Business Statistics, Canadian Edition, 4th edition Norean R. Sharpe Test Bank

Type:

Test Bank

Resource:

Business Statistics

Edition:

4th Edition

Author(s):

Norean Sharpe Richard De Veaux Paul Velleman David Wright

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 1: An Introduction to Statistics Chapter 1 has no questions.

1) There are no questions in this chapter.

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Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 2: Data Short Answer - Quiz A 1) The mission of a research firm is to "explore the impact of the Internet on families, communities, work, home, and daily life." In August - September 2015 they conducted telephone interviews with a sample of Canadian adults aged 18 and older about online shopping. Describe the W's for the information given.

• Who: • What: • When: • Where: • How: • Why: Answer: • Who: Canadian adults aged 18 and older • What: online shopping • When: August - September 2015 • Where: Canada • How: telephone interviews • Why: to explore the impact of the Internet on daily life, specifically online shopping L.O.: 1

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2) The following table displays some of the data collected by the above research firm in their study of online shopping. List the variables in the data set. Indicate whether each variable is categorical or quantitative. If the variable is quantitative, give the units.

Age 25 47 38 30

Gender Male Female Female Male

Household Income $55,000 $60,000 $110,000 $62,000

Participated in online auction?

Yes No No No

Monthly Time (hours) per amount spent week browsing online online retailers $250 6 $50 4 $120 10 $75 4

Answer: Categorical: Gender, Participated in online auction?

Quantitative: Age (years), Household Income ($), Monthly amount spent online ($), Time per week browsing online retailers (hours).

L.O.: 2 3) In addition to the variables listed above, data were also collected on the variables listed below.

Indicate whether each is nominal or ordinal.

• Region (Urban, Suburban, Rural) • Education (Less than High School, High School, College, University) • Marital Status (Single, Widowed, Divorced, Married) Answer: • Region (Urban, Suburban, Rural) Nominal • Education (Less than High School, High School, College, University) Ordinal • Marital Status (Single, Widowed, Divorced, Married) Nominal L.O.: 2 4) For each of the following, indicate whether the data are cross-sectional or time series: • Weekly receipts at a clothing boutique • Monthly demand for an automotive part • Percentage of adults who bank online Answer: • Weekly receipts at a clothing boutique Time Series • Monthly demand for an automotive part Time Series • Percentage of adults who bank online Cross-Sectional L.O.: 2

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5) Eastland College instructors and students are asking to review a new computer tutorial. Peter, author of the tutorial, wants to analyze the feedback. He gets a spreadsheet. List the variables in the data set. Indicate whether each variable is categorical or quantitative. If the variable is categorical, indicate whether it is nominal or ordinal. Does the table contain an identifier variable?

Number of Tutorial Level of visits Name Status Access ID satisfaction per week Ann Instructor AB235 Moderately helpful 3 Boris Student BC1090 Very helpful 4 Parul Student PR1841 Not helpful 1 Paul Instructor PG145 Somewhat helpful 2

Time (minutes) spent per week 60 120 30 45

Answer: Quantitative: Number of visits per week, Time spent per week (minutes) Categorical: Name (nominal), Status (nominal), Tutorial Access ID (nominal, identifier), Level of satisfaction (ordinal).

L.O.: 2 Short Answer - Quiz B 1) Consumer Reports Health routinely compares drugs in terms of effectiveness and safety.

Suppose that in the summer of 2014 they reviewed drugs used to treat arthritis. Information was reported on convenience of use (how many pills required each day), possible side effects (e.g., dizziness, stomach upset), cost, and ratings of effectiveness in relieving symptoms (very effective, somewhat effective, not effective). Describe the W's for the information given.

• Who: • What: • When: • Where: • How: • Why: Answer: • Who: drugs to treat arthritis currently on the market • What: convenience of use, side effects, cost, effectiveness ratings • When: summer 2014 • Where: not specified • How: testing on drugs • Why: to compare arthritis drugs it terms of effectiveness and safety L.O.: 1

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2) List the variables reported in the Consumer Reports Health article on drugs used to treat arthritis. If the variable is quantitative, give the units. If the variable is categorical, indicate whether it is nominal or ordinal.

Answer: Categorical: Side effect (nominal), Effectiveness Rating (ordinal) Quantitative: Convenience of use (number of pills), Cost ($) L.O.: 2 3) The Human Resources Department of a large corporation maintains records on its employees.

The table displays some of these data. List the variables in the data set. Indicate whether each variable is categorical or quantitative. If the variable is quantitative, give the units. If the variable is categorical, indicate whether it is nominal or ordinal.

Age 32 52 60 28

Employment Category Clerical Professional Professional Clerical

Education High School College University High School

Participates in Wellness Program?

Yes No Yes No

Paycheck Benefit Deductions $250 $120 $0 $120

Answer: Categorical: Employment Category (nominal), Education (ordinal), Participates in Wellness Program? (nominal) Quantitative: Age (years), Paycheck Benefit Deductions ($) L.O.: 2 4) For each of the following, indicate whether the data are cross-sectional or time series: • Company quarterly profits • Percentage of Canadian adults who work full time • Historical closing stock prices Answer: • Company quarterly profits Time Series • Percentage of Canadian adults who work full time Cross-Sectional • Historical closing stock prices Time Series L.O.: 2

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Multiple Choice - Quiz C 1) In the fall of 2015 a research company conducted its Internet & Life Project through telephone interviews about online shopping with a sample of Canadian adults aged 18 and older. Canadian adults aged 18 and older constitute the ________ of the study.

A) Who B) What C) When D) Where E) How Answer: A L.O.: 1 2) A few of the variables for which data were collected in the Internet & Life Project study include age, gender, income, monthly Internet bill, and number of hours spent shopping online per month. Which of the variables is categorical?

A) Age B) Gender C) Income D) Number of hours spent shopping online E) Monthly Internet bill Answer: B L.O.: 2 3) The Internet & Life Project study also asked respondents to indicate their education level on the following scale: Less than High School, High School, Some College, College, University.

Which of the following statements is true?

A) Education level is a time series variable.

B) Education level is nominal scaled.

C) Education level is a quantitative variable.

D) Education level is a categorical (ordinal) variable.

E) Education level is a nominal variable.

Answer: D L.O.: 2 4) Consumer Reports Health routinely compares drugs in terms of effectiveness and safety. In summer 2014 they reviewed drugs used to treat arthritis. Among the information reported was convenience of use (how many pills required each day) and possible side effects (e.g., dizziness, stomach upset). Convenience of use and possible side effects constitute the ________ of the study.

A) Who B) What C) When D) Where E) How Answer: B L.O.: 1 5 .

5) What is the "Who" in the Consumer Reports Health study on the effectiveness and safety of drugs used to treat arthritis?

A) drugs to treat arthritis B) convenience of use and possible side effects C) summer 2014 D) Canada E) testing on drugs Answer: A L.O.: 1 6) In the Consumer Reports Health study on arthritis drugs, possible side effects is what kind of variable?

A) Quantitative B) Ordinal C) Identifier D) Time series E) Categorical (nominal) Answer: E L.O.: 2 7) The Consumer Reports Health study on arthritis drugs also took into consideration cost. Cost is A) a nominal variable.

B) a categorical variable.

C) a quantitative variable.

D) an ordinal variable.

E) an irrelevant variable.

Answer: C L.O.: 2 8) The Human Resources Department of a large corporation maintains records on its employees.

Data are maintained for the following variables: Age, Employment Category, Education, Whether or not the employee participates in a wellness program, and Paycheck benefit deductions. Which of these variables are categorical?

A) Age and Paycheck benefit deductions B) Employment Category, Education, and Whether or not the employee participates in a wellness program C) Paycheck benefit deductions only D) Age only E) Education only Answer: B L.O.: 2

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9) Which of the following is based on cross-sectional data?

A) Company quarterly profits B) Percentage of Canadian adults who work full time C) Historical closing stock prices D) Yearly student enrollments E) Annual costs Answer: B L.O.: 2 10) Which of the following is time series data?

A) Number of employees in 2013 B) This month's demand for an automotive part C) This quarter's sales of automobiles D) Weekly receipts at a clothing boutique E) Percentage of employees who are female Answer: D L.O.: 2 11) A company conducted a survey of its employees to determine their level of satisfaction with various company policies. The data collected from this survey are A) primary data.

B) secondary data.

C) transactional data.

D) census data.

E) quantitative data.

Answer: A L.O.: 2 12) Bell Canada tracks employee turnover annually. It currently has a data set that contains turnover for the past 20 years. What type of data does it have?

A) time series data B) cross-sectional data C) nominal data D) ordinal data E) categorical data Answer: A L.O.: 2

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13) The human resources department at a major high tech company recently conducted an employee satisfaction survey of 100 of its 3,000 employees. Data were collected on such variables as age, gender, marital status, current salary, level of overall satisfaction on a scale from 1 to 5, number of years with the company, and job title. Which of the following best describes the overall data set that was generated from the study?

A) cross-sectional data B) time series data C) nominal data D) quantitative data E) categorical data Answer: A L.O.: 2 14) The human resources department at Bell Canada recently conducted an employee satisfaction survey of 100 of its employees. Data were collected on such variables as age, gender, marital status, current salary, level of overall satisfaction on a scale from 1 to 5, number of years with the company, and job title. Which of the variables would be classified as nominal data?

