenue and the number of downloads are linearly related at a 5% level of significance.

Answer: TRUE Difficulty: Easy Keywords: conclusion, slope, t test for slope 12-38 .

179) Referring to Table 12-11, what are the lower and upper limits of the 95% confidence interval estimate for population slope?

Answer: 2.9082 and 4.5513 thousand dollars Difficulty: Easy Keywords: slope, confidence interval 180) Referring to Table 12-11, what are the lower and upper limits of the 95% confidence interval estimate for the mean change in revenue as a result of a 1 thousand increase in the number of downloads?

Answer: 2.9082 and 4.5513 thousand dollars Difficulty: Difficult Keywords: slope, confidence interval TABLE 12-12 The manager of the purchasing department of a large savings 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:

Note: 4.3946E-15 is 4.3946 x 10-15.

12-39 .

181) Referring to Table 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 Difficulty: Easy Keywords: slope, interpretation

12-40 .

182) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, slope, test statistic 183) Referring to Table 12-12, the p-value of the measured F test statistic to test whether the number of loan applications record affects the amount of time is ________.

A) (4.3946E-15)/2 B) 4.3946E-15 C) (0.0030)/2 D) 0.0030 Answer: B Difficulty: Moderate Keywords: F test on slope, slope, test statistic 184) Referring to Table 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 ________.

A) (4.3946E-15)/2 B) 4.3946E-15 C) (0.0030)/2 D) 0.0030 Answer: B Difficulty: Moderate Keywords: t test on slope, slope, test statistic 185) Referring to Table 12-12, the degrees of freedom for the F test on whether the number of loan applications recorded affects the amount of time are ________.

A) 1, 28 B) 1, 29 C) 28, 1 D) 29, 1 Answer: A Difficulty: Moderate Keywords: F test on slope, slope, degrees of freedom 186) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, slope, degrees of freedom 12-41 .

187) Referring to Table 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 Difficulty: Moderate Keywords: sum of squares 188) Referring to Table 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 Difficulty: Moderate Keywords: slope, interpretation, confidence interval 189) True or False: Referring to Table 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 Difficulty: Moderate Keywords: confidence interval, slope, interpretation 190) True or False: Referring to Table 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 Difficulty: Difficult Keywords: confidence interval, slope, interpretation 191) True or False: Referring to Table 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 Difficulty: Easy Keywords: conclusion, slope, t test for slope 192) True or False: Referring to Table 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 Difficulty: Easy Keywords: conclusion, slope, t test for slope

12-42 .

193) Referring to Table 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 ________.

A) (4.3946E-15)/2 B) 4.3946E-15 C) (4.3946E-15)*2 D) 0.0030 Answer: A Difficulty: Difficult Keywords: t test on slope, slope, p-value 194) Referring to Table 12-12, predict the amount of time it would take to process 150 invoices.

Answer: 2.2924 hours Difficulty: Easy Keywords: prediction of individual values 195) Referring to Table 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% Difficulty: Moderate Keywords: coefficient of determination, interpretation 196) True or False: Referring to Table 12-12, the model appears to be adequate based on the residual analyses.

Answer: TRUE Difficulty: Moderate Keywords: residual plot, homoscedasticity, autocorrelation 197) Referring to Table 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 Difficulty: Easy Keywords: autocorrelation, Durbin-Watson statistic, critical value 198) True or False: Referring to Table 12-12, there is no evidence of positive autocorrelation if the Durbin-Watson test statistic is found to be 1.78.

Answer: TRUE Difficulty: Moderate Keywords: autocorrelation, Durbin-Watson statistic, decision

12-43 .

TABLE 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.

199) Referring to Table 12-13, if the state decides to spend 1,000 dollars more per student, the estimated change in mean composite score is ________.

Answer: 8.0 Difficulty: Moderate Keywords: slope, interpretation 200) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, slope, test statistic 201) Referring to Table 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 Minitab or "between 0.05 and 0.10" using Table E.3.

Difficulty: Easy Keywords: t test on slope, slope, p-value

12-44 .

202) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, slope, decision 203) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, slope, conclusion 204) Referring to Table 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 or Minitab Difficulty: Moderate Keywords: F test on slope, slope, p-value 205) Referring to Table 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 Difficulty: Easy Keywords: F test on slope, slope, degrees of freedom 206) Referring to Table 12-13, the value of the F test on whether spending per student affects composite score is ________.

Answer: 3.5644 Difficulty: Moderate Keywords: F test on slope, slope, test statistic 207) Referring to Table 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, 30 Difficulty: Moderate Keywords: F test on slope, slope, critical value 208) Referring to Table 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 Difficulty: Easy Keywords: F test on slope, slope, decision

12-45 .

209) Referring to Table 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 Difficulty: Easy Keywords: F test on slope, slope, conclusion 210) Referring to Table 12-13, the error sum of squares (SSE) of the above regression is ________.

Answer: 23,900.8241 Difficulty: Moderate Keywords: sum of squares 211) Referring to Table 12-13, the regression mean square (MSR) of the above regression is ________.

Answer: 2,581.5759 Difficulty: Easy Keywords: mean square 212) Referring to Table 12-13, what percentage of the variation in composite score can be explained by the variation in spending per student?

Answer: 9.75% Difficulty: Easy Keywords: coefficient of determination, interpretation 213) Referring to Table 12-13, what is the standard deviation of the composite score around the regression line?

Answer: 26.9122 Difficulty: Easy Keywords: standard error of estimate, interpretation

12-46 .

Business Statistics: A First Course, 6e (Levine) Chapter 13 Introduction to 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 Difficulty: Easy Keywords: slope, interpretation 2) The coefficient of multiple determination r2Y.12 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 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 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 r2 ?

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: A Difficulty: Moderate Keywords: adjusted r-square, properties

13-1 .

TABLE 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 eight employees provides the following: Employee 1 2 3 4 5 6 7 8

Y 100 90 80 70 60 50 40 30

X1 10 3 8 5 5 7 1 1

X2 7 10 9 4 8 5 4 1

5) Referring to Table 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 Difficulty: Moderate Keywords: intercept, estimation 6) Referring to Table 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 Difficulty: Moderate Keywords: slope, estimation 7) Referring to Table 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 Difficulty: Moderate Keywords: slope, estimation

13-2 .

8) Referring to Table 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 Difficulty: Moderate Keywords: estimation of mean values TABLE 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 six workers and collects the following information: Employee 1 2 3 4 5 6

Y ($) 10 12 15 17 20 25

X1 3 1 8 5 7 10

X2 0 5 1 8 12 9

9) Referring to Table 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 Difficulty: Moderate Keywords: intercept, estimation 10) Referring to Table 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 Difficulty: Moderate Keywords: slope, estimation

13-3 .

11) Referring to Table 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 Difficulty: Moderate Keywords: slope, estimation 12) Referring to Table 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 Difficulty: Moderate Keywords: estimation of mean values 13) Referring to Table 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 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 Difficulty: Moderate Keywords: sum of squares

13-4 .

TABLE 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.

15) Referring to Table 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 Difficulty: Moderate Keywords: coefficient of multiple determination 16) Referring to Table 13-3, the p-value for GDP is ________.

A) 0.05 B) 0.01 C) 0.001 D) none of the above Answer: D Difficulty: Easy Keywords: t test on slope, p-value

13-5 .

17) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, p-value 18) Referring to Table 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 Difficulty: Easy Keywords: F test for the entire regression, p-value 19) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values 20) Referring to Table 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 Difficulty: Moderate Keywords: estimation of mean values 21) Referring to Table 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 Difficulty: Moderate Keywords: estimation of mean values

13-6 .

22) Referring to Table 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 Difficulty: Moderate Keywords: residual 23) Referring to Table 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 Difficulty: Moderate Keywords: residual 24) Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the value of the relevant t-statistic is ________.

A) 2.365 B) 0.143 C) -0.219 D) -1.960 Answer: C Difficulty: Easy Keywords: t test on slope, test statistic 25) Referring to Table 13-3, to test for the significance of the coefficient on aggregate price index, the pvalue is ________.

A) 0.0001 B) 0.8330 C) 0.8837 D) 0.9999 Answer: B Difficulty: Easy Keywords: t test on slope, p-value 26) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, p-value 13-7 .

27) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, p-value 28) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, p-value 29) Referring to Table 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: A Difficulty: Easy Keywords: t test on slope, p-value

13-8 .

TABLE 13-4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft® Excel output is provided below:

30) Referring to Table 13-4, what fraction of the variability in house size is explained by income, size of family, and education?

A) 27.0% B) 33.4% C) 74.8% D) 86.5% Answer: C Difficulty: Easy Keywords: coefficient of multiple determination, interpretation 31) Referring to Table 13-4, which of the independent variables in the model are significant at the 5% level?

A) Income, Size, School B) Income, Size C) Size, School D) Income, School Answer: B Difficulty: Easy Keywords: t test on slope, critical value, p-value, decision, conclusion

13-9 .

32) Referring to Table 13-4, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, he obtained an r2 value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

A) 2.8% B) 51.8% C) 72.6% D) 74.8% Answer: B Difficulty: Moderate Keywords: coefficient of multiple determination 33) Referring to Table 13-4, which of the following values for the level of significance is the smallest for which every explanatory variable is significant individually?

A) 0.01 B) 0.025 C) 0.05 D) 0.15 Answer: D Difficulty: Moderate Keywords: p-value, interpretation 34) Referring to Table 13-4, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?

A) 0.01 B) 0.025 C) 0.05 D) 0.15 Answer: A Difficulty: Moderate Keywords: p-value, interpretation 35) Referring to Table 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 Difficulty: Moderate Keywords: p-value, interpretation

13-10 .

36) Referring to Table 13-4, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of $40,000, having a family size of 4, and going to school a total of 13 years?

A) 11.43 B) 15.15 C) 24.88 D) 53.87 Answer: C Difficulty: Moderate Keywords: prediction of individual values 37) Referring to Table 13-4, what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square foot home (House = 100)?

A) $44.14 thousand B) $56.75 thousand C) $178.33 thousand D) $211.85 thousand Answer: D Difficulty: Moderate Keywords: prediction of individual values 38) Referring to Table 13-4, what minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square foot home (House = 50)?

A) $44.14 thousand B) $56.75 thousand C) $178.33 thousand D) $211.85 thousand Answer: A Difficulty: Moderate Keywords: prediction of individual values 39) Referring to Table 13-4, one individual in the sample had an annual income of $100,000, a family size of 10, and an education of 16 years. 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?

A) 7.40 B) 2.52 C) -2.52 D) -5.40 Answer: D Difficulty: Moderate Keywords: residual

13-11 .

40) Referring to Table 13-4, one individual in the sample had an annual income of $40,000, a family size of 1, and an education of 8 years. 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?

A) -6.99 B) -5.35 C) 5.40 D) 16.99 Answer: B Difficulty: Moderate Keywords: residual 41) Referring to Table 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) 5.286 B) 5.195 C) 3.945 D) -1.509 Answer: C Difficulty: Easy Keywords: t test on slope, test statistic 42) Referring to Table 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 pvalue is less than 0.01.