A) gender, marital status, and job title B) age and gender C) age and number of years with the company D) age E) level of overall satisfaction Answer: A L.O.: 2 15) The human resources department at Bell Canada recently conducted an employee satisfaction survey of 100 of its employees. Data were collected on such variables as age, gender, marital status, current salary, level of overall satisfaction on a scale from 1 to 5, number of years with the company, and job title. Which of the variables would be considered to be quantitative data?

A) age, number of years with the company, and current salary B) gender and current salary C) age and gender D) marital status and current salary E) level of overall satisfaction on a scale from 1 to 5, number of years with the company, and job title Answer: A L.O.: 2

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16) Tim Hortons conducts a random survey of 1000 customers in their Ottawa outlets on a particular day. For each customer they collect data on the time taken to fill the order, how frequently the customer comes to Tim Hortons in a week, whether the customer purchased only coffee or additional item(s), and the level of overall satisfaction using a scale from 1 to 5. What is the "Who" of this study?

A) the 1000 customers B) the time taken to fill the customer order C) whether the customer purchased only coffee or additional item(s) D) the level of overall satisfaction E) how frequently the customer comes to Tim Hortons in a week Answer: A L.O.: 1 17) Tim Hortons conducts a random survey of 1000 customers in their Ottawa outlets on a particular day. For each customer they collect data on the time taken to fill the order, how frequently the customer comes to Tim Hortons in a week, and the level of overall satisfaction using a scale from 1 to 5.

Time taken to fill the order, how frequently the customer comes to Tim Hortons in a week, and the level of satisfaction constitute the ________ of the study.

A) How B) Who C) What D) When E) Where Answer: C L.O.: 1 18) Tim Hortons conducts a random survey of 1000 customers in their Ottawa outlets on a particular day. For each customer they collect data on the time taken to fill the order, how frequently the customer comes to Tim Hortons in a week, whether the customer purchased only coffee or additional item(s), and the level of overall satisfaction using a scale from 1 to 5. Which of the variables is quantitative?

A) the time taken to fill the order, and how frequently the customer comes to Tim Hortons in a week B) whether the customer purchased only coffee or additional item(s) C) the level of overall satisfaction D) whether the customer purchased only coffee or additional item(s) and the level of overall satisfaction E) the level of overall satisfaction and how frequently the customer comes to Tim Hortons in a week Answer: A L.O.: 2

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19) When a survey uses the responses strongly disagree, disagree, neutral, agree, strongly agree, what type of data are collected?

A) ordinal data B) nominal data C) cross-sectional data D) time series data E) quantitative data Answer: A L.O.: 2 20) Which of the following is a secondary data source?

A) using Statistics Canada data B) conducting a telephone survey C) conducting a mail out written survey D) conducting personal interviews E) conducting an experiment Answer: A L.O.: 2 21) Vitamin D insufficiency is associated with many diseases including multiple sclerosis, breast and other cancers, bone diseases, tuberculosis. A variable which represents the vitamin D level (ng/ml) of a hospital patient is A) a categorical variable.

B) a quantitative variable.

C) a nominal variable.

D) an ordinal variable.

E) an identifier variable.

Answer: B L.O.: 2

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Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 3: Surveys and Sampling Short Answer - Quiz A 1) The administration of a large university is interested in learning about the types of wellness programs that would interest its employees. To do this, they plan to survey a random sample of employees. Under consideration are several plans for selecting the sample. Name the sampling strategy for each. a. There are five categories of employees (administration, faculty, professional staff, clerical, and maintenance). Randomly select ten individuals from each category. b. Each employee has an ID number. Randomly select 50 numbers. c. Randomly select a school within the university (e.g., Business School) and survey all of the individuals (administration, faculty, professional staff, clerical and maintenance) who work in that school. d. The HR Department has an alphabetized list of newly hired employees (hired within the last five years). After starting the process by randomly selecting an employee from the list, then every 5th name is chosen to be included in the sample.

Answer: a. Stratified b. Simple Random Sample c. Cluster d. Systematic L.O.: 1, 3 2) Suppose the administration decides to do the following. At a Starbucks located on campus, every tenth person who enters on a Monday morning is selected to be surveyed. Explain why this may be biased.

Answer: Depending on the time during which individuals are surveyed, undercoverage may be an issue. For example, different categories of employees have different levels of flexibility (clerical and maintenance workers don't have as much flexibility in their work days as do administration, faculty and professional staff). In addition, persons other than employees would presumably enter Starbucks, although a screening question can be used to make sure those interviewed are employees.

L.O.: 2, 3

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3) Two of the questions asked in the survey of employees are shown below.

• Since exercise is so important to good health, would you be willing to participate in organized walks during lunch hour?

• Would you attend a "low fat cooking" demonstration? a. Are these questions valid (appropriately worded)? Explain. b. Which question is more neutral? Explain.

Answer: a. The first question is "leading" the respondent to answer yes and therefore is not quite appropriately worded. b. The second question is more neutral because it does not lead to a yes response.

L.O.: 2 4) A consumer research group is interested in how older drivers view hybrid cars. Specifically, they wish to assess the percentage of drivers in Canada, 50 years of age or older who intend to purchase a hybrid in the next two years. Suppose that a list of CARP (Canadian Association of Retired Persons) members is used as the sampling frame. Based on a systematic sample, they estimated the percentage to be 17%. a. Define the target population. b. Define the parameter. c. What is the statistic? d. How might the results be biased?

Answer: a. All Canadian drivers 50 years old or older b. Percentage of drivers in Canada, 50 years of age or older who intend to purchase a hybrid in the next two years c. 17% based on the sample d. The sampling frame does not include all Canadian drivers 50 years old or older (not everyone 50 years old or older is a member of CARP).

L.O.: 1, 2, 3

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Short Answer - Quiz B 1) ASW, a regional shoe chain, has recently launched an online store. Sales via the Internet have been sluggish compared to their brick and mortar stores, and management suspects that its regular customers have concerns regarding the security of online transactions. To determine if this is the case, they plan to survey a random sample of their regular customers. Under consideration are several plans for selecting the sample. Name the sampling strategy for each. a. Regular customers belong to a rewards program and have a customer rewards ID number.

Randomly select 100 numbers. b. ASW has stores in five different cities in Canada. Randomly select one of the stores and survey all regular customers that belong to its rewards program. c. ASW has an alphabetized list of regular customers who belong to their rewards program.

After randomly selecting a customer on the list, every 25th customer from that point on is chosen to be in the sample. d. Customers who belong to the rewards program are grouped into four age categories (under 21, 21 to 35, 36 to 50, and over 50). Randomly select 10 regular customers in each age category.

Answer: a. Simple random b. Cluster c. Systematic d. Stratified L.O.: 1, 3 2) In the ASW study described above, a. Define the target population. b. Define the parameter. c. What is the sampling frame? d. How might the results be biased?

Answer: a. All regular ASW customers b. % of regular ASW customers who have concerns about online security c. ASW customers who belong to the rewards program d. Not all regular customers belong to the rewards program, and ASW should also consider how others (potential customers) feel.

L.O.: 1, 2, 3 3) One member of the management team at ASW suggests that their survey could be conducted online. Customers logging on to the online store would be asked to take a few minutes to complete the survey and would be offered a coupon as incentive to participate. Explain how this approach might be biased.

Answer: This is a voluntary response sample. This sample consists of customers already visiting the online store; the bias would probably be toward not having concerns about online security.

L.O.: 2

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4) Two of the questions asked in the survey of customers are shown below.

• Given the prevalence of identity theft, are you reluctant to provide credit card information online?

• Are you confident that any information you provide online is secure? a. Are these questions valid (appropriately worded)? Explain. b. Which question is more neutral? Explain.

Answer: a. The first question is leading by mentioning the prevalence of identity theft and therefore is not quite appropriately worded. b. The second question is more neutral because it does not lead the customer to a specific response.

L.O.: 2 Multiple Choice - Quiz C Consider the following to answer the question(s) below.

KiPLEX manufactures plastic pipes. KiPLEX piping is a less expensive alternative to copper piping. BPLEX's marketing department wants to determine plumbers' satisfaction with KiPLEX piping. To do this, they plan to survey plumbers who purchase KiPLEX pipes on regular basis.

1) Suppose that there are five categories of plumbers (individuals, small local businesses, home renovation companies, condo renovation companies, and high rise construction companies). The marketing specialists decide to randomly select 20 individuals from each category. This sampling method is called A) simple random.

B) stratified.

C) cluster.

D) systematic.

E) convenience.

Answer: B L.O.: 1 2) Office of the KiPLEX marketing department is located next to a large construction site. The marketing department employees ask everyone who enters or leaves the construction site what they think about their product. This sampling method is called A) simple random.

B) stratified.

C) cluster.

D) systematic.

E) convenience.

Answer: E L.O.: 1

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Consider the following to answer the question(s) below.

ASW, a regional shoe chain, has recently launched an online store. Sales via the Internet have been sluggish compared to their brick and mortar stores, and management suspects that its regular customers have concerns regarding the security of online transactions. To determine if this is the case, they plan to survey a sample of their regular customers.

3) Suppose that ASW's regular customers belong to a rewards program and have a customer rewards ID number. ASW decides to randomly select 100 numbers. This sampling method is called A) simple random.

B) stratified.

C) cluster.

D) systematic.

E) convenience.

Answer: A L.O.: 1 4) Suppose that ASW has an alphabetized list of regular customers who belong to their rewards program. After randomly selecting a customer on the list, every 25th customer from that point on is chosen to be in the sample. This sampling method is called A) simple random.

B) stratified.

C) cluster.

D) systematic.

E) convenience.

Answer: D L.O.: 1 5) The entire group of regular ASW customers is known as the ________ of the study.

A) parameter B) statistic C) target population D) sampling frame E) sample Answer: C L.O.: 3 6) Which of the following is the parameter of interest in the ASW study?

A) All regular ASW customers B) % of regular ASW customers who have concerns about online security C) ASW customers who belong to the rewards program D) % of ASW customers who belong to the rewards program that don't shop online E) All customer rewards ID numbers Answer: B L.O.: 3 5 .

7) One member of the management team at ASW suggests that their survey could be conducted online. Customers logging on to the online store would be asked to take a few minutes to complete the survey and would be offered a coupon as incentive to participate. Which of the following statements is true?

A) This is a stratified random sample.

B) This would result in an unbiased random sample.

C) This would result in a nonresponse bias.

D) This is a systematic sample.

E) This would result a voluntary response bias.

Answer: E L.O.: 1, 2 Consider the following to answer the question(s) below.

A consumer research group is interested in how older drivers view hybrid cars. Specifically, they wish to assess the percentage of drivers in Canada 50 years of age or older who intend to purchase a hybrid in the next two years. Suppose that they selected a systematic sample from a list of CARP (Canadian Association of Retired Persons) members. Based on this sample, they estimated the percentage to be 17%.

8) The sampling frame for this study is A) all drivers in Canada 50 years of age or older.

B) 17%.

C) the list of CARP members.

D) how older drivers view hybrid cars.

E) 83%.

Answer: C L.O.: 3 9) Which of the following statements about this study is false?

A) Most likely, 17% of those sampled intend to purchase a hybrid in the next two years.

B) Systematic random sampling is a valid sampling technique.

C) 17% is a statistic.

D) 17% is a parameter.

E) The value of the population parameter is unknown.

Answer: D L.O.: 1, 3

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10) A leading question is a question which subtly prompts the respondent to answer in a particular way. Leading questions are generally undesirable as they result in false or slanted information. Which of the following survey questions is leading?

A) Given the prevalence of identity theft, are you reluctant to provide credit card information online?

B) Are you confident that credit card information you provide online is secure?

C) Are you okay with providing credit card information online?

D) How do you feel about shopping online?

E) Are you satisfied with shopping online?

Answer: A L.O.: 2 11) In developing and conducting a survey, what is the main purpose of the pilot test phase?

A) To point out flaws in the survey B) To generate whole data set to analyze C) To determine the cost of the survey D) To make sure that the respondents like the questions E) To make sure that the manager likes the questions Answer: A L.O.: 2, 3 12) In conducting a personal interview, the interviewer is allowed to arbitrarily decide who should be interviewed. Which of the following statements is true?

A) This is a biased sample.

B) This is a voluntary response sample.

C) This is a simple random sample.

D) This is an unbiased sample E) This is a representative sample.

Answer: A L.O.: 2 13) When a tax auditor randomly selects 20 accounts from all the accounts of a business to check for accuracy, she has selected A) a sample from a population.

B) a census.

C) a convenience sample.

D) a biased sample.

E) a stratified sample.

Answer: A L.O.: 1, 3

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14) An Internet service provider has the capability of tracking the time that each of its customers spends connected to the Internet during a month. These data would constitute A) a population.

B) a convenience sample.

C) a simple random sample.

D) a cluster sample.

E) a multistage sample.

Answer: A L.O.: 3 15) A professor hands out survey forms to the students in her own classes. If the population is all students attending the university, this is an example of A) a convenience sample.

B) a random sample.

C) a stratified sample.

D) a census.

E) an unbiased sample.

Answer: A L.O.: 1, 2 16) An attribute of a population is called A) a statistic.

B) a parameter.

C) a census.

D) a real number.

E) an integer.

Answer: B L.O.: 1 17) The National Capital Commission recently performed a quality check on the length of fence posts being installed in a new park area. To do this, each of the 400 posts in inventory was numbered. Twenty numbers from 1 and 400 were randomly selected. These 20 poles were the ones selected for the study. This type of sampling is called A) simple random.

B) convenience.

C) cluster.

D) stratified.

E) systematic.

Answer: A L.O.: 1

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18) In order to estimate a parameter (such as the mean) of a population you would need which of the following?

A) sample B) population C) census D) cluster E) pilot test Answer: A L.O.: 1 19) An attribute of a sample is called a A) parameter.

B) statistic.

C) real number.

D) integer.

E) census.

Answer: B L.O.: 1 20) A simple random sample experiment is repeated four times choosing the same sample size each time. Which of the following statements can be made about the different outcomes?

A) The samples will usually be different from one another.

B) The samples will always be the same.

C) Measurements calculated from the samples will always be different.

D) The samples will always be different from one another.

E) Measurements calculated from the samples will always be the same.

Answer: A L.O.: 1, 3

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Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 4: Displaying and Describing Categorical Data Short Answer - Quiz A Consider the following to answer the question(s) below: A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

Sony Cyber-Shot Kodak - Easy Share Cannon Power Shot Pentax Olympus Other Brands Total

Female Male 73 59 49 47 58 33 37 41 45 28 86 67 348 275

Total 132 96 91 78 73 153 623

1) Identify the variables and tell whether each is categorical or quantitative.

Answer: Gender and Brand; both categorical.

L.O.: 2 2) Find each of the following percentages. a. What percentage of the responses were males who prefer Pentax? b. What percentage of the male responses prefer Pentax? c. What percentage of the consumers who chose Pentax were males?

Answer: a. 6.6% (41/623) b. 14.9% (41/275) c. 52.6% (41/78) L.O.: 2 3) What is the marginal distribution of brands?

Answer: Total Sony Cyber-Shot 132 Kodak - Easy Share 96 Cannon Power Shot 91 Pentax 78 Olympus 73 Other Brands 153 L.O.: 2

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4) Prepare an appropriate chart to display the marginal distribution of brands.

Answer: Either a bar chart (shown below) or a pie chart is appropriate.

L.O.: 1 5) Write a sentence or two about the conditional relative frequency distribution of the brands among female respondents.

Answer: Among females, 21.0% prefer Sony, 14.1% prefer Kodak, 16.7% prefer Cannon, 10.6% prefer Pentax, and 12.9 % prefer Olympus. The remaining 24.7% of females preferred other brands.

L.O.: 2

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6) Consider the following side-by-side bar chart for the data:

Does the chart indicate that brand preference is independent of gender? Explain.

Answer: Brand preference does not appear to be independent of gender. Brand preferences seem to differ based on gender.

L.O.: 2 Short Answer - Quiz B Consider the following to answer the question(s) below: A full service brokerage firm gathered information on how their clients were investing for retirement. Based on age, clients were categorized according to where the largest percentage of their retirement portfolio was invested. The table below summarized the data.

Age 50 or Over Younger Age 50 Mutual Funds 30 34 Stocks 37 45 Bonds 19 23 Total 86 102

Total 64 82 42 188

1) Identify the variables and tell whether each is categorical or quantitative.

Answer: Mode of investment and age; mode of investment is categorical; age is quantitative.

L.O.: 2

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2) Find each of the following percentages. a. What percentage of the clients invest in mutual funds and are over age 50? b. What percentage of clients over age 50 invest in mutual funds? c. What percentage of the mutual fund investors are over age 50?

Answer: a. 18.1% (34/188) b. 33.3% (34/102) c. 53.1% (34/64) L.O.: 2 3) What is the marginal distribution of age?

Answer: 86 clients are age 50 or younger and 102 are over age 50.

L.O.: 2 4) Prepare an appropriate chart to display the marginal distribution of age.

Answer: Either a bar chart (shown below) or a pie chart is appropriate.

L.O.: 1 5) Write a sentence or two about the conditional relative frequency distribution of mode of investment for clients age 50 or younger.

Answer: Among clients age 50 or younger, 34.9% invest in mutual funds, 43.0% invest in stocks, while 22.1% invest in bonds.

L.O.: 2

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6) Consider the following side-by-side bar chart for the data below:

Does the chart indicate that mode of investment is independent of age? Explain.

Answer: The way clients invest for retirement does seem to be independent of age. These data provide little indication of a difference in mode of investing for retirement based on clients' ages at this firm.

L.O.: 2

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Multiple Choice - Quiz C Consider the following to answer the question(s) below: A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

Sony Cyber-Shot Kodak - Easy Share Cannon Power Shot Pentax Olympus Other Brands Total

Female 73 49 58 37 45 86 348

Male 59 47 33 41 28 67 275

Total 132 96 91 78 73 153 623

1) The percentage of consumers who are male and prefer Pentax is A) 44.1% (275/623).

B) 6.6% (41/623).

C) 52.6% (41/78).

D) 14.9% (41/275).

E) 12.5% (78/623).

Answer: B L.O.: 2 2) Of the consumers who are male, the percentage who prefer Pentax is A) 44.1% (275/623).

B) 6.6% (41/623).

C) 52.6% (41/78).

D) 14.9% (41/275).

E) 12.5% (78/623).