B) Income is significant in explaining house size and should be included in the model because its pvalue 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 Difficulty: Moderate Keywords: t test on slope, decision, conclusion 43) Referring to Table 13-4, suppose the builder wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

A) 5.286 B) 5.195 C) 3.945 D) -1.509 Answer: D Difficulty: Easy Keywords: t test on slope, test statistic

13-12 .

44) Referring to Table 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?

A) 0.0001 B) 0.0299 C) 0.726 D) 45.5340 Answer: D Difficulty: Moderate Keywords: F test on the entire regression, test statistic 45) Referring to Table 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) 46 for the numerator, 3 for the denominator B) 3 for the numerator, 49 for the denominator C) 46 for the numerator, 49 for the denominator D) 3 for the numerator, 46 for the denominator Answer: D Difficulty: Easy Keywords: F test on the entire regression, degrees of freedom 46) Referring to Table 13-4, at the 0.01 level of significance, what conclusion should the builder draw regarding the inclusion of School in the regression model?

A) School is significant in explaining house size and should be included in the model because its p-value is less than 0.01.

B) School is significant in explaining house size and should be included in the model because its p-value is more than 0.01.

C) School 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) School 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: D Difficulty: Moderate Keywords: t test on slope, critical value, p-value, decision, conclusion 47) Referring to Table 13-4, what are the regression degrees of freedom that are missing from the output?

A) 3 B) 46 C) 49 D) 50 Answer: A Difficulty: Easy Keywords: degrees of freedom

13-13 .

48) Referring to Table 13-4, what are the residual degrees of freedom that are missing from the output?

A) 3 B) 46 C) 49 D) 50 Answer: B Difficulty: Easy Keywords: degrees of freedom TABLE 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.

49) Referring to Table 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 Difficulty: Easy Keywords: coefficient of multiple determination, interpretation

13-14 .

50) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, critical value, p-value, decision, conclusion 51) Referring to Table 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 Difficulty: Moderate Keywords: coefficient of multiple determination 52) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, p-value 53) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, p-value 54) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, p-value 13-15 .

55) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, p-value 56) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, p-value 57) Referring to Table 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 Difficulty: Moderate Keywords: t test on slope, p-value 58) Referring to Table 13-5, which of the following values for α 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 Difficulty: Moderate Keywords: F test on the entire regression, p-value, interpretation 59) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values

13-16 .

60) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values 61) Referring to Table 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 Difficulty: Moderate Keywords: residual 62) Referring to Table 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 Difficulty: Moderate Keywords: residual 63) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, test statistic

13-17 .

64) Referring to Table 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 pvalue is less than 0.01.

B) Capital is significant in explaining corporate sales and should be included in the model because its pvalue 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 Difficulty: Moderate Keywords: t test on the slope, critical value, p-value, decision, conclusion 65) Referring to Table 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 Difficulty: Easy Keywords: F test on the entire regression, degrees of freedom TABLE 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 four variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X1), the amount of insulation in inches (X2), the number of windows in the house (X3), and the age of the furnace in years (X4). Given below are the Microsoft® Excel outputs of two regression models.

13-18 .

66) Referring to Table 13-6, the estimated value of the partial regression parameter β1 in Model 1 means that A) holding the effect of the other independent variables constant, an estimated expected $1 increase in heating costs is associated with a decrease in the daily minimum outside temperature by 4.51 degrees.

B) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in a decrease in heating costs by $4.51.

C) holding the effect of the other independent variables constant, a 1 degree increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by $4.51.

D) holding the effect of the other independent variables constant, a 1% increase in the daily minimum outside temperature results in an estimated decrease in mean heating costs by 4.51%.

Answer: C Difficulty: Easy Keywords: slope, interpretation 67) Referring to Table 13-6, what can we say about Model 1?

A) The model explains 77.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.1% of the sample variability of heating costs.

B) The model explains 75.1% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 77.7% of the sample variability of heating costs.

C) The model explains 80.8% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 75.7% of the sample variability of heating costs.

D) The model explains 75.7% of the sample variability of heating costs; after correcting for the degrees of freedom, the model explains 80.8% of the sample variability of heating costs.

Answer: C Difficulty: Moderate Keywords: adjusted r-square

13-19 .

68) Referring to Table 13-6, what is your decision and conclusion for the test H0: β2 = 0 vs. H1: β2 < 0 at the α = 0.01 level of significance using Model 1?

A) Do not reject H0 and conclude that the amount of insulation has a linear effect on heating cots.

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 negative linear effect on heating costs.

D) Do not reject H0 and conclude that the amount of insulation has a negative linear effect on heating costs.

Answer: C Difficulty: Easy Keywords: t test on slope, critical value, p-value, decision, conclusion 69) Referring to Table 13-6, what is the 90% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature using Model 1?

A) [6.58, 3.65] B) [6.24, 2.78] C) [5.94, 3.08] D) [2.37, 15.12] Answer: C Difficulty: Moderate Keywords: confidence interval, slope, interpretation 70) Referring to Table 13-6 and allowing for a 1% probability of committing a Type I error, what is the decision and conclusion for the test H0: β1 = β2 = β3 = β4 = 0 vs. H1: At least one βj ≠ 0, j = 1, 2, ..., 4 using Model 1?

A) Do not reject H0 and conclude that the four independent variables have significant individual linear effects on heating costs.

B) Reject H0 and conclude that the four independent variables taken as a group have significant linear effects on heating costs.

C) Do not reject H0 and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.

D) Reject H0 and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.

Answer: B Difficulty: Easy Keywords: F test on the entire regression, critical value, p-value, decision, conclusion 71) 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 Difficulty: Easy Keywords: slope, interpretation 72) True or False: The coefficient of multiple determination, r2, measures the proportion of variation in Y that is explained by X1 and X2.

Answer: TRUE Difficulty: Easy Keywords: coefficient of multiple determination 13-20 .

73) 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 Difficulty: Moderate Keywords: coefficient of multiple determination, properties 74) True or False: When an additional explanatory variable is introduced into a multiple regression model, the adjusted r2 can never decrease.

Answer: FALSE Difficulty: Moderate Keywords: adjusted r-square, properties 75) True or False: When an explanatory variable is dropped from a multiple regression model, the coefficient of multiple determination can increase.

Answer: FALSE Difficulty: Moderate Keywords: coefficient of multiple determination, properties 76) True or False: When an explanatory variable is dropped from a multiple regression model, the adjusted r2 can increase.

Answer: TRUE Difficulty: Moderate Keywords: adjusted r-square, properties 77) True or False: The slopes in a multiple regression model are called net regression coefficients.

Answer: TRUE Difficulty: Easy Keywords: slope 78) True or False: In calculating the standard error of the estimate, SYX = , 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 Difficulty: Easy Keywords: standard error of estimate 79) 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 Difficulty: Easy Keywords: sum of squares, properties 80) 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 Difficulty: Easy Keywords: coefficient of multiple determination, interpretation 13-21 .

81) 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 Difficulty: Easy Keywords: coefficient of multiple determination, properties 82) 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 24.911.

Answer: FALSE Difficulty: Easy Keywords: sum of squares, standard error of estimate, properties 83) True or False: A multiple regression is called "multiple" because it has several data points.

Answer: FALSE Difficulty: Easy Keywords: properties, interpretation 84) True or False: A multiple regression is called "multiple" because it has several explanatory variables.

Answer: TRUE Difficulty: Easy Keywords: properties, interpretation 85) True or False: If you have taken into account all relevant explanatory factors, the residuals from a multiple regression model should be random.

Answer: TRUE Difficulty: Moderate Keywords: residual, properties 86) True or False: Multiple regression is the process of using several independent variables to predict a number of dependent variables.

Answer: FALSE Difficulty: Easy Keywords: properties 87) 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 F test.

Answer: TRUE Difficulty: Easy Keywords: F test on the entire regression 88) 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 Difficulty: Moderate Keywords: coefficient of multiple determination, interpretation

13-22 .

89) 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 Difficulty: Easy Keywords: t test on slope, test statistic 90) 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 Difficulty: Easy Keywords: coefficient multiple determination, sum of squares, properties 91) 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 Difficulty: Easy Keywords: coefficient multiple determination, sum of squares, properties 92) 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 Difficulty: Easy Keywords: coefficient multiple determination, sum of squares, properties 93) 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 Difficulty: Easy Keywords: coefficient multiple determination, sum of squares, properties

13-23 .

TABLE 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 (credits) and total SAT scores of each. She takes a sample of students and generates the following Microsoft® Excel output:

94) Referring to Table 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 Difficulty: Easy Keywords: slope, interpretation 95) Referring to Table 13-7, the net regression coefficient of X2 is ________.

Answer: 0.001443 Difficulty: Easy Keywords: slope, interpretation 96) Referring to Table 13-7, the predicted GPA for a student carrying 15 course units and having a total SAT of 1,100 is ________.

Answer: 2.472 Difficulty: Moderate Keywords: prediction of individual values 97) Referring to Table 13-7, the value of the coefficient of multiple determination, r2Y.12, is ________.

Answer: 0.839 Difficulty: Easy Keywords: coefficient of multiple determination

13-24 .

98) Referring to Table 13-7, the value of the adjusted coefficient of multiple determination, r2adj, is ________.

Answer: 0.732 Difficulty: Easy Keywords: adjusted r-square 99) Referring to Table 13-7, the department head wants to test H0: β1 = β2 = 0. The appropriate alternative hypothesis is ________.

Answer: at least one βi ≠ 0.

Difficulty: Easy Keywords: F test on the entire regression, form of hypothesis 100) Referring to Table 13-7, the department head wants to test H0: β1 = β2 = 0. The critical value of the F test for a level of significance of 0.05 is ________.

Answer: 9.55 Difficulty: Easy Keywords: F test on the entire regression, critical value 101) Referring to Table 13-7, the department head wants to test H0: β1 = β2 = 0. The value of the F test statistic is ________.

Answer: 7.813 Difficulty: Easy Keywords: F test on the entire regression, test statistic 102) Referring to Table 13-7, the department head wants to test H0: β1 = β2 = 0. The p-value of the test is ________.

Answer: 0.0646 Difficulty: Easy Keywords: F test on the entire regression, p-value 103) True or False: Referring to Table 13-7, the department head wants to test H0: β1 = β2 = 0. At a level of significance of 0.05, the null hypothesis is rejected.

Answer: FALSE Difficulty: Easy Keywords: F test on the entire regression, decision 104) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, critical value 105) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, test statistic 13-25 .

106) Referring to Table 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 Difficulty: Easy Keywords: t test on slope, p-value 107) True or False: Referring to Table 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 β1 ≠ 0.

Answer: TRUE Difficulty: Moderate Keywords: t test on slope, decision, conclusion 108) Referring to Table 13-7, the department head decided to construct a 95% confidence interval for β1. The confidence interval is from ________ to ________.

Answer: -0.4468 to -0.0478 Difficulty: Moderate Keywords: slope, confidence interval TABLE 13-8 A financial analyst wanted to examine the relationship between salary (in $1,000) and four variables: age (X1 = Age), experience in the field (X2 = Exper), number of degrees (X3 = Degrees), and number of previous jobs in the field (X4 = Prevjobs). He took a sample of 20 employees and obtained the following Microsoft® Excel output:

109) Referring to Table 13-8, the estimate of the unit change in the mean of Y per unit change in X4, taking into account the effects of the other three variables, is ________.

Answer: -0.504 13-26 .

Difficulty: Easy Keywords: slope, interpretation 110) Referring to Table 13-8, the net regression coefficient of X2 is ________.

Answer: -0.107 Difficulty: Easy Keywords: slope, interpretation 111) Referring to Table 13-8, the predicted salary for a 35-year-old person with 10 years of experience, 3 degrees, and 1 previous job is ________.

Answer: 57.2 Difficulty: Moderate Keywords: prediction of individual values 112) Referring to Table 13-8, the value of the coefficient of multiple determination, r2Y.1234, is ________.

Answer: 0.984 Difficulty: Easy Keywords: coefficient of multiple determination 113) Referring to Table 13-8, the value of the adjusted coefficient of multiple determination, adjusted r2, is ________.

Answer: 0.979 Difficulty: Easy Keywords: adjusted r-square 114) Referring to Table 13-8, the analyst wants to use an F test to test H0: β1 = β2 = β3 = β4 = 0. The appropriate alternative hypothesis is ________.

Answer: at least one βi ≠ 0 Difficulty: Easy Keywords: F test on the entire regression, form of hypothesis 115) Referring to Table 13-8, the critical value of an F test on the entire regression for a level of significance of 0.01 is ________.

Answer: 4.89 Difficulty: Easy Keywords: F test on the entire regression, critical value 116) Referring to Table 13-8, the value of the F-statistic for testing the significance of the entire regression is ________.

Answer: 224.160 Difficulty: Easy Keywords: F test on the entire regression, test statistic 117) Referring to Table 13-8, the p-value of the F test for the significance of the entire regression is ________.

Answer: 0.0001 Difficulty: Easy Keywords: F test on the entire regression, p-value 13-27 .

118) True or False: Referring to Table 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 Difficulty: Easy Keywords: F test on the entire regression, decision 119) Referring to Table 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X3. For a level of significance of 0.01, the critical values of the test are ________.

Answer: ±2.9467 Difficulty: Easy Keywords: t test on the slope, critical value 120) Referring to Table 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X3. The value of the test statistic is ________.

Answer: 9.102 Difficulty: Easy Keywords: t test on the slope, test statistic 121) Referring to Table 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X3. The p-value of the test is ________.

Answer: 0.0001 Difficulty: Easy Keywords: t test on the slope, p-value 122) True or False: Referring to Table 13-8, the analyst wants to use a t test to test for the significance of the coefficient of X3. At a level of significance of 0.01, the department head would decide that β3 ≠ 0.

Answer: TRUE Difficulty: Easy Keywords: t test on the slope, decision, conclusion 123) Referring to Table 13-8, the analyst decided to construct a 99% confidence interval for β3. The confidence interval is from ________ to ________.

Answer: 4.944 to 9.678 Difficulty: Moderate Keywords: slope, confidence interval

13-28 .

TABLE 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, the number of firms that manufacture automobile parts in and around the city, the number of new business starts in the last year, population density of the city, percentage of local taxes on gasoline, and the number of people using public transportation. 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.

124) Referring to Table 13-9, what is the value of the coefficient of multiple determination?

A) 0.2225 B) 0.4576 C) 0.5626 D) 0.6472 Answer: C Explanation: C)

Difficulty: Difficult Keywords: coefficient of multiple determination 125) Referring to Table 13-9, the value of adjusted r2 is ________.

A) 0.4576 B) 0.5626 C) 0.6472 D) 95.5414 Answer: A Difficulty: Moderate Keywords: adjusted r-square 126) Referring to Table 13-9, if variables that measure the number of new business starts in the last year and population density of the city were removed from the multiple regression model, which of the following would be true?

A) The adjusted r2 will definitely increase.

B) The adjusted r2 cannot increase.

C) The coefficient of multiple determination will not increase.

D) The coefficient of multiple determination will definitely increase.

Answer: C Difficulty: Moderate Keywords: coefficient of multiple determination, adjusted r-square, properties

13-29 .

TABLE 13-10 You worked as an intern at We Always Win Car Insurance Company last summer. You noticed that individual car insurance premiums depend very much on the age of the individual, the number of traffic tickets received by the individual, and the population density of the city in which the individual lives.

You performed a regression analysis in Microsoft® Excel and obtained the following information:

127) Referring to Table 13-10, the proportion of the total variability in insurance premiums that can be explained by AGE, TICKETS, and DENSITY is ________.

Answer: 0.40 Difficulty: Easy Keywords: coefficient of multiple determination, interpretation 128) Referring to Table 13-10, the adjusted r2 is _________.

Answer: 0.23 Difficulty: Easy Keywords: adjusted r-square 129) Referring to Table 13-10, the standard error of the estimate is _________.

Answer: 50.0 Difficulty: Easy Keywords: standard error of estimate 130) Referring to Table 13-10, the estimated mean change in insurance premiums for every two additional tickets received is ________.

Answer: 42.5 Difficulty: Difficult Keywords: slope, interpretation 13-30 .

131) Referring to Table 13-10, the 99% confidence interval for the change in mean insurance premiums of a person who has become one year older (i.e., the slope coefficient for AGE) is -0.82 ± ________.

Answer: 2.69 Difficulty: Moderate Keywords: slope, interpretation, confidence interval 132) Referring to Table 13-10, the total degrees of freedom that are missing in the ANOVA table should be ________.

Answer: 14 Difficulty: Easy Keywords: degrees of freedom 133) Referring to Table 13-10, the regression sum of squares that is missing in the ANOVA table should be ________.

Answer: 17,982.72 Difficulty: Easy Keywords: sum of squares 134) Referring to Table 13-10, the residual mean squares (MSE) that are missing in the ANOVA table should be ________.

Answer: 2,499.71 Difficulty: Easy Keywords: mean squares 135) Referring to Table 13-10, to test the significance of the multiple regression model, what is the form of the null hypothesis?

A) H0: β0 B) H0: β1 C) H0: β1 = β2 = β3 D) H0: β0 = β1 = β2 = β3 Answer: C Difficulty: Easy Keywords: F test on the entire regression, form of hypothesis 136) Referring to Table 13-10, to test the significance of the multiple regression model, the value of the test statistic is ________.

Answer: 2.40 Difficulty: Easy Keywords: F test on the entire regression, test statistic 137) Referring to Table 13-10, to test the significance of the multiple regression model, the p-value of the test statistic in the sample is ________.

Answer: 0.12 Difficulty: Easy Keywords: F test on the entire regression, p-value

13-31 .

138) Referring to Table 13-10, to test the significance of the multiple regression model, what are the degrees of freedom?

Answer: 3 for the numerator, 11 for the denominator Difficulty: Easy Keywords: F test on the entire regression, degrees of freedom 139) True or False: Referring to Table 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: FALSE Difficulty: Easy Keywords: F test on the entire regression, decision 140) True or False: Referring to Table 13-10, the multiple regression model is significant at a 10% level of significance.

Answer: FALSE Difficulty: Easy Keywords: F test on the entire regression, decision, conclusion 141) 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 Difficulty: Easy Keywords: dummy variable, properties 142) 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 two independent variables interact.

Answer: B Difficulty: Easy Keywords: dummy variable, properties 143) 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 two independent variables contribute significantly to the regression model.

D) the relationship between X1 and Y changes for differing values of X2.

Answer: D Difficulty: Moderate Keywords: interaction, properties

13-32 .

144) 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 log(CRDTLIM), log(APR), log(ADVT), and GENDER as the independent variables. The estimated model was = 2.28 - 0.29 log(CRDTLIM) + 5.77 log(APR) + 2.35 log(ADVT) + 0.39 SEX What is the correct interpretation for the estimated coefficient for GENDER? 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 Difficulty: Easy Keywords: dummy variable, slope, interpretation

13-33 .

TABLE 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 X3 = 1 if afternoon session, 0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + β1X1 + β2X2 + β3X3 + β4X1X2 + β5X1X3 + ε Partial output from Microsoft® Excel follows:

145) Referring to Table 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 Difficulty: Moderate Keywords: model building

13-34 .

146) Referring to Table 13-11, what null hypothesis would you test to determine whether the slope of the linear relationship between weight loss (Y) and time in the program (X1) varies according to time of session?

A) H0: β1 = β2 = β3 = β4 = β5 = 0 B) H0: β2 = β3 = β4 = β5 = 0 C) H0: β4 = β5 = 0 D) H0: β2 = β3 = 0 Answer: C Difficulty: Moderate Keywords: interaction, form of hypothesis 147) Referring to Table 13-11, in terms of the βs in the model, give the mean change in weight loss (Y) for every one-month increase in time in the program (X1) when attending the evening session.

A) β1 + β4 B) β1 + β5 C) β1 D) β4 + β5 Answer: C Difficulty: Moderate Keywords: interaction, slope, interpretation 148) Referring to Table 13-11, in terms of the βs in the model, give the mean change in weight loss (Y) for every one-month increase in time in the program (X1) when attending the morning session.

A) β1 + β4 B) β1 + β5 C) β1 D) β4 + β5 Answer: A Difficulty: Moderate Keywords: interaction, slope, interpretation 149) Referring to Table 13-11, in terms of the βs in the model, give the mean change in weight loss (Y) for every one-month increase in time in the program (X1) when attending the afternoon session.

A) β1 + β4 B) β1 + β5 C) β1 D) β4 + β5 Answer: B Difficulty: Moderate Keywords: interaction, slope, interpretation 150) True or False: Referring to Table 13-11, the overall model for predicting weight loss (Y) is statistically significant at the 0.05 level.

Answer: TRUE Difficulty: Easy Keywords: interaction, F test on the entire regression, decision, conclusion 13-35 .

151) Referring to Table 13-11, which of the following statements is supported by the analysis shown?

A) There is sufficient evidence (at α = 0.05) of curvature in the relationship between weight loss (Y) and months in program(X1).

B) There is sufficient evidence (at α = 0.05) to indicate that the relationship between weight loss (Y) and months in program (X1) depends on session time.

C) There is sufficient evidence (at α = 0.10) to indicate that the session time (morning, afternoon, evening) affects weight loss (Y).

D) There is insufficient evidence (at α = 0.10) to indicate that the relationship between weight loss (Y) and months in program(X1) depends on session time.