Answer: D L.O.: 2 3) Of the consumers who prefer Pentax, what percentage is male?

A) 44.1% (275/623) B) 6.6% (41/623) C) 52.6% (41/78) D) 14.9% (41/275) E) 12.5% (78/623) Answer: C L.O.: 2

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4) Of the consumers who prefer Canon, what percentage is female?

A) 63.74% (58/91) B) 16.67% (58/348) C) 9.31% (58/623) D) 14.61% (91/623) E) 55.86% (348/623) Answer: A L.O.: 2 5) Of the consumers who are female, the percentage who prefer Canon is A) 63.74% (58/91).

B) 16.67% (58/348).

C) 9.31% (58/623).

D) 14.61% (91/623).

E) 55.86% (348/623).

Answer: B L.O.: 2 6) Here is the side-by-side bar chart for these data.

Which of the following statements is true?

A) It appears that camera preference and gender are not related.

B) It appears that camera preference and gender are not independent.

C) It appears that camera preference and gender are independent.

D) More males than females prefer Cannon.

E) More females than males prefer Pentax.

Answer: B L.O.: 1, 2 7 .

7) The following bar chart for these data shows

A) the marginal distribution of brands.

B) the conditional distribution of brands.

C) the marginal distribution of gender.

D) the conditional distribution of gender.

E) the joint distribution of brands and gender.

Answer: A L.O.: 1, 2

8 .

Consider the following to answer the question(s) below: A full service brokerage firm gathered information on how their clients were investing for retirement. Based on age, clients were categorized according to where the largest percentage of their retirement portfolio was invested and shown in the table below.

Age 50 or Over Age Younger 50 Total Mutual Funds 30 34 64 Stocks 37 45 82 Bonds 19 23 42 Total 86 102 188 8) The percentage of clients who are over age 50 and invest in mutual funds is A) 53.1% (34/64).

B) 33.3% (34/102).

C) 18.1% (34/188).

D) 34.0% (64/188).

E) 54.3% (102/188).

Answer: C L.O.: 2 9) Of the clients over age 50, the percentage who invest in mutual funds is A) 53.1% (34/64).

B) 33.3% (34/102).

C) 18.1% (34/188).

D) 34.0% (64/188).

E) 54.3% (102/188).

Answer: B L.O.: 2 10) Of the clients who invest in mutual funds, the percentage over age 50 is A) 53.1% (34/64).

B) 33.3% (34/102).

C) 18.1% (34/188).

D) 34.0% (64/188).

E) 54.3% (102/188).

Answer: A L.O.: 2

9 .

11) The percentage of clients over age 50 is A) 53.1% (34/64).

B) 33.3% (34/102).

C) 18.1% (34/188).

D) 34.0% (64/188).

E) 54.3% (102/188).

Answer: E L.O.: 2 12) The pie chart below for these data shows

A) the marginal distribution of client age.

B) the conditional distribution of client age.

C) the conditional distribution of investment type.

D) the marginal distribution of investment type.

E) the joint distribution of client age and investment type.

Answer: D L.O.: 1, 2

10 .

13) A contingency table is used to display A) the count for each possible joint occurrence of two variables.

B) the cumulative frequency of two variables.

C) the cumulative distribution of a variable with two possible outcomes.

D) the relative frequency of one variable.

E) the relative frequency of nominal variable only.

Answer: A L.O.: 2 14) A study was recently done in which the brand preference for coffee was analyzed against the gender of the shopper. The study consisted of 200 male shoppers and 300 female shoppers.

Three different coffee brands were considered: A, B, and C. A total of 250 female shoppers preferred brand A and 25 female shoppers preferred brand C. A total of 125 male shoppers preferred brand B and 50 male shoppers preferred brand C. What percentage of those who preferred brand B were female shoppers?

A) 5.0% (25/500) B) 8.3% (25/300) C) 16.7% (25/150) D) 30.0% (150/500) E) 50.0% (150/300) Answer: C L.O.: 2 15) One characteristic of a bar chart is A) The bars can be displayed either vertically or horizontally.

B) There can be no gaps between the bars.

C) The bars should be of different widths.

D) It is used to display the distribution of a continuous variable.

E) It shows cumulative frequency.

Answer: A L.O.: 1 16) The city council has just voted to pass the budget for next year. If you were writing a report describing the budget so the citizens could understand how the total tax dollars will be spent, and you decided to show each category of expenses as a wedge of a circle, which of the following graphs would be most appropriate?

A) segmented bar chart B) scatter plot C) bar chart D) side-by-side bar chart E) pie chart Answer: E L.O.: 1

11 .

17) The city council has just voted to pass the budget for next year. If you were writing a report describing the budget so the citizens could understand how the total tax dollars will be spent, and you decided to show each category of expenses as a bar, which of the following graphs would be most appropriate?

A) segmented bar chart B) scatter plot C) bar chart D) side-by-side bar chart E) pie chart Answer: C L.O.: 1 Consider the following to answer the question(s) below: The option to buy extended warranties is commonplace with most electronics purchases. Does the type of purchase affect a consumer's willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table.

18) Of those who made a purchase, the percentage of those who chose the warranty is A) 41.67% (175/420).

B) 7.14% (30/420).

C) 17.14% (30/175).

D) 82.86% (145/175).

E) 71.43% (175/245).

Answer: A L.O.: 2 19) Of those who bought a digital camera, the percentage of those who purchased the warranty is A) 41.67% (30/72).

B) 17.14% (72/420).

C) 7.14% (30/420).

D) 41.14% (72/175).

E) 12.24% (30/245).

Answer: A L.O.: 2

12 .

20) Of the consumers who bought the extended warranty, what percentage purchased a digital camera?

A) 41.67% (175/420) B) 7.14% (30/420) C) 17.14% (30/175) D) 82.86% (145/175) E) 71.43% (175/245) Answer: C L.O.: 2

13 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 5: Displaying and Describing Quantitative Data Short Answer - Quiz A 1) Below is a histogram of salaries (in $) for a sample of marketing managers. Comment on the shape of the distribution.

Answer: The distribution is unimodal and skewed to the right.

L.O.: 1

1 .

2) Below is the five-number summary of salaries (in $) for a sample of marketing managers.

Min 46,360

Q1 69,693

Median 77,020

Q3 91,750

Max 129,420

a. Would you expect the mean salary for this sample of marketing managers to be higher or lower than the median? Explain. b. Which would be a more appropriate measure of central tendency for these data, the mean or median? Explain. c. Calculate the range. d. Calculate the IQR. Answer: a. We would expect the mean salary to be higher than the median because the distribution is skewed to the right. b. The median is preferred over the mean when the distribution is skewed. c. $83,060 d. $22,057 L.O.: 2, 3 3) Below is the five-number summary of salaries (in $) for a sample of marketing managers.

Min 46,360

Q1 69,693

Median 77,020

Q3 91,750

Max 129,420

Suppose the marketing manager who was earning $129,420 got a raise and is now earning $140,000. Indicate how this change would affect the following summary statistics (increase, decrease, or stay about the same). a. Mean b. Median c. Range d. IQR e. Standard deviation Answer: a. Increase b. Stay the same c. Increase d. Stay the same e. Increase L.O.: 2, 3

2 .

4) The table below shows data on total assets ($ million) for a sample of bank branches. Prepare a stem-and-leaf display. Comment on the shape of the distribution.

BRANCH 1 2 3 4 5 6 7 8

ASSETS ($ million) 88 80 58 92 81 70 89 84

Answer: Stem-and-Leaf Display: Assets ($ million)

The shape of the distribution is skewed to the left.

L.O.: 1 5) The table below shows data on total assets ($ million) for a sample of bank branches.

BRANCH 1 2 3 4 5 6 7 8

ASSETS ($ million) 88 80 58 92 81 70 89 84

For the data on total assets ($ million) for the sample provided: a. Calculate the mean. b. Calculate the standard deviation. c. Standardize the asset value of the third branch (find the z-score). Interpret its meaning.

Answer: a. -80.25 ($million) b. -11.27 ($million) c. z = -1.97. This value is approximately 2 standard deviations below the mean.

L.O.: 2, 3, 6 3 .

6) The boxplots show monthly sales revenue figures ($ thousands) for a discount office supply company with locations in three different regions in Canada (Atlantic, Central and West).

a. Which region has the highest median sales revenue? b. Which region has the lowest median sales revenue? c. Which region has the most variable sales revenue values? Explain.

Answer: a. Atlantic. b. Central. c. West. It has the largest range and IQR. L.O.: 4

4 .

Short Answer - Quiz B 1) Data were collected on the hourly wage ($) for two types of marketing managers: (1) advertising / promotion managers and (2) sales managers. The results were used to create the histograms below.

a. Describe the hourly wage distribution for advertising/promotion managers. b. Describe the hourly wage distribution for sales managers. c. Compare the hourly wages for the two types of marketing managers based on the histograms.

Answer: a. Unimodal and right-skewed b. Unimodal and left-skewed c. It appears that sales managers earn higher hourly wages compared to advertising/promotion managers.

L.O.: 2

5 .

2) Below is the five-number summary of the hourly wages ($) for advertising / promotion managers.