Answer: D Difficulty: Difficult Keywords: interaction, t test on slope, decision, conclusion 152) In a multiple regression model, the adjusted 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 Difficulty: Difficult Keywords: adjusted r-square, properties

13-36 .

TABLE 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 one of the three jurisdictions: on campus, in downtown and off campus, or outside of downtown and off campus. The population regression model hypothesized is Yi = α + β1X1i + β2X2i + β3X3i + ε where Y is the meter price X1 is the number of blocks to the quad X2 is a dummy variable that takes the value 1 if the meter is located in downtown and off campus and the value 0 otherwise X3 is a dummy variable that takes the value 1 if the meter is located outside of downtown and off campus, and the value 0 otherwise The following Microsoft® Excel results are obtained.

153) Referring to Table 13-12, what is the correct interpretation for the estimated coefficient for X2?

A) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking on campus, and parking outside of downtown and off campus is $0.24 per hour.

B) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in downtown and off campus, and parking on campus is $0.24 per hour.

C) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in downtown and off campus, and parking outside of downtown and off campus is $0.24 per hour.

D) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in downtown and off campus, and parking either outside of downtown and off campus or on campus is $0.24 per hour.

Answer: B 13-37 .

Difficulty: Moderate Keywords: dummy variable, slope, interpretation 154) Referring to Table 13-12, predict the meter rate per hour if one parks outside of downtown and off campus three blocks from the quad.

A) $0.0139 B) $0.2589 C) $0.2604 D) $0.4981 Answer: D Difficulty: Easy Keywords: prediction of individual values 155) Referring to Table 13-12, if one is already outside of downtown and off campus but decides to park three more blocks from the quad, the estimated mean parking meter rate will A) decrease by 0.0045.

B) decrease by 0.0135.

C) decrease by 0.0139.

D) decrease by 0.4979.

Answer: B Difficulty: Moderate Keywords: dummy variable, slope, interpretation 156) 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 Difficulty: Moderate Keywords: interaction, properties 157) 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 Difficulty: Easy Keywords: dummy variable, slope, interpretation 158) 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 nonrepeaters, with all other factors the same.

Answer: TRUE Difficulty: Moderate Keywords: dummy variable, slope, interpretation

13-38 .

TABLE 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

159) Referring to Table 13-13, holding constant the effect of city, each additional increase of 1% in the mortgage rate would lead to an estimated increase of ________ per capita in the mean demand.

Answer: $500 Difficulty: Moderate Keywords: slope, interpretation 160) Referring to Table 13-13, the effect of living in San Francisco rather than Los Angeles is to increase the mean demand by an estimated ________ per capita.

Answer: $800 Difficulty: Moderate Keywords: dummy variable, slope, interpretation 161) Referring to Table 13-13, the predicted demand in Los Angeles when the mortgage rate is 8% is ________ per capita.

Answer: $5,000 Difficulty: Moderate Keywords: prediction of individual values, dummy variable 162) Referring to Table 13-13, the predicted demand in San Francisco when the mortgage rate is 10% is per capita________.

Answer: $6,800 Difficulty: Moderate Keywords: prediction of individual values, dummy variable 163) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values, dummy variable

13-39 .

164) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values, dummy variable TABLE 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.

165) Referring to Table 13-14, the predicted mileage for a 300 horsepower, 6-cylinder car is ________.

Answer: 25 Difficulty: Moderate Keywords: prediction of individual values, dummy variable 166) Referring to Table 13-14, the predicted mileage for a 200 horsepower, 4-cylinder car is ________.

Answer: 30 Difficulty: Moderate Keywords: prediction of individual values, dummy variable 167) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values, dummy variable 168) Referring to Table 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 Difficulty: Moderate Keywords: prediction of individual values, dummy variable 13-40 .

TABLE 13-15 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state.

Following is the multiple regression output with Y = % Passing as the dependent variable, Attendance,

= Salaries and

=:%

= Spending:

169) Referring to Table 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 8.50% when daily average of percentage of students attending class increases by 1%.

B) The daily mean of the percentage of students attending class is expected to go up by an estimated 8.50% when the 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 8.50% when daily average of the percentage of students attending class increases by 1%, holding constant the effects of all the remaining independent variables.

D) The daily mean of the percentage of students attending class is expected to go up by an estimated 8.50% when the percentage of students passing the proficiency test increases by 1%, holding constant the effects of all the remaining independent variables.

Answer: C Difficulty: Moderate Keywords: interpretation, slope

13-41 .

170) Referring to Table 13-15, which of the following is a correct statement?

A) 62.88% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil.

B) 62.88% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil, after adjusting for the number of predictors and sample size.

C) 62.88% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, holding constant the effect of mean teacher salary and instructional spending per pupil.

D) 62.88% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, after adjusting for the effect of mean teacher salary and instructional spending per pupil.

Answer: A Difficulty: Moderate Keywords: interpretation, coefficient of multiple determination 171) Referring to Table 13-15, which of the following is a correct statement?

A) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil.

B) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, mean teacher salary, and instructional spending per pupil, after adjusting for the number of predictors and sample size.

C) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, holding constant the effect of mean teacher salary and instructional spending per pupil.

D) 60.29% of the total variation in the percentage of students passing the proficiency test can be explained by daily mean of the percentage of students attending class, after adjusting for the effect of mean teacher salary and instructional spending per pupil.

Answer: B Difficulty: Moderate Keywords: interpretation, adjusted r-square 172) Referring to Table 13-15, what is the standard error of estimate?

Answer: 10.46 (%) Difficulty: Easy Keywords: standard error of estimate 173) Referring to Table 13-15, predict the percentage of students passing the proficiency test for a school which has a daily mean of 95% of students attending class, a mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

Answer: 66.20 (%) Difficulty: Easy Keywords: prediction of individual values

13-42 .

174) Referring to Table 13-15, estimate the mean percentage of students passing the proficiency test for all the schools that have a daily mean of 95% of students attending class, an mean teacher salary of 40,000 dollars, and an instructional spending per pupil of 2,000 dollars.

Answer: 66.20 (%) Difficulty: Easy Keywords: estimation of mean values 175) Referring to Table 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, taking into account the effect of all the other independent variables?

A) H0: β0 = 0 B) H0: β1 = 0 C) H0: β2 = 0 D) H0: β3 = 0 Answer: D Difficulty: Easy Keywords: t test on slope, form of hypothesis 176) Referring to Table 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, taking into account the effect of all the other independent variables?

A) H1: β0 ≠ 0 B) H1: β1 ≠ 0 C) H1: β2 ≠ 0 D) H1: β3 ≠ 0 Answer: D Difficulty: Easy Keywords: t test on slope, form of hypothesis 177) Referring to Table 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, taking into account the effect of all the other independent variables?

Answer: 1.2879 Difficulty: Easy Keywords: t test on slope, test statistic 178) Referring to Table 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, taking into account the effect of all the other independent variables?

Answer: 0.2047 Difficulty: Easy Keywords: t test on slope, p-value 179) True or False: Referring to Table 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, taking into account the effect of all the other independent variables.

Answer: FALSE Difficulty: Easy Keywords: t test on slope, decision 13-43 .

180) True or False: Referring to Table 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 all the other independent variables at a 5% level of significance.

Answer: FALSE Difficulty: Easy Keywords: t test on slope, conclusion 181) Referring to Table 13-15, which of the following is the correct null hypothesis to test whether daily mean of the percentage of students attending class has any effect on percentage of students passing the proficiency test, taking into account the effect of all the other independent variables?

A) H0: β0 = 0 B) H0: β1 = 0 C) H0: β2 = 0 D) H0: β3 = 0 Answer: B Difficulty: Easy Keywords: t test on slope, form of hypothesis 182) Referring to Table 13-15, which of the following is the correct alternative hypothesis to test whether daily mean of the percentage of students attending class has any effect on percentage of students passing the proficiency test, taking into account the effect of all the other independent variables?

A) H1: β0 ≠ 0 B) H1: β1 ≠ 0 C) H1: β2 ≠ 0 D) H1: β3 ≠ 0 Answer: B Difficulty: Easy Keywords: t test on slope, form of hypothesis 183) Referring to Table 13-15, what is the value of the test statistic when testing whether daily mean of the percentage of students attending class has any effect on percentage of students passing the proficiency test, taking into account the effect of all the other independent variables?

Answer: 7.8929 Difficulty: Easy Keywords: t test on slope, test statistic 184) Referring to Table 13-15, what is the p-value of the test statistic when testing whether daily average of the percentage of students attending class has any effect on percentage of students passing the proficiency test, taking into account the effect of all the other independent variables?

Answer: 6.73E−10 or virtually zero Difficulty: Easy Keywords: t test on slope, p-value

13-44 .

185) True or False: Referring to Table 13-15, the null hypothesis should be rejected at a 5% level of significance when testing whether daily mean of the percentage of students attending class has any effect on percentage of students passing the proficiency test, taking into account the effect of all the other independent variables.

Answer: TRUE Difficulty: Easy Keywords: t test on slope, decision 186) True or False: Referring to Table 13-15, there is sufficient evidence that daily mean of the percentage of students attending class has an effect on percentage of students passing the proficiency test, while holding constant the effect of all the other independent variables at a 5% level of significance.

Answer: TRUE Difficulty: Easy Keywords: t test on slope, conclusion 187) Referring to Table 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: β0 = β1 = β2 = β3 = 0 B) H0: β1 = β2 = β3 = 0 C) H0: β0 = β1 = β2 = β3 ≠ 0 D) H0: β1 = β2 = β3 ≠ 0 Answer: B Difficulty: Easy Keywords: F test on the entire regression, form of hypothesis 188) Referring to Table 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: β0 = β1 = β2 = β3 ≠ 0 B) H1: β1 = β2 = β3 ≠ 0 C) H1: At least one of βj ≠ 0 for j = 0, 1, 2, 3 D) H1: At least one of βj ≠ 0 for j = 1, 2, 3 Answer: D Difficulty: Easy Keywords: F test on the entire regression, form of hypothesis 189) True or False: Referring to Table 13-15, the null hypothesis H0: β1 = β2 = β3 = 0 implies that percentage of students passing the proficiency test is not affected by any of the explanatory variables.

Answer: TRUE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 190) True or False: Referring to Table 13-15, the null hypothesis H0: β1 = β2 = β3 = 0 implies that percentage of students passing the proficiency test is not affected by some of the explanatory variables.

Answer: FALSE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 13-45 .

191) True or False: Referring to Table 13-15, the null hypothesis H0: β1 = β2 = β3 = 0 implies that percentage of students passing the proficiency test is not related to any of the explanatory variables.

Answer: TRUE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 192) True or False: Referring to Table 13-15, the null hypothesis H0: β1 = β2 = β3 = 0 implies that percentage of students passing the proficiency test is not related to one of the explanatory variables.

Answer: FALSE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 193) True or False: Referring to Table 13-15, the alternative hypothesis H1: At least one of βj ≠ 0 for j = 1, 2, 3 implies that percentage of students passing the proficiency test is related to all of the explanatory variables.

Answer: FALSE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 194) True or False: Referring to Table 13-15, the alternative hypothesis H1: At least one of βj ≠ 0 for j = 1, 2, 3 implies that percentage of students passing the proficiency test is related to at least one of the explanatory variables.

Answer: TRUE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 195) True or False: Referring to Table 13-15, the alternative hypothesis H1: At least one of βj ≠ 0 for j = 1, 2, 3 implies that percentage of students passing the proficiency test is affected by all of the explanatory variables.

Answer: FALSE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 196) True or False: Referring to Table 13-15, the alternative hypothesis H1: At least one of βj ≠ 0 for j = 1, 2, 3 implies that percentage of students passing the proficiency test is affected by at least one of the explanatory variables.

Answer: TRUE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 197) Referring to Table 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: 3 and 43 Difficulty: Easy Keywords: F test on the entire regression, degrees of freedom

13-46 .

198) Referring to Table 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: 24.2802 Difficulty: Easy Keywords: F test on the entire regression, test statistic 199) Referring to Table 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: 2.3853E−09 or virtually zero Difficulty: Easy Keywords: F test on the entire regression, p-value 200) True or False: Referring to Table 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 Difficulty: Easy Keywords: F test on the entire regression, decision 201) True or False: Referring to Table 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 Difficulty: Easy Keywords: F test on the entire regression, conclusion 202) True or False: Referring to Table 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 Difficulty: Easy Keywords: F test on the entire regression, conclusion 203) True or False: Referring to Table 13-15, there is sufficient evidence that all of the explanatory variables are related to the percentage of students passing the proficiency test at a 5% level of significance.

Answer: FALSE Difficulty: Moderate Keywords: F test on the entire regression, conclusion 204) True or False: Referring to Table 13-15, there is sufficient evidence that the percentage of students passing the proficiency test depends on all of the explanatory variables at a 5% level of significance.

Answer: FALSE Difficulty: Moderate Keywords: F test on the entire regression, conclusion

13-47 .

205) Referring to Table 13-15, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one dollar increase in instructional spending per pupil on the mean percentage of students passing the proficiency test?

Answer: −0.0034 (%) to 0.0153 (%) Difficulty: Moderate Keywords: confidence interval, slope, interpretation 206) Referring to Table 13-15, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one dollar increase in mean teacher salary on the mean percentage of students passing the proficiency test?

Answer: −0.0013 (%) to 0.0013 (%) Difficulty: Moderate Keywords: confidence interval, slope, interpretation 207) True or False: Referring to Table 13-15, you can conclude that mean teacher salary has no impact on the mean percentage of students passing the proficiency test at a 5% level of significance using the 95% confidence interval estimate for β2.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, t test on slope, decision 208) True or False: Referring to Table 13-15, you can conclude that instructional spending per pupil has no impact on the mean percentage of students passing the proficiency test, taking into account the effect of all the other independent variables, at a 5% level of significance using the 95% confidence interval estimate for β3.

Answer: TRUE Difficulty: Easy Keywords: confidence interval, t test on slope, decision 209) True or False: Referring to Table 13-15, you can conclude that mean teacher salary individually has no impact on the mean percentage of students passing the proficiency test, taking into account the effect of all the other independent variables, at a 1% level of significance based solely on the 95% confidence interval estimate for β2.

Answer: TRUE Difficulty: Moderate Keywords: confidence interval, t test on slope, decision 210) True or False: Referring to Table 13-15, you can conclude that instructional spending per pupil individually has no impact on the mean percentage of students passing the proficiency test, taking into account the effect of all the other independent variables, at a 1% level of significance based solely on the 95% confidence interval estimate for β3.

Answer: TRUE Difficulty: Moderate Keywords: confidence interval, t test on slope, decision

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211) True or False: Referring to Table 13-15, you can conclude that average teacher salary individually has no impact on the mean percentage of students passing the proficiency test, taking into account the effect of all the other independent variables, at a 10% level of significance based solely on the 95% confidence interval estimate for β2.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, t test on slope, decision 212) True or False: Referring to Table 13-15, you can conclude that instructional spending per pupil individually has no impact on the mean percentage of students passing the proficiency test, taking into account the effect of all the other independent variables, at a 10% level of significance based solely on the 95% confidence interval estimate for β3.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, t test on slope, decision TABLE 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 171 different vehicle models were collected: Accel Time: Acceleration time in sec.

Cargo Vol: Cargo volume in cu. ft.

HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.

13-49 .

The various residual plots are as shown below.

13-50 .

The coefficient of multiple determination for the regression model using each of the 5 variables Xj as the dependent variable and all other X variables as independent variables (Rj2) are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632.

213) Referring to Table 13-16, what is the correct interpretation for the estimated coefficient for Cargo Vol? A) As the 0 to 60 miles per hour acceleration time increases by one second, the mean cargo volume will increase by an estimated 0.0259 cubic foot, without taking into consideration all the other independent variables included in the model.

B) As the cargo volume increases by one cubic foot, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds, without taking into consideration all the other independent variables included in the model.

C) As the 0 to 60 miles per hour acceleration time increases by one second, the mean cargo volume will increase by an estimated 0.0259 cubic foot, taking into consideration all the other independent variables included in the model.

D) As the cargo volume increases by one cubic foot, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds, taking into consideration all the other independent variables included in the model.

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Answer: D Difficulty: Moderate Keywords: slope, interpretation 214) Referring to Table 13-16, what is the correct interpretation for the estimated coefficient for HP? A) As the horsepower increases by one unit, the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0200 seconds, without taking into consideration all the other independent variables included in the model.

B) As the 0 to 60 miles per hour acceleration time increases by one second, the mean horsepower will decrease by an estimated 0.0200 unit, without taking into consideration all the other independent variables included in the model.

C) As the horsepower increases by one unit, the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0200 seconds, taking into consideration all the other independent variables included in the model.

D) As the 0 to 60 miles per hour acceleration time increases by one second, the mean horsepower will decrease by an estimated 0.0200 unit, taking into consideration all the other independent variables included in the model.

Answer: C Difficulty: Moderate Keywords: slope, interpretation 215) Referring to Table 13-16, what is the correct interpretation for the estimated coefficient for MPG? A) As the miles per gallon decreases by one unit, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0620 seconds, without taking into consideration all the other independent variables included in the model.

B) As the 0 to 60 miles per hour acceleration time decreases by one second, the mean miles per gallon will increase by an estimated 0.0620 unit, without taking into consideration all the other independent variables included in the model.

C) As the miles per gallon decreases by one unit, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0620 seconds, taking into consideration all the other independent variables included in the model.

D) As the 0 to 60 miles per hour acceleration time decreases by one second, the mean miles per gallon will increase by an estimated 0.0620 unit, taking into consideration all the other independent variables included in the model.

Answer: C Difficulty: Difficult Keywords: slope, interpretation 216) Referring to Table 13-16, what is the correct interpretation for the estimated coefficient for SUV? A) The mean 0 to 60 miles per hour acceleration time of an SUV is estimated to be 0.7679 seconds higher than that of a coupe after considering the effect of all the other independent variables in the model.

B) The mean 0 to 60 miles per hour acceleration time of an SUV is estimated to be 0.7679 seconds higher than that of a sedan after considering the effect of all the other independent variables in the model.

C) The mean 0 to 60 miles per hour acceleration time of an SUV is estimated to be 0.7679 seconds lower than that of a coupe after considering the effect of all the other independent variables in the model.

D) The mean 0 to 60 miles per hour acceleration time of an SUV is estimated to be 0.7679 seconds lower than that of a sedan after considering the effect of all the other independent variables in the model.

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Answer: A Difficulty: Difficult Keywords: slope, interpretation, dummy variable 217) Referring to Table 13-16, what is the correct interpretation for the estimated coefficient for Sedan?

A) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.6427 seconds higher than that of a coupe after considering the effect of all the other independent variables in the model.

B) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.6427 seconds higher than that of an SUV after considering the effect of all the other independent variables in the model.

C) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.6427 seconds lower than that of a coupe after considering the effect of all the other independent variables in the model.

D) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.6427 seconds lower than that of an SUV after considering the effect of all the other independent variables in the model.

Answer: A Difficulty: Difficult Keywords: slope, interpretation, dummy variable 218) True or False: Referring to Table 13-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.1252 seconds higher than that of an SUV. Answer: FALSE Difficulty: Moderate Keywords: slope, interpretation, dummy variable 219) True or False: Referring to Table 13-16, the 0 to 60 miles per hour acceleration time of an SUV is predicted to be 0.1252 seconds higher than that of a sedan.

Answer: TRUE Difficulty: Moderate Keywords: slope, interpretation, dummy variable 220) True or False: Referring to Table 13-16, the 0 to 60 miles per hour acceleration time of a coupe is predicted to be 0.6427 seconds lower than that of a sedan.

Answer: TRUE Difficulty: Moderate Keywords: slope, interpretation, dummy variable 221) True or False: Referring to Table 13-16, the 0 to 60 miles per hour acceleration time of a coupe is predicted to be 0.7679 seconds lower than that of an SUV. Answer: TRUE Difficulty: Moderate Keywords: slope, interpretation, dummy variable 222) True or False: Referring to Table 13-16, the 0 to 60 miles per hour acceleration time of a coupe is predicted to be 0.7679 seconds higher than that of a sedan.

Answer: FALSE Difficulty: Moderate Keywords: slope, interpretation, dummy variable

13-53 .

223) True or False: Referring to Table 13-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.7679 seconds higher than that of an SUV. Answer: FALSE Difficulty: Moderate Keywords: slope, interpretation, dummy variable 224) True or False: Referring to Table 13-16, the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.6427 seconds higher than that of an SUV. Answer: FALSE Difficulty: Moderate Keywords: slope, interpretation, dummy variable 225) Referring to Table 13-16, what is the value of the test statistic to determine whether Cargo Vol makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Answer: 2.5518 Difficulty: Easy Keywords: model building, t test on slope, test statistic 226) Referring to Table 13-16, what is the p-value of the test statistic to determine whether Cargo Vol makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Answer: 0.0116 Difficulty: Easy Keywords: model building, t test on slope, p-value 227) True or False: Referring to Table 13-16, there is enough evidence to conclude that Cargo Vol makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

Answer: TRUE Difficulty: Easy Keywords: model building, t test on slope, decision 228) Referring to Table 13-16, what is the value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Answer: -11.3307 Difficulty: Easy Keywords: model building, t test on slope, test statistic 229) Referring to Table 13-16, what is the p-value of the test statistic to determine whether HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Answer: 0.0000 or virtually zero Difficulty: Easy Keywords: model building, t test on slope, p-value

13-54 .