Min 19.64

Q1 29.36

Median 34.18

Q3 40.86

Max 57.26

a. Would you expect the mean salary for this sample of marketing managers to be higher or lower than the median? Explain. b. Which would be a more appropriate measure of central tendency for these data, the mean or median? Explain. c. Calculate the range. d. Calculate the IQR. Answer: a. We would expect the mean salary to be higher than the median because the distribution is skewed to the right. b. The median is preferred over the mean as the distribution is skewed. c. $37.62 d. $11.50 L.O.: 2, 3 3) Below is the five-number summary of the hourly wages ($) for sales managers.

Min 20.94

Q1 37.64

Median 44.77

Q3 49.34

Max 67.11

Suppose there had been an error and that the lowest hourly wage for sales managers was $18.50 instead of $20.94. Indicate how this change would affect the following summary statistics (increase, decrease, or stay about the same). a. Mean b. Median c. Range d. IQR e. Standard deviation Answer: a. Decrease b. Stay the same c. Increase d. Stay the same e. Increase L.O.: 2, 3

6 .

4) The table below shows closing share prices (on the first trading day of August, 2007) for a small sample of companies.

CLOSING SHARE PRICE COMPANY ($)08/07 3M Dental Products 86.95 Tyco Electronics Power Systems 47.45 Kyocera America Inc. 94.10 Pfizer Inc. 22.39 Xerox Company 17.56 Northrop Grumman Corporation 75.81 Lockheed Martin Maritime Systems 100.17 Sony DADC 51.91 Matsushita Electronic Components 17.91 Foster Wheeler Environmental Corp.

55.67 a. Calculate the mean. b. Calculate the standard deviation. c. Standardize the share price for Matsushita Electronic Components (find the z-score).

Interpret its meaning.

Answer: a. $56.99 b. $31.43 c. z = -1.24; the share price for Matsushita Electronic Components is 1.24 standard deviations below the mean.

L.O.: 2, 3, 6

7 .

5) The boxplots below show the closing share prices for a sample of companies on the first trading days in August 2015 and in August 2010.

a. For which day was the median closing share price higher? b. For which day were the closing share prices more variable? Explain. c. Which distribution is more symmetric? Explain.

Answer: a. August 2015 b. August 2015, as the range and IQR are higher. c. August 2015, as the median line is near the middle of the box.

L.O.: 4

8 .

6) Below is a time series plot for monthly closing price of 3M Dental Products stock (beginning June 2005).

a. Are the closing prices for shares of 3M Dental Products from June 2005 through August 2007 stationary? Explain. b. Would a histogram provide a good summary of these stock prices? Explain.

Answer: a. No, an upward trend is evident. b. No, because these data are not stationary.

L.O.: 7

9 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: Below is a histogram and the five-number summary for salaries (in $) for a sample of marketing managers.

Min 46,360

Q1 69,693

Median 77,020

Q3 91,750

Max 129,420

1) The shape of this distribution is A) symmetric.

B) bimodal.

C) unimodal and right-skewed.

D) left-skewed.

E) multimodal.

Answer: C L.O.: 2 2) The most appropriate measure of central tendency for these data is the A) median.

B) mean.

C) mode.

D) range.

E) standard deviation.

Answer: A L.O.: 2 3) The IQR for these data is 10 .

A) $83,060.

B) $22,057.

C) $69,693.

D) $77,020.

E) $14,566.

Answer: B L.O.: 3 4) Suppose the marketing manager who was earning $129,420 got a raise and is now earning $140,000. Which one of the following statements is true?

A) The mean would increase.

B) The median would increase.

C) The range would stay the same.

D) The IQR would increase.

E) The IQR would decrease.

Answer: A L.O.: 2, 3 5) The upper and lower "fences" for a boxplot of these data are A) $47,636 and $113,807.

B) $43,934.5 and $110,105.5.

C) $54,963 and $99,077.

D) $36,607.5 and $124,835.5.

E) $58,664.5 and $102,778.5.

Answer: D L.O.: 4 6) Do the data contain any outliers as determined by the five-number summary?

A) only at the upper end B) only at the lower end C) at the upper and the lower ends D) There are no outliers.

E) There are two outliers.

Answer: A L.O.: 4

11 .

Consider the following to answer the question(s) below: The table below shows closing share prices for a small sample of companies.

CLOSING SHARE PRICE ($) COMPANY 08/07 3M Dental Products 86.95 Tyco Electronics Power Systems 47.45 Kyocera America Inc. 94.10 Pfizer Inc. 22.39 Xerox Company 17.56 Northrop Grumman Corporation 75.81 Lockheed Martin Maritime Systems 100.17 Sony DADC 51.91 Matsushita Electronic Components 17.91 Foster Wheeler Environmental Corp.

55.67 7) The mean closing share price is A) $31.23.

B) $44.65.

C) $56.99.

D) $62.19.

E) $75.77.

Answer: C L.O.: 2 8) The standard deviation of the closing share prices is A) $31.43.

B) $44.65.

C) $56.99.

D) $62.19.

E) $75.77.

Answer: A L.O.: 3 9) The z-score for the share price of Matsushita Electronic Components is A) 1.24.

B) 2.34.

C) -2.34.

D) -3.00.

E) -1.24.

Answer: E L.O.: 6

12 .

Consider the following to answer the question(s) below: The boxplots below show monthly sales revenue figures ($ thousands) for a discount office supply company with locations in three different regions of Canada (Atlantic, Central and West).

10) Which of the following statements is true?

A) The Atlantic region has the lowest sales revenues.

B) The Central region has the lowest median sales revenue.

C) The West region has the lowest mean sales revenue.

D) The West region has the lowest median sales revenue.

E) The Atlantic region has the lowest mean sales.

Answer: B L.O.: 4 11) Which of the following statements is false?

A) The West region has the most variable sales revenues.

B) The West region has the largest IQR. C) The Central region has the smallest IQR. D) The Atlantic region has the most variable sales revenues.

E) The Central region has the least variable sales revenues.

Answer: D L.O.: 4

13 .

12) Below is a time series plot for monthly closing stock prices of 3M Dental Products. Which of the following statements is true?

A) The data are stationary.

B) The data show an upward trend.

C) A histogram would provide the best representation of these data.

D) The data show a downward trend.

E) A boxplot would provide the best representation of this data.

Answer: B L.O.: 1, 7 13) Which of the following best describes the difference between stem-and-leaf displays and histograms?

A) There is no difference.

B) Histograms show the shape and spread but not the centre.

C) Histograms show the shape, centre, and spread of the distribution while the stem-and-leaf displays do not.

D) Histograms show the data values themselves while stem-and-leaf displays do not.

E) Histograms provide an easy-to-understand summary of distribution. The stem-and-leaf displays show the individual values while the histogram does not.

Answer: E L.O.: 1

14 .

14) A sample of families with children at a local school is found to have a mean of 3.2 members per family. The mode number of family members is 2 and the median number is 2.0. Based on this information, which statement is true?

A) The skewness of the distribution is unknown.

B) The distribution is symmetric.

C) The distribution is right-skewed.

D) The distribution is left-skewed.

E) The distribution is symmetric and bell-shaped.

Answer: C L.O.: 2 15) A student recently wrote an entrance exam and was informed that his score placed him at the 80th percentile. This indicates that A) 80 students who also took the exam scored below him.

B) he scored as high or higher than 80 percent of all those who wrote the exam.

C) he was in the bottom 20 percent of those who wrote the exam.

D) his z-score was 80.

E) his exam mark was 80 out of 100.

Answer: B L.O.: 3 16) A z-score of -2.7 indicates that a data value is A) 2.7 standard deviations above the median.

B) 2.7 standard deviations above the mean.

C) 2.7 standard deviations above the mode.

D) 2.7 standard deviations below the median.

E) 2.7 standard deviations below the mean.

Answer: E L.O.: 6 17) Which of the following statements is false?

A) The length of the box in a boxplot is equal to IQR. B) The median and quartiles divide data into four equal parts.

C) The median and quartiles divide data into three equal parts.

D) The upper quartile (Q3) is the value with a quarter of the data above it.

E) The lower quartile (Q1) is the value with a quarter of the data below it.

Answer: C L.O.: 2, 3

15 .

18) Sample data were collected on the number of hours per day students spent at the computer or iPad. MALE FEMALE

8 12

5 6

2 3

8 2

10 4

6 6

Which one of the following statements is true?

A) Females have the larger mean.

B) Males have the larger range.

C) The coefficient of variation is larger for males.

D) The coefficient of variation is larger for females.

E) The variance for males is larger.

Answer: D L.O.: 3 19) The asking price for homes in the Winnipeg real estate market has a mean value of $286,455 and a standard deviation of $11,200. The mean and standard deviation in asking price for homes in Moncton are $188,468 and $8,230, respectively. Recently, one home sold in each city where the asking price for each home was $225,000. Based on these data, which of the following statements is true?

A) The variance for Winnipeg real estate market is lower than that for Moncton.

B) The Moncton home has a negative standardized value.

C) The coefficients of variation are very close to each other (both are about 0.04).

D) The Winnipeg home has a positive standardized value.

E) Both homes have the same z-score.

Answer: C L.O.: 3, 6 20) Given the boxplot below, which one of the following statements is correct?

A) The distribution is symmetric.

B) The distribution is skewed to the left.

C) The distribution is skewed to the right.

D) The distribution has no extreme values.

E) The IQR is over 50.

Answer: C L.O.: 4

16 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 6: Scatterplots, Association, and Correlation Short Answer - Quiz A 1) In discussing how its customers use online services, a bank manager noted "there seems to be a strong correlation between the use of the online bill paying feature and gender". Comment on this statement.

Answer: There may be an association between the use of online bill paying and gender, but these variables are both categorical so they cannot be correlated.

L.O.: 2 2) The following scatterplot shows a relationship between x and y that results in a correlation coefficient of r = 0. Explain why r = 0 in this situation even though there appears to be a strong relationship between the x and y variables.

Answer: The correlation measures the direction and strength of a linear association between two variables. This relationship is strong but not linear so the correlation coefficient is zero.

L.O.: 2

1 .

3) For each of the following scenarios, indicate which is the predictor variable and which is the response variable. a. A study examined consumption levels of oil and carbon dioxide emissions for a sample of municipalities. b. Data were collected on job performance rating and hours of training for a sample of employees at a telecommunications repair facility. c. Salary data as well as years of managerial experience were collected for a sample of executives in the high tech industry.

Answer: a. Oil consumption level is the predictor variable, carbon dioxide emissions is the response variable. b. Job performance rating is the response variable, and hours of training is the predictor variable. c. Salary is the response variable, and years of managerial experience is the predictor variable.

L.O.: 1

2 .

4) The following scatterplot shows monthly sales figures (in units) and number of months of experience on the job for a sample of 18 salespeople.

a. Describe the association between monthly sales and level of experience. b. Do these data satisfy the conditions for computing a correlation coefficient? Explain. c. Estimate the correlation. Which value of r looks most probable: 0.1, 0.3, or 0.9?

Answer: a. Direction: positive; form: straight; strength: quite strong scatter around a generally straight form; unusual features: no outliers. b. Yes, variables are quantitative, the relationship is straight enough, and there are no apparent outliers. c. There is a quite strong and positive linear relationship between monthly sales and level of experience. The correlation coefficient is approximately 0.9.

L.O.: 1, 2

3 .

5) Shown below is a correlation table showing correlation coefficients between stock price, earnings per share (EPS), and the price/earnings (P/E) ratio for a sample of 19 publicly traded companies.

Correlation: Stock Price, EPS, P/E

Stock Price EPS P/E

Stock Price 1.000 0.875 0.323

EPS

P/E

1.000 -0.111

1.000

a. What is the correlation between stock price and EPS? Interpret. b. What is the correlation between stock price and P/E? Interpret. c. What is the correlation between EPS and P/E? Interpret.

Answer: a. 0875, positive and strong b. 0.323, positive and weak c. -0.111, negative and very weak L.O.: 2

4 .

6) Based on the scatterplots shown below, describe the association between x and y. a.

b.

Answer: a. The association between x and y is positive and moderately strong. b. There is no apparent relationship between x and y.

L.O.: 1

5 .

Short Answer - Quiz B 1) In commenting on the increase in home foreclosures, a news reporter stated "there appears to be a strong correlation between home foreclosures and job loss of the head of household."

Comment on this statement.

Answer: There may be an association between home foreclosures and the head of household losing his/her job, but these variables are both categorical so they cannot be correlated.

L.O.: 2 2) For each of the following scenarios, indicate which is the predictor variable and which is the response variable. a. A supermarket chain gathers data on the amount they spend on promotional material (specials, coupons, etc.) and sales revenue generated each quarter. b. Government sponsored research investigated the relationship between the number of hours individuals spend on the Internet and age. c. A real estate association conducted a study on home prices and economic strength for different regions of Canada.

Answer: a. Amount spent on promotional material is the predictor variable, and sales revenue is the response variable. b. Number of hours spent on the Internet is the response variable, and age is the predictor variable. c. Home price is the response variable, and economic strength is the predictor variable.

L.O.: 1

6 .

3) The following scatterplot shows Internet Usage and PC household adoption rate (per 100 inhabitants) for a sample of 15 countries.

a. Describe the association between Internet usage and PC household adoption rate. b. Do these data satisfy the conditions for computing a correlation coefficient? Explain. c. Estimate the correlation. Which value of r looks most probable: 0.1, 0.3, or 0.9?

Answer: a. Direction: positive; form: straight; strength: strong scatter around a generally straight form; unusual features: no outliers. b. Yes, variables are quantitative, the relationship is straight enough, and there are no apparent outliers (although the concentration of points at the lower end and higher end of PC household adoption rate may inflate the correlation). c. There is a strong linear and positive relationship between Internet usage and PC household adoption rate. The correlation coefficient is about 0.9.

L.O.: 1, 2

7 .

4) Shown below is a correlation table showing correlation coefficients between population (in millions), PC household adoption rate and cell phone adoption rate for a sample of 16 countries.

Correlation: PC Adoption, Cell Phone Adoption, Population

PC Adoption PC Adoption 1.000 Cell Phone Adoption 0.671 Population 0.376

Cell Phone Adoption

Population

1.000 0.016

1.000

a. What is the correlation between PC household adoption rate and population? Interpret. b. What is the correlation between cell phone adoption rate and population? Interpret. c. What is the correlation between PC household adoption rate and cell phone adoption rate?

Interpret.

Answer: a. 0.376, positive and weak. b. 0.016, positive and very weak. c. 0.671, positive and moderately strong.

L.O.: 2

8 .

5) A consumer research group investigating the relationship between the price of meat (per kilogram) and the fat content (grams) gathered data that produced the following scatterplot.

a. Describe the association between the price of meat and fat content. b. Estimate the correlation. Which value of r looks most probable: -0.9, -0.5, or -0.1? c. If the point in the lower left hand corner ($2.00 per kilogram, 6 grams of fat) is removed, would the correlation become stronger, weaker, or remain the same? Explain.

Answer: a. Direction: negative; form: moderate straight; strength: moderate; unusual features: one point in the lower left hand corner stands away from the overall pattern. b. There is a moderate linear and negative relationship between the price of meat and fat content. The correlation coefficient is around -0.5. c. It would become stronger because correlation is sensitive to unusual observations. This point stands out of the overall pattern.

L.O.: 1, 2

9 .

6) Based on the scatterplots shown below, describe the association between x and y. a.

b.

Answer: a. There is no apparent relationship between x and y. b. There is a very strong positive linear relationship between x and y.

L.O.: 1

10 .

Multiple Choice - Quiz C 1) A study examined consumption levels of oil and carbon dioxide emissions for a sample of municipalities. The response variable in this study is A) oil brands.

B) oil consumption levels.

C) carbon dioxide emissions.

D) municipalities.

E) oil prices.

Answer: C L.O.: 1 2) A supermarket chain gathers data on the amount they spend on promotional material (specials, coupons, etc.) and sales revenue generated each quarter. The predictor variable is A) sales revenue.

B) amount spent on promotional material.

C) number of coupons offered.

D) supermarket chains.

E) number of quarter.

Answer: B L.O.: 1 3) Government sponsored research investigated the relationship between the number of hours individuals spend on the Internet and age. Which of the following statements is true?

A) Age is the predictor variable and number of hours spent on the Internet is the response variable.

B) Government is the predictor variable and the number of hours spent on the Internet is the response variable.

C) Age is the response variable and the number of hours spent on the Internet is the predictor variable.

D) Age is the predictor variable and government sponsored research is the response variable.

E) Number of individuals is the predictor variable and government sponsored research is the response variable.

Answer: A L.O.: 1 4) In discussing how its customers use online services, a bank manager noted "there seems to be a strong correlation between the use of the online bill paying feature and gender". Which of the following is true regarding this statement?

A) The correlation between the use of online bill paying feature and gender is negative.

B) The correlation between the use of online bill paying feature and gender is positive.

C) There may be an association between the use of online bill paying feature and gender, but these variables are both categorical so they cannot be correlated.

D) More males will bank online compared with females.

E) More females will bank online compared with males.

Answer: C L.O.: 2 11 .

Consider the following to answer the question(s) below: The following scatterplot shows monthly sales figures (in units) and the number of months of experience on the job for a sample of 18 salespeople.

5) The association between monthly sales and number of months of experience can be described as A) positive and weak.

B) negative and weak.

C) negative and strong.

D) positive and strong.

E) nonlinear.

Answer: D L.O.: 1 6) The correlation coefficient between monthly sales and number of months of experience is most likely A) -0.235.

B) 0.

C) 0.180.

D) -0.914.

E) 0.914.

Answer: E L.O.: 2

12 .

Consider the following to answer the question(s) below: A consumer research group investigating the relationship between the price of meat (per kilogram) and the fat content (grams) gathered data that produced the following scatterplot.

7) Which best describes the association between the price of meat and fat content?

A) Negative, moderately strong, linear B) Negative, very weak, linear C) Positive, strong, linear D) Positive, weak, linear E) Nonlinear Answer: A L.O.: 1 8) If the point in the lower left hand corner ($2.00 per kilogram, 6 grams of fat) were removed, the correlation would most likely A) remain the same.

B) become stronger negative.

C) become weaker negative.

D) become positive.

E) become nonlinear.

Answer: B L.O.: 1

13 .

9) Which of the following statements about the relationship associated with the given scatterplot is true?

A) The scatterplot indicates strong linear correlation and r is about 0.70.

B) The scatterplot indicates strong linear correlation and r is about -0.70.

C) The scatterplot indicates moderate linear correlation and r is about 0.50.