230) True or False: Referring to Table 13-16, there is enough evidence to conclude that HP makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

Answer: TRUE Difficulty: Easy Keywords: model building, t test on slope, decision 231) Referring to Table 13-16, what is the value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Answer: -2.0464 Difficulty: Easy Keywords: model building, t test on slope, test statistic 232) Referring to Table 13-16, what is the p-value of the test statistic to determine whether MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Answer: 0.0423 Difficulty: Easy Keywords: model building, t test on slope, p-value 233) True or False: Referring to Table 13-16, there is enough evidence to conclude that MPG makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

Answer: TRUE Difficulty: Easy Keywords: model building, t test on slope, decision 234) Referring to Table 13-16, what is the value of the test statistic to determine whether SUV makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Answer: 1.7802 Difficulty: Easy Keywords: model building, t test on slope, test statistic 235) Referring to Table 13-16, what is the p-value of the test statistic to determine whether SUV makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance?

Answer: 0.0769 Difficulty: Easy Keywords: model building, t test on slope, p-value 236) True or False: Referring to Table 13-16, there is enough evidence to conclude that SUV makes a significant contribution to the regression model in the presence of the other independent variables at a 5% level of significance.

Answer: FALSE Difficulty: Easy Keywords: model building, t test on slope, decision

13-55 .

237) Referring to Table 13-16, ________ of the variation in Accel Time can be explained by the five independent variables after taking into consideration the number of independent variables and the number of observations.

Answer: 0.6313 or 63.13% Difficulty: Moderate Keywords: model building, adjusted r-square 238) Referring to Table 13-16, ________ of the variation in Accel Time can be explained by the five independent variables.

Answer: 0.6421 or 64.21% Difficulty: Moderate Keywords: model building, coefficient of multiple determination 239) Referring to Table 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 Difficulty: Moderate Keywords: assumption, homoscedasticity 240) Referring to Table 13-16, which of the following assumptions is most likely violated based on the residual plot for HP? A) linearity B) normality of errors C) independence of errors D) none Answer: A Difficulty: Moderate Keywords: assumption, linearity 241) Referring to Table 13-16, which of the following assumptions is most likely violated based on the normal probability plot?

A) linearity B) normality of errors C) equal variance D) none Answer: B Difficulty: Moderate Keywords: assumption, normality

13-56 .

242) True or False: Referring to Table 13-16, the error appears to be left-skewed.

Answer: TRUE Difficulty: Easy Keywords: assumption, normality 243) True or False: Referring to Table 13-16, the error appears to be right-skewed.

Answer: FALSE Difficulty: Easy Keywords: assumption, normality 244) True or False: Referring to Table 13-16, the error appears to be normally distributed.

Answer: FALSE Difficulty: Easy Keywords: assumption, normality TABLE 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), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1.

13-57 .

Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below:

245) Referring to Table 13-17 Model 1, which of the following is a correct statement?

A) On average, a worker who is a year older is estimated to stay jobless longer by approximately 32.66 weeks, while holding constant the effects of all the remaining independent variables.

B) On average, a worker who is a year older is estimated to stay jobless longer by approximately 1.29 weeks, while holding constant the effects of all the remaining independent variables.

C) On average, a worker who is a year older is estimated to stay jobless shorter by approximately 1.35 weeks, while holding constant the effects of all the remaining independent variables.

D) On average, a worker who is a year older is estimated to stay jobless longer by approximately 0.62 weeks, while holding constant the effects of all the remaining independent variables.

Answer: B Difficulty: Moderate Keywords: interpretation, slope 246) Referring to Table 13-17 Model 1, 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 1.35 weeks, while holding constant the effects of all the remaining independent variables.

B) On average, those who are in a management position are estimated to stay jobless shorter by approximately 5.22 weeks, while holding constant the effects of all the remaining independent variables.

C) On average, those who are in a management position are estimated to stay jobless shorter by approximately 14.30 weeks, while holding constant the effects of all the remaining independent variables.

D) On average, those who are in a management position are estimated to stay jobless shorter by approximately 24.82 weeks, while holding constant the effects of all the remaining independent variables.

Answer: D Difficulty: Moderate Keywords: interpretation, slope, dummy variable 13-58 .

247) Referring to Table 13-17 Model 1, which of the following is a correct statement?

A) 49.49% 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, the number of years of education received, the number of years at the previous job, marital status, whether the worker is the head of household, and whether the worker is a manager.

B) 49.49% 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, the number of years of education received, the number of years at the previous job, marital status, whether the worker is the head of household, and whether the worker is a manager, after adjusting for the number of predictors and sample size.

C) 49.49% 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, the number of years of education received, the number of years at the previous job, marital status, whether the worker is the head of household, and whether the worker is a manager, after adjusting for the level of significance D) 49.49% 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, the number of years of education received, the number of years at the previous job, marital status, whether the worker is the head of household, and whether the worker is a manager, holding constant the effect of all the independent variables.

Answer: A Difficulty: Moderate Keywords: interpretation, coefficient of multiple determination 248) Referring to Table 13-17 Model 1, which of the following is a correct statement?

A) 40.30% 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, the number of years of education received, the number of years at the previous job, marital status, whether the worker is the head of household, and whether the worker is a manager.

B) 40.30% 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, the number of years of education received, the number of years at the previous job, marital status, whether the worker is the head of household, and whether the worker is a manager, after adjusting for the number of predictors and sample size.

C) 40.30% 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, the number of years of education received, the number of years at the previous job, marital status, whether the worker is the head of household, and whether the worker is a manager, after adjusting for the level of significance D) 40.30% 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, the number of years of education received, the number of years at the previous job, marital status, whether the worker is the head of household, and whether the worker is a manager, holding constant the effect of all the independent variables.

Answer: B Difficulty: Moderate Keywords: interpretation, adjusted r-square 249) Referring to Table 13-17 Model 1, what is the standard error of estimate?

Answer: 18.4861 Difficulty: Easy Keywords: standard error of estimate

13-59 .

250) Referring to Table 13-17 Model 1, predict the number of weeks being unemployed due to a layoff for a worker who is a thirty-year-old, has 10 years of education, has 15 years of experience at the previous job, is married, is the head of household, and is a manager.

Answer: 22.79 Difficulty: Easy Keywords: prediction of individual values 251) Referring to Table 13-17 Model 1, estimate the mean number of weeks being unemployed due to a layoff for a worker who is a thirty-year-old, has 10 years of education, has 15 years of experience at the previous job, is married, is the head of household, and is a manager.

Answer: 22.79 Difficulty: Easy Keywords: estimation of mean values 252) Referring to Table 13-17 Model 1, which of the following is the correct null hypothesis to test whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff, while holding constant the effect of all the other independent variables?

A) H0: β1 = 0 B) H0: β2 = 0 C) H0: β3 = 0 D) H0: β4 = 0 Answer: D Difficulty: Easy Keywords: t test on slope, form of hypothesis 253) Referring to Table 13-17 Model 1, which of the following is the correct alternative hypothesis to test whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff, while holding constant the effect of all the other independent variables?

A) H1: β1 ≠ 0 B) H1: β2 ≠ 0 C) H1: β3 ≠ 0 D) H1: β4 ≠ 0 Answer: D Difficulty: Easy Keywords: t test on slope, form of hypothesis 254) Referring to Table 13-17 Model 1, what is the value of the test statistic when testing whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff, while holding constant the effect of all the other independent variables?

Answer: -0.6861 Difficulty: Easy Keywords: t test on slope, test statistic 255) Referring to Table 13-17 Model 1, what is the p-value of the test statistic when testing whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff, while holding constant the effect of all the other independent variables?

Answer: 0.4974 Difficulty: Easy Keywords: t test on slope, p-value 13-60 .

256) True or False: Referring to Table 13-17 Model 1, the null hypothesis should be rejected at a 10% level of significance when testing whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff, while holding constant the effect of all the other independent variables.

Answer: FALSE Difficulty: Easy Keywords: t test on slope, decision 257) True or False: Referring to Table 13-17 Model 1, there is sufficient evidence that being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff, while holding constant the effect of all the other independent variables at a 10% level of significance.

Answer: FALSE Difficulty: Easy Keywords: t test on slope, conclusion 258) Referring to Table 13-17 Model 1, 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 all the other independent variables?

A) H0: β1 = 0 B) H0: β2 = 0 C) H0: β3 = 0 D) H0: β4 = 0 Answer: B Difficulty: Easy Keywords: t test on slope, form of hypothesis 259) Referring to Table 13-17 Model 1, 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 all the other independent variables?

A) H1: β1 ≠ 0 B) H1: β2 ≠ 0 C) H1: β3 ≠ 0 D) H1: β4 ≠ 0 Answer: B Difficulty: Easy Keywords: t test on slope, form of hypothesis 260) Referring to Table 13-17 Model 1, 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 all the other independent variables?

Answer: 3.5883 Difficulty: Easy Keywords: t test on slope, test statistic

13-61 .

261) Referring to Table 13-17 Model 1, 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 all the other independent variables?

Answer: 0.0011 Difficulty: Easy Keywords: t test on slope, p-value 262) True or False: Referring to Table 13-17 Model 1, 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.

Answer: TRUE Difficulty: Easy Keywords: t test on slope, decision 263) True or False: Referring to Table 13-17 Model 1, 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 all the other independent variables at a 10% level of significance.

Answer: TRUE Difficulty: Easy Keywords: t test on slope, conclusion 264) Referring to Table 13-17 Model 1, 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: β0 = β1 = β2 = β3 = β4 = β5 = β6 = 0 B) H0: β1 = β2 = β3 = β4 = β5 = β6 = 0 C) H0: β0 = β1 = β2 = β3 = β4 = β5 = β6 D) H0: β1 = β2 = β3 = β4 = β5 = β6 Answer: B Difficulty: Easy Keywords: F test on the entire regression, form of hypothesis 265) Referring to Table 13-17 Model 1, 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: All βj ≠ 0 for j = 0, 1, 2, 3, 4, 5, 6 B) H1: All βj ≠ 0 for j = 1, 2, 3, 4, 5, 6 C) H1: At least one of βj ≠ 0 for j = 0, 1, 2, 3, 4, 5, 6 D) H1: At least one of βj ≠ 0 for j = 1, 2, 3, 4, 5, 6 Answer: D Difficulty: Easy Keywords: F test on the entire regression, form of hypothesis

13-62 .

266) True or False: Referring to Table 13-17 Model 1, the null hypothesis H0: β1 = β2 = β3 = β4 = β5 = β6 = 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 Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 267) True or False: Referring to Table 13-17 Model 1, the null hypothesis H0: β1 = β2 = β3 = β4 = β5 = β6 = 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 Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 268) True or False: Referring to Table 13-17 Model 1, the null hypothesis H0: β1 = β2 = β3 = β4 = β5 = β6 = 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 Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 269) True or False: Referring to Table 13-17 Model 1, the null hypothesis H0: β1 = β2 = β3 = β4 = β5 = β6 = 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 Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 270) True or False: Referring to Table 13-17 Model 1, the alternative hypothesis H1: At least one of βj ≠ 0 for j = 1, 2, 3, 4, 5, 6 implies that the number of weeks a worker is unemployed due to a layoff is related to all of the explanatory variables.