D) The scatterplot indicates moderate linear correlation and r is about -0.50.

E) There is a certain association, but not linear.

Answer: E L.O.: 2

14 .

10) Shown below is a correlation table showing correlation coefficients between stock price, earnings per share (EPS), and the price/earnings (P/E) ratio for a sample of 19 publicly traded companies. Which of the following statements is false?

Correlation: Stock Price, EPS, P/E

Stock Price EPS P/E

Stock Price 1.000 0.875 0.323

EPS

P/E

1.000 -0.111

1.000

A) Since r = 0.323 for P/E and Stock Price, there is a relatively weak positive correlation between P/E and Stock Price.

B) The strongest correlation is between EPS and Stock Price.

C) There is a weak negative correlation between P/E and EPS. D) The strongest correlation is between P/E and Stock Price.

E) The weakest correlation is between P/E and EPS. Answer: D L.O.: 1, 2 11) A student wants to investigate the association between number of cases of mosquito-borne diseases and ice cream sales in the campus area. Which of the following statements is true?

A) It looks like there is a strong positive correlation.

B) It looks like there is a strong negative correlation.

C) The variables are not quantitative, so the student reports about a strong positive association.

D) The variables are not quantitative, so the student reports about nonlinear association.

E) There is a lurking variable, weather, in this study. As the weather grows warmer, more people buy ice cream and more people go outside.

Answer: E L.O.: 3 12) If the correlation coefficient for the variables is determined to be 0.70, which of the following is known to be true?

A) The relationship between the variables is nonlinear.

B) The correlation is negative.

C) The scatterplot for the variables will be upward sloping from left to right.

D) The scatterplot for the variables will be downward sloping from left to right.

E) The scatterplot shows a curvilinear pattern.

Answer: C L.O.: 1, 2

15 .

13) If two variables have a curvilinear relationship, which of the following is true?

A) The correlation coefficient will not be able to measure strength of the association.

B) The correlation coefficient will be equal to-1.

C) The correlation coefficient will be equal to 1.

D) The scatter plot is useless to indicate that the relationship is curved.

E) Only outliers make the curvilinear pattern.

Answer: A L.O.: 2 14) Which of the following statements is correct?

A) A scatter plot showing two variables with a positive linear relationship will have all points on a straight line.

B) The stronger the linear positive relationship between two variables, the closer the correlation coefficient will be to -1.

C) Two variables that are uncorrelated with one another may still be related in a nonlinear manner.

D) A curvilinear relationship will always have a correlation coefficient of exactly zero.

E) The stronger the linear and negative association between two variables, the closer the correlation coefficient will be to +1.

Answer: C L.O.: 1, 2 15) Assume that a medical research study found a correlation coefficient of -0.73 between regular use of sunscreen and the skin cancer rate. This could be interpreted to mean that A) the greater the regular use of sunscreen, the lower the person's chances of getting skin cancer.

B) skin cancer is caused by not using sunscreen regularly.

C) the greater the regular use of sunscreen, the higher the person's chances of getting skin cancer.

D) skin cancer can be prevented by regular use of sunscreen.

E) the lower the regular use of sunscreen, the lower the person's chances of getting skin cancer.

Answer: A L.O.: 2, 3

16 .

16) A study was done in which the daily temperature and the number of traffic accidents within the city were recorded. The standard deviations for the samples are 13.13 for temperature and 2.55 for accidents. These sample data are shown as follows: Temperature 33 13 24 20 -2

Traffic accidents 7 4 9 10 5

Given these data, the sample correlation coefficient is approximately A) 0.55.

B) -0.12.

C) 0.39.

D) -0.55.

E) -0.39.

Answer: A L.O.: 2 17) A perfect correlation between two variables will always produce which of the following?

A) a correlation coefficient of -1.0 B) a scatterplot with a pattern running from lower left to upper right C) a correlation coefficient of 1.0 D) a scatterplot where all points lie on a single straight line E) a scatterplot with a pattern running from upper left to lower right Answer: D L.O.: 1, 2 18) Consider the following sample data. The standard deviations from the data are 3.67 for Y, and 45.28 for X. These sample data are shown as follows: Y 10 7 12 15 16

X 100 110 90 200 150

Given this data, the sample correlation is approximately A) 0.68.

B) 0.54.

C) 0.16.

D) 0.39.

E) 0.20.

Answer: A L.O.: 2 17 .

19) In a university statistics course a correlation coefficient of -0.8 was found between the number of classes missed and the course grade. This can be interpreted to mean that A) the more classes missed, the lower the course grade.

B) a lower course grade is caused by missing more classes.

C) the correlation is strong and positive.

D) a higher grade can be achieved by missing fewer classes.

E) the more classes missed, the higher the course grade.

Answer: A L.O.: 2, 3 20) The University recently sampled five full time students who work off campus in order to look at their GPA and their work schedules. The standard deviation for GPA is 0.91 and the standard deviation for hours worked is 6.78. These sample data are shown as follows: GPA 9.1 8.9 10.1 9.3 7.6

HOURS 26 30 12 20 22

Given these data the sample correlation is A) -0.49.

B) -0.39.

C) -0.42.

D) -0.34.

E) -0.36.

Answer: A L.O.: 2

18 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 7: Introduction to Linear Regression Short Answer - Quiz A Consider the following to answer the question(s) below: To determine whether the cash bonuses paid by Johnson Financial Group are related to annual pay, data were gathered for 10 account executives who received such bonuses in 2007. The data, scatterplot and summary statistics are shown below.

ANNUAL PAY $ 70,609 $ 58,487 $ 104,561 $ 43,922 $ 82,613 $ 116,250 $ 76,751 $ 68,513 $ 137,000 $ 94,469 Mean $ 85,318 Standard Deviation $ 28,077 Correlation

CASH BONUS $ 11,225 $ 6,238 $ 14,194 $ 4,188 $ 11,863 $ 13,671 $ 7,758 $ 20,760 $ 55,000 $ 34,368 $ 17,927 $ 15,618

0.735

1 .

Note: In answers to problems 2, 4, and 5 we will be using regression equation coefficients received by computer software. If we apply textbook formulae, the value of intercept will be a little bit different.

1) Comment on whether each of the following conditions for correlation / linear regression is met. a. Quantitative Variables Condition b. Linearity Condition c. Outlier Condition Answer: a. Yes, both variables are quantitative. b. Yes, the relationship appears to be straight enough. c. Yes, no obvious outliers.

L.O.: 1 2) Estimate the linear regression model that relates the response variable (Cash Bonus) to the predictor variable (Annual Pay). a. Find the slope of the regression line. b. Find the intercept of the regression line. c. Write the equation of the linear model.

Answer: a. 0.409 b. -16,945 c. Cash Bonus = -16,945 + 0.409 Annual Pay L.O.: 1 3) Find the value of R2. Interpret its meaning in this context.

Answer: R2 = 0.54 = 54%, which means that 54% of the variation of the cash bonus can be explained by variation in the annual pay.

L.O.: 2 4) Using the regression equation, a. Estimate the cash bonus for an executive at Johnson Financial Group earning $82,613 a year. b. What is the residual for this estimate? What does it mean?

Answer: a. $16,844 b. -$4,981. It tells us that the actual cash bonus was $4,981 less than the model predicted.

L.O.: 1 5) Using the regression equation, a. Estimate the cash bonus for an executive at Johnson Financial earning $200,000 a year. b. How confident should you be in this estimate? Explain.

Answer: a. $64,855. b. Not very, since we are predicting for a value of annual pay beyond the range of the data. We should be careful about extrapolating beyond the range of the predictor variable.

L.O.: 1 2 .

6) Below is a plot showing residuals versus fitted values for the estimated regression equation relating cash bonus to annual pay for the account executives at Johnson Financial Group. Are all the conditions for linear regression met? Explain.

Answer: The residual plot shows that the Equal Spread Condition is violated. The residuals "fan out" from left to right in a cone shape.

L.O.: 1

3 .

Short Answer - Quiz B Consider the following to answer the question(s) below: A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many kilograms of each variety of coffee were sold last month. The data, scatterplot, and summary statistics are shown below.

PRICE PER KILOGRAM $ 3.99 $ 5.99 $ 7.00 $ 12.00 $ 4.50 $ 7.50 $ 15.00 $ 10.00 $ 12.50 $ 8.99 Mean $ 8.75 Standard Deviation $ 3.63 Correlation

KILOGRAMS SOLD 75 60 65 45 80 70 25 35 40 50 54.50 18.33

-0.927

4 .

Note: In answers to problems 2, 4, and 5 we will be using regression equation coefficients received by computer software. If we apply textbook formulae, the value of intercept will be a little bit different.

1) Comment on whether each of the following conditions for correlation / linear regression is met. a. Quantitative Variables Condition b. Linearity Condition c. Outlier Condition Answer: a. Yes, both variables are quantitative. b. Yes, the relationship appears straight enough. c. Yes, no obvious outliers.

L.O.: 1 2) Estimate the linear regression model that relates the response variable (Kilograms Sold) to the predictor variable (Price per Kilogram). a. Find the slope of the regression line. b. Find the intercept of the regression line. c. Write the equation of the linear model.

Answer: a. -4.684 b. 95.47 c. Kilograms sold = 95.47 - 4.684 Price per kilogram L.O.: 1 3) Find the value of R2. Interpret its meaning in this context.

Answer: R2 = 0.86 = 86%, which means that 86% of the variation of the number of kilograms of coffee sold per month can be explained by the variation of coffee price.

L.O.: 2 4) Using the estimated regression equation, a. Estimate the monthly sales (kilograms sold) for a variety of coffee that costs $12.00 per kilogram. b. What is the residual for this estimate? What does it mean?

Answer: a. 39.26 kilograms b. 5.74 kilograms. It tells us that the actual number of kilograms sold were 5.74 kilograms more than the model predicted.

L.O.: 1

5 .

5) Using the estimated regression equation, a. Estimate the monthly sales for a variety of coffee that costs $20.00 per kilogram. b. How confident should you be in this estimate? Explain.

Answer: a. 1.79 kilograms b. Not very, since we are predicting for a value of price per kilogram beyond the range of the data. We should be careful about extrapolating beyond the range of predictor variable.

L.O.: 1 6) Below is a plot showing residuals versus fitted values for the estimated regression equation relating monthly sales of coffee to price per kilogram. Are all the conditions for linear regression met? Explain.

Answer: The residual plot indicates that all conditions are reasonably met although a slight spreading is noted. A further analysis may determine the reason for this pattern.

L.O.: 1

6 .

Multiple Choice - Quiz C Note: In the following problems we will be using regression equation coefficients received by computer software. Sometimes, they might be a little bit different as compared to coefficients calculated by textbook formulae.

Consider the following to answer the question(s) below: To determine whether the cash bonuses paid by Johnson Financial Group are related to annual pay, data were gathered for 10 account executives who received such bonuses in 2007. The data, scatterplot and summary statistics are shown below.

ANNUAL PAY $ 70,609 $ 58,487 $ 104,561 $ 43,922 $ 82,613 $ 116,250 $ 76,751 $ 68,513 $ 137,000 $ 94,469 Mean $ 85,318 Standard Deviation $ 28,077 Correlation

CASH BONUS $ 11,225 $ 6,238 $ 14,194 $ 4,188 $ 11,863 $ 13,671 $ 7,758 $ 20,760 $ 55,000 $ 34,368 $ 17,927 $ 15,618

0.735

7 .

1) The slope of the estimated regression line that relates the response variable (Cash Bonus) to the predictor variable (Annual Pay) is A) 0.409.

B) -16,945.

C) 0.54.

D) 3.45.

E) 1.32.

Answer: A L.O.: 1 2) The intercept of the estimated regression line that relates the response variable (Cash Bonus) to the predictor variable (Annual Pay) is A) 0.409.

B) -16,945.

C) 0.54.

D) 3.45.

E) 1.32.

Answer: B L.O.: 1 3) What percent of the variation of the cash bonus can be explained by variation of the annual pay?

A) 100% B) 85% C) 73% D) 30% E) 54% Answer: E L.O.: 2 4) Based on the estimated regression equation, the cash bonus for an executive at Johnson Financial Group earning $82,613 a year would be A) $11,863.

B) $16,844.

C) $27,682.

D) $4,958.

E) $15,819.

Answer: B L.O.: 1

8 .

5) Based on the estimated regression equation, the residual for the estimated cash bonus of an executive at Johnson Financial Group earning $82,613 a year would be A) $0.

B) -$4,981.

C) -$15,819.

D) -$4,958.

E) $15,819.

Answer: B L.O.: 1 Consider the following to answer the question(s) below: A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many kilograms of each variety of coffee were sold last month. The data, scatterplot and summary statistics are shown below.

PRICE PER KILOGRAM $ 3.99 $ 5.99 $ 7.00 $ 12.00 $ 4.50 $ 7.50 $ 15.00 $ 10.00 $ 12.50 $ 8.99 Mean $ 8.75 Standard Deviation $ 3.63 Correlation

KILOGRAMS SOLD 75 60 65 45 80 70 25 35 40 50 54.50 18.33

-0.927

9 .

6) Which of the following statements is true?

A) The Quantitative Variables Condition is not satisfied.

B) The Linearity Condition is not satisfied.

C) There are obvious outliers.

D) The Quantitative Variables Condition is satisfied.

E) The intercept of the line of best fit is approximately zero.

Answer: D L.O.: 1 7) The slope of the estimated regression line that relates the response variable (Kilograms Sold) to the predictor variable (Price per Kilogram) is A) 95.47 B) 0.858 C) -4.684 D) -0.858 E) -8.999 Answer: C L.O.: 1 8) The intercept of the estimated regression line that relates the response variable (Kilograms Sold) to the predictor variable (Price per Kilogram) is A) 95.47.

B) 0.858.

C) -4.684.

D) -0.858.

E) -8.999.

Answer: A L.O.: 1 10 .

9) What percent of the variation of the number of kilograms of coffee sold per month can be explained by variation of price per kilogram?

A) 93% B) 100% C) 86% D) 96% E) 14% Answer: C L.O.: 2 10) Below is a plot showing residuals versus fitted values for the estimated regression equation relating monthly sales (kilograms sold) of coffee to price per kilogram. Based on this plot we can say

A) the Linearity Condition is not satisfied.

B) the Linearity Condition is reasonably satisfied.

C) there are several extreme outliers.

D) the correlation coefficient is close to 1.

E) the correlation coefficient is 0.

Answer: B L.O.: 1

11 .

11) A regression of two variables, x and y, results in the value of R2 equal to 0.7834. Which of the following statements is true?

A) The correlation coefficient must be 0.7834.

B) The correlation coefficient must be -0.8851.

C) The correlation coefficient must be -0.7834.

D) The correlation coefficient can be either 0.8851 or -0.8851.

E) The correlation coefficient must be 0.8851.

Answer: D L.O.: 2 12) A pair of variables, x and y, have a correlation coefficient of -0.8851. Which of the following statements is true?

A) variation of x explains about 78.34 % of the variation of y B) variation of x explains about 88.51 % of the variation of y C) variation of y explains about 78.34% of the variation of x D) variation of x cannot explain about 78.34 % of the variation of y E) variation of y explains about 88.51% of the variation of x Answer: A L.O.: 2

12 .

Consider the following to answer the question(s) below: To determine whether the tip left at the end of a meal is related to the size of the total bill at their restaurant, Chez Michelle, data were gathered for 10 customers. The data and summary statistics are shown below.

Total Bill $126 $58 $86 $20 $59 $120 $14 $17 $26 $74

Tip $19 $11 $20 $3 $14 $30 $2 $4 $2 $16

Mean Standard deviation

$60 41.57

$12 9.45

Correlation

0.937

13) The slope of the estimated regression line that relates the response variable (Tip) to the predictor variable (Total Bill) is A) 0.213.

B) -0.213.

C) 0.877.

D) 0.937.

E) -0.937.

Answer: A L.O.: 1 14) The intercept of the estimated regression line that relates the response variable (Tip) to the predictor variable (Total Bill) is A) -0.6684.

B) 0.6684.

C) 57.42.

D) -57.42.

E) 12.0.

Answer: A L.O.: 1

13 .

15) The percentage of the variation of the tip that can be explained by the variation of the total bill is A) 87.7%.

B) 93.7%.

C) 21.3%.

D) 66.8%.

E) 96.8%.

Answer: A L.O.: 2 16) The regression equation would predict what size of tip if the total bill was $120?

A) $24.89 B) $15.55 C) $26.03 D) $30.00 E) $20.62 Answer: A L.O.: 1 17) The residual for the estimated tip for a total bill of $120 would be A) $5.11 B) $19.00 C) 0 D) -$11.45 E) $9.38 Answer: A L.O.: 1

14 .

18) Analyze the scatterplot below. What solution strategy would be most appropriate?

A) The relationship is perfectly linear. We should construct a linear regression model.

B) The relationship is straight enough. We should construct a linear regression model.

C) The scatterplot shows extreme outliers. We can swap the variables to transform it to linear model.

D) We should collect new data as we cannot identify the type of relationship.

E) This is an example of non-linear relationship. We can try to transform it to linear model by a function such as logarithm.

Answer: E L.O.: 3 19) Which of the following is a correct interpretation for the regression slope coefficient b1?

A) The average change in y of a one-unit change in x will be b1 units.

B) For a one-unit change in y, we can expect the value of the independent variable to change by b1 units on average.

C) For each unit change in x, the dependent variable will change by b1 units.

D) The average change in x of a one-unit change in y will be b1 units.

E) The change in y of a one-unit change in x will always be b1 units.

Answer: A L.O.: 2 20) The regression equation, = -3.61+0.106x, expresses statistical dependence of vacation expenses (y) on personal income (x) in a sample of 45 clients of a large travel agency (both numbers in $thousands). A client with $80,000 income is expected to spend A) $12,090.

B) $8,476.

C) $8,467.

D) $4,870.

E) $1,209.

Answer: D L.O.: 1 15 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 8: Randomness and Probability Short Answer - Quiz A 1) During its grand opening week, Stickler's bicycle shop offers a "wheel of discount savings".

After customers select the items they wish to purchase, they spin the wheel to determine the discount they will receive. The wheel is divided into 12 slices. Six slices are red and award a 10% discount, three slices are white and award a 20% discount, and two slices are blue and award a 40% discount. The remaining slice is gold and awards a 100% discount!

a. What is the probability that a customer gets at least a 40% discount? b. What is the probability that a customer