Answer: FALSE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 271) True or False: Referring to Table 13-17 Model 1, the alternative hypothesis H1: At least one of βj ≠ 0 for j = 1, 2, 3, 4, 5, 6 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 Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 272) True or False: Referring to Table 13-17 Model 1, the alternative hypothesis H1: At least one of βj ≠ 0 for j = 1, 2, 3, 4, 5, 6 implies that the number of weeks a worker is unemployed due to a layoff is affected by all of the explanatory variables.

Answer: FALSE Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 13-63 .

273) True or False: Referring to Table 13-17 Model 1, the alternative hypothesis H1: At least one of βj ≠ 0 for j = 1, 2, 3, 4, 5, 6 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 Difficulty: Easy Keywords: F test on the entire regression, interpretation, form of hypothesis 274) Referring to Table 13-17 Model 1, 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: 6 and 33 Difficulty: Easy Keywords: F test on the entire regression, degrees of freedom 275) Referring to Table 13-17 Model 1, 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: 5.3885 Difficulty: Easy Keywords: F test on the entire regression, test statistic 276) Referring to Table 13-17 Model 1, 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: 0.00057 Difficulty: Easy Keywords: F test on the entire regression, p-value 277) True or False: Referring to Table 13-17 Model 1, 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 Difficulty: Easy Keywords: F test on the entire regression, decision 278) True or False: Referring to Table 13-17 Model 1, 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 Difficulty: Easy Keywords: F test on the entire regression, conclusion 279) True or False: Referring to Table 13-17 Model 1, 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 Difficulty: Easy Keywords: F test on the entire regression, conclusion 13-64 .

280) True or False: Referring to Table 13-17 Model 1, 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 Difficulty: Moderate Keywords: F test on the entire regression, conclusion 281) True or False: Referring to Table 13-17 Model 1, 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 Difficulty: Moderate Keywords: F test on the entire regression, conclusion 282) Referring to Table 13-17 Model 1, what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one year increase in education received 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: -3.7476 to 1.0402 Difficulty: Moderate Keywords: confidence interval, slope, interpretation 283) Referring to Table 13-17 Model 1, 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 married and one who is not after taking into consideration the effect of all the other independent variables?

Answer: -20.6950 to 10.2571 Difficulty: Moderate Keywords: confidence interval, slope, interpretation 284) True or False: Referring to Table 13-17 Model 1, you can conclude that, holding constant the effect of the other independent variables, the number of years of education received 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 β2.

Answer: TRUE Difficulty: Moderate Keywords: confidence interval, t test on slope, decision 285) True or False: Referring to Table 13-17 Model 1, we can conclude that, holding constant the effect of the other independent variables, there is a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is married and one who is not at a 5% level of significance if we use only the information of the 95% confidence interval estimate for β4.

Answer: FALSE Difficulty: Moderate Keywords: confidence interval, t test on slope, decision

13-65 .

286) True or False: Referring to Table 13-17 Model 1, we can conclude that, holding constant the effect of the other independent variables, the number of years of education received 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 β2.

Answer: TRUE Explanation: Since the 99% confidence interval estimate for β2 will be wider than the 95% confidence interval and still contains 0, we can conclude that holding constant the effect of the other independent variables, the number of years of education received has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 1% level of significance.

Difficulty: Difficult Keywords: confidence interval, t test on slope, decision 287) True or False: Referring to Table 13-17 Model 1, we can conclude that, holding constant the effect of the other independent variables, there is a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is married 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 β4.

Answer: FALSE Explanation: Since the 99% confidence interval estimate for β4 will be wider than the 95% confidence interval and still contains 0, we can conclude 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 married and one who is not at a 1% level of significance.

Difficulty: Difficult Keywords: confidence interval, t test on slope, decision 288) True or False: Referring to Table 13-17 Model 1, we can conclude that, holding constant the effect of the other independent variables, the number of years of education received has no 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 on the 95% confidence interval estimate for β2.

Answer: FALSE Explanation: Since the 90% confidence interval estimate for β2 will be narrower than the 95% confidence interval and we cannot be sure that it still contains 0, you cannot conclude that holding constant the effect of the other independent variables, the number of years of education received has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

Difficulty: Difficult Keywords: confidence interval, t test on slope, decision 289) True or False: Referring to Table 13-17 Model 1, we can conclude that, holding constant the effect of the other independent variables, there is a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is married and one who is not at a 10% level of significance if we use only the information of the 95% confidence interval estimate for β4.

Answer: FALSE Explanation: Since the 90% confidence interval estimate for β4 will be narrower than the 95% confidence interval and we are not sure if it contains 0, we cannot conclude that, holding constant the effect of the other independent variables, there is a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is married and one who is not at a 10% level of significance.

Difficulty: Difficult Keywords: confidence interval, t test on slope, decision 13-66 .

290) Referring to Table 13-17 Model 1, which of the six independent variables (Age, Edu, Job Yr, Married, Head and Manager) is (are) insignificant in affecting the dependent variable using a 5% level of significance after taking into account the effect of the remaining independent variables?

Answer: Edu, Job Yr, Married, and Head Difficulty: Moderate Keywords: t test on slope 291) Referring to Table 13-17 Model 1, ________ of the variation in the number of weeks a worker is unemployed due to a layoff can be explained by the six independent variables after taking into consideration the number of independent variables and the number of observations.

Answer: 0.4030 or 40.30% Difficulty: Moderate Keywords: model building, adjusted r-square

13-67 .

Business Statistics: A First Course, 6e (Levine) Chapter 14 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 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 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 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 Difficulty: Easy Keywords: common causes of variation 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 Difficulty: Easy Keywords: control chart 14-1 .

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 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 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 Difficulty: Moderate Keywords: statistical control 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 Difficulty: Moderate Keywords: red bead experiment

14-2 .

TABLE 14- 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.

Day 1 2 3 4 5 6 7 8 9 10

Number of Papers Delivered on Time 46 45 46 45 43 48 46 49 48 47

10) Referring to Table 14- 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 Difficulty: Moderate Keywords: p chart, center line 11) Referring to Table 14-1, 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 Difficulty: Moderate Keywords: p chart, control limit 12) Referring to Table 14-1, 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 Difficulty: Moderate Keywords: p chart, control limit

14-3 .

13) Referring to Table 14-1, which expression best characterizes the p chart?

A) cycles B) increasing trend C) in control D) individual outliers Answer: C Difficulty: Moderate Keywords: p chart TABLE 14-2 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 (Day) 1 2 3 4 5 6 7 8

Number Favoring Incumbent Candidate 57 57 53 51 55 60 56 59

14) Referring to Table 14-2, 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 Difficulty: Moderate Keywords: p chart, center line 15) Referring to Table 14-2, 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 Difficulty: Moderate Keywords: p chart, control limit

14-4 .

16) Referring to Table 14-2, 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 Difficulty: Moderate Keywords: p chart, control limit 17) Referring to Table 14-2, which expression best characterizes the p chart?

A) in control B) increasing trend C) decreasing trend D) individual outliers Answer: A Difficulty: Moderate Keywords: p chart TABLE 14-3 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14

(in minutes) 58.5 47.6 64.3 60.6 63.7 57.5 55.0 54.9 55.0 62.7 61.9 60.0 58.3 52.0

R 5.1 7.8 6.1 5.7 6.2 6.0 5.4 6.1 5.9 5.0 7.1 6.5 5.9 5.2

18) Referring to Table 14-3, 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 Difficulty: Moderate Keywords: R chart, center line 14-5 .

19) Referring to Table 14-3, 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 Difficulty: Moderate Keywords: R chart, control limit 20) Referring to Table 14-3, 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 Difficulty: Moderate Keywords: R chart, control limit 21) Referring to Table 14-3, 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 Difficulty: Moderate Keywords: R chart 22) Referring to Table 14-3, 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 Difficulty: Moderate Keywords: control limit 23) Referring to Table 14-3, suppose the analyst constructs an in control. What is the center line for this chart?

A) 64.3 B) 59.5 C) 58.0 D) 57.1 Answer: C Difficulty: Moderate Keywords: XBar chart, center line 14-6 .

chart to see if the production process is

24) Referring to Table 14-3, suppose the analyst constructs an 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 Difficulty: Moderate Keywords: XBar chart, control limit 25) Referring to Table 14-3, suppose the analyst constructs an 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 Difficulty: Moderate Keywords: XBar chart, control limit 26) Referring to Table 14-3, suppose the analyst constructs an in control. Which expression best describes this chart?

A) in control B) increasing trend C) decreasing trend D) individual outliers Answer: D Difficulty: Moderate Keywords: XBar chart

14-7 .

chart to see if the production process is

TABLE 14-4 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 1 2 3 4 5 6 7 8 9 10

18.4 16.9 23.0 21.2 21.0 24.0 19.3 15.8 20.0 23.0

R 25 27 30 23 24 25 12 14 13 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 Table 14-4, 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 Difficulty: Moderate Keywords: R chart, center line 28) Referring to Table 14-4, 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 Difficulty: Moderate Keywords: R chart, control limit

14-8 .

29) Referring to Table 14-4, 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 Difficulty: Moderate Keywords: R chart 30) Referring to Table 14-4, 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 Difficulty: Moderate Keywords: R chart, control limit 31) Referring to Table 14-4, suppose the supervisor constructs an control. What is the center line of the chart?

A) 20.00 B) 20.26 C) 21.00 D) 24.26 Answer: B Difficulty: Moderate Keywords: XBar chart, center line

chart to see if the process is in

32) Referring to Table 14-4, suppose the supervisor constructs an 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 Difficulty: Moderate Keywords: XBar chart, control limit

chart to see if the process is in

33) Referring to Table 14-4, suppose the supervisor constructs an control. Which expression best describes this chart?

A) decreasing trend B) in control C) increasing trend D) individual outliers Answer: B Difficulty: Moderate Keywords: XBar chart

chart to see if the process is in

14-9 .

34) Referring to Table 14-4, what is the value of d2 factor?

Answer: 2.326 Difficulty: Easy Keywords: d2 factor 35) True or False: The control limits are based on the standard deviation of the process.

Answer: TRUE Difficulty: Moderate Keywords: control limit 36) True or False: The purpose of a control chart is to eliminate common cause variation.

Answer: FALSE Difficulty: Easy Keywords: control chart, common causes of variation 37) True or False: Special or assignable causes of variation are signaled by individual fluctuations or patterns in the data.

Answer: TRUE Difficulty: Easy Keywords: special causes of variation 38) True or False: Common causes of variation represent variation due to the inherent variability in the system.

Answer: TRUE Difficulty: Easy Keywords: common causes of variation 39) True or False: Common causes of variation are correctable without modifying the system.

Answer: FALSE Difficulty: Moderate Keywords: common causes of variation 40) True or False: Changes in the system to reduce common cause variation are the responsibility of management.

Answer: TRUE Difficulty: Moderate Keywords: common causes of variation 41) True or False: One of the morals of the red bead experiment is that variation is part of any process.

Answer: TRUE Difficulty: Easy Keywords: red bead experiment 42) 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 Difficulty: Easy Keywords: control chart, control limit 14-10 .

43) True or False: The p chart is a control chart used for monitoring the proportion of items that meet given specifications.

Answer: TRUE Difficulty: Easy Keywords: p chart 44) True or False: The R chart is a control chart used to monitor a process mean.

Answer: FALSE Difficulty: Moderate Keywords: R chart 45) True or False: It is not possible for the chart to be out of control when the R chart is in control.

Answer: FALSE Difficulty: Moderate Keywords: XBar chart, R chart, statistical control 46) The cause of variation that can be reduced only by changing the system is ________ cause variation.

Answer: common Difficulty: Easy Keywords: common causes of variation 47) ________ causes of variation are correctable without modifying the system.

Answer: Special Difficulty: Easy Keywords: special causes of variation

14-11 .

TABLE 14-5 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

48) Referring to Table 14-5, the best estimate of the mean proportion of disks with bad sectors is ________.

Answer: 0.0375 Difficulty: Moderate Keywords: p chart, center line 49) Referring to Table 14-5, a p control chart is to be made for these data. The center line of the control chart is ________.

Answer: 0.0375 Difficulty: Moderate Keywords: p chart, center line 50) Referring to Table 14-5, 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: 0.036793 or 0.01226 Difficulty: Moderate Keywords: p chart, standard error 51) Referring to Table 14-5, 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 Difficulty: Moderate Keywords: p chart, control limit

14-12 .

52) Referring to Table 14-5, construct a p control chart for these data.

Answer:

Difficulty: Difficult Keywords: p chart 53) True or False: Referring to Table 14-5, the process seems to be in control.

Answer: FALSE Difficulty: Moderate Keywords: p chart, statistical control

14-13 .

TABLE 14-6 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.

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Number Poor 33 29 31 32 43 45 46 48 48 46 28 32 28 32 31 24

Proportion Poor 0.0550000 0.0483333 0.0516667 0.0533333 0.0716667 0.0750000 0.0766667 0.0800000 0.0800000 0.0766667 0.0466667 0.0533333 0.0466667 0.0533333 0.0516667 0.0400000

54) Referring to Table 14-6, the estimate of the proportion of poor quality bags of candy is ________.

Answer: 0.06 Difficulty: Moderate Keywords: p chart, center line 55) Referring to Table 14-6, a p control chart is to be constructed for these data. The center line for the chart should be located at ________.

Answer: 0.06 Difficulty: Moderate Keywords: p chart, center line 56) Referring to Table 14-6, 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 Difficulty: Moderate Keywords: p chart, standard error 57) Referring to Table 14-6, a p control chart is to be constructed for these data. The lower control limit is ________, while the upper control limit is ________.

Answer: 0.0309139; 0.0890861 Difficulty: Moderate Keywords: p chart, control limit

14-14 .

58) Referring to Table 14-6, construct a p control chart for these data.

Answer: P Chart: Sample Sizes = 600

Difficulty: Difficult Keywords: p chart 59) True or False: Referring to Table 14-6, the process seems to be in control.

Answer: TRUE Difficulty: Moderate Keywords: p chart, statistical control

14-15 .

TABLE 14-7 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.

She also decides that the upper specification limit is 10 blemishes.

60) Referring to Table 14-7, 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 Difficulty: Moderate Keywords: R chart, center line 61) Referring to Table 14-7, 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 Difficulty: Easy Keywords: R chart, D3 factor 62) Referring to Table 14-7, 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 Difficulty: Easy Keywords: R chart, D4 factor

14-16 .

63) Referring to Table 14-7, 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 Difficulty: Moderate Keywords: R chart, control limit 64) Referring to Table 14-7, an R chart is to be constructed for the number of blemishes. The upper control limit for this data set is ________.

Answer: 11.52 Difficulty: Moderate Keywords: R chart, control limit 65) Referring to Table 14-7, construct an R chart for the number of blemishes.

Answer:

Difficulty: Difficult Keywords: R chart 66) True or False: Referring to Table 14-7, based on the R chart, it appears that the process is out of control.

Answer: FALSE Difficulty: Moderate Keywords: R chart, statistical control 67) Referring to Table 14-7, an chart is to be used for the number of blemishes. The center line of this chart is located at ________.

Answer: 7.930 Difficulty: Moderate Keywords: XBar chart, center line

14-17 .

68) Referring to Table 14-7, an 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 Difficulty: Easy Keywords: XBar chart, A2 factor 69) Referring to Table 14-7, an 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 Difficulty: Moderate Keywords: XBar chart, control limit 70) Referring to Table 14-7, construct an Answer:

chart for the number of blemishes.

Difficulty: Difficult Keywords: XBar chart 71) True or False: Referring to Table 14-7, based on the that the process is out of control.

Answer: FALSE Difficulty: Moderate Keywords: XBar chart, statistical control 72) Referring to Table 14-7, what is the value of

chart for the number of blemishes, it appears

factor?

Answer: 2.326 Difficulty: Easy Keywords: d2 factor 14-18 .

TABLE 14-8 Recently, a university switched to a new type of computer-based registration. The registrar is concerned with the amount of time 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 1 2 3 4 5 6 7 8 9 10 11 12

Range 10 31 13 21 35 18 25 30 17 22 27 26

Mean 5.250 15.250 20.375 22.875 8.500 7.875 11.250 7.875 10.250 9.500 7.875 12.875

Std.Dev. 3.4949 10.3060 4.9262 8.3911 11.3767 6.9372 8.5815 9.5235 6.3640 7.8740 8.7086 9.3723

73) Referring to Table 14-8, 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 Difficulty: Moderate Keywords: R chart, center line 74) Referring to Table 14-8, 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 Difficulty: Easy Keywords: R chart, D3 factor 75) Referring to Table 14-8, 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 Difficulty: Easy Keywords: R chart, D4 factor 76) Referring to Table 14-8, 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 Difficulty: Moderate Keywords: R chart, control limit

14-19 .

77) Referring to Table 14-8, 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 Difficulty: Moderate Keywords: R chart, control limit 78) Referring to Table 14-8, construct an R chart for the time required to register.

Answer:

Difficulty: Difficult Keywords: R chart 79) True or False: Referring to Table 14-8, based on the R chart, it appears that the process is out of control.

Answer: FALSE Difficulty: Moderate Keywords: R chart, statistical control 80) Referring to Table 14-8, an chart is to be used for the time required to register. The center line of this chart is located at ________.

Answer: 11.65 Difficulty: Moderate Keywords: XBar chart, center line 81) Referring to Table 14-8, an 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 Difficulty: Easy Keywords: XBar chart, A2 factor 14-20 .

82) Referring to Table 14-8, an 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 Difficulty: Moderate Keywords: XBar chart, control limit 83) Referring to Table 14-8, construct an Answer:

chart for the time required to register.

Difficulty: Moderate Keywords: XBar char 84) True or False: Referring to Table 14-8, based on the Answer: FALSE Difficulty: Moderate Keywords: XBar chart, statistical control

chart, it appears that the process is in control.

85) Which of the following is a method for breaking a 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 chart Answer: B Difficulty: Easy Keywords: six sigma management

14-21 .

86) 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 Difficulty: Easy Keywords: six sigma management 87) 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 Difficulty: Easy Keywords: six sigma management 88) 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 Difficulty: Easy Keywords: six sigma management 89) 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 Difficulty: Easy Keywords: six sigma management

14-22 .

TABLE 14-9 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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

XBar 3.05072 3.01228 3.03558 3.01014 3.00858 3.02704 3.04268 3.01052 3.03464 3.02034 3.03764 3.0409 3.0519 3.03994 3.03788

Range 0.0215 0.087 0.0851 0.0674 0.0983 0.0527 0.0508 0.0791 0.0663 0.0538 0.0584 0.0434 0.0762 0.0833 0.0601

Number 16 17 18 19 20 21 22 23 24 25 26 27 28 29

XBar 3.04646 3.03868 3.03338 3.03322 3.05078 3.04808 3.05348 3.05516 3.03426 3.0516 3.05562 3.04402 3.06458 3.0544

Range 0.073 0.0696 0.0329 0.0455 0.0215 0.0396 0.0581 0.0682 0.0325 0.0641 0.0809 0.0374 0.0284 0.0738

90) Referring to Table 14-9, an R chart is to be constructed for the weight. The center line of this R chart is located at ________.

Answer: 0.0589 Difficulty: Moderate Keywords: R chart, center line 91) Referring to Table 14-9, 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 Difficulty: Easy Keywords: R chart, D3 factor 92) Referring to Table 14-9, 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 Difficulty: Easy Keywords: R chart, D4 factor 93) Referring to Table 14-9, an R chart is to be constructed for the weight. The lower control limit for this data set is ________.

Answer: 0 Difficulty: Moderate Keywords: R chart, control limit 14-23 .

94) Referring to Table 14-9, an R chart is to be constructed for the weight. The upper control limit for this data set is ________.

Answer: 0.1246 Difficulty: Moderate Keywords: R chart, control limit 95) Referring to Table 14-9, construct an R chart for the time required to register.

Answer:

Difficulty: Difficult Keywords: R chart 96) True or False: Referring to Table 14-9, based on the R chart, it appears that the process is out of control.

Answer: FALSE Difficulty: Easy Keywords: R chart, statistical control 97) Referring to Table 14-9, an chart is to be used for the weight. The center line of this chart is located at ________.

Answer: 3.0388 Difficulty: Moderate Keywords: XBar chart, center line 98) Referring to Table 14-9, an 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 Difficulty: Easy Keywords: XBar chart, A2 factor 14-24 .

99) Referring to Table 14-9, an 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 Difficulty: Moderate Keywords: XBar chart, control limit 100) Referring to Table 14-9, construct an Answer:

chart for the weight.

Difficulty: Moderate Keywords: XBar char 101) True or False: Referring to Table 14-9, based on the control.

Answer: TRUE Difficulty: Easy Keywords: XBar chart, statistical control

chart, it appears that the process is in

102) Referring to Table 14-9, estimate the percentage of the cans whose weight is inside the specification limit.

Answer: 0.9998 or 99.98% Difficulty: Difficult Keywords: XBar chart, control limit 103) 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 Difficulty: Moderate Keywords: Deming's 14 points 14-25 .

104) 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 Difficulty: Moderate Keywords: Deming's 14 points 105) Which of the following is NOT part of the Shewhart-Deming cycle?

A) Plan B) Do C) React D) Act Answer: C Difficulty: Moderate Keywords: Shewhart-Deming cycle 106) 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 Difficulty: Moderate Keywords: Shewhart-Deming cycle 107) Which famous statistician developed the 14 Points of Quality?

A) Shewhart B) Deming C) Chebyshev D) Taguchi Answer: B Difficulty: Easy Keywords: Deming's 14 points

14-26 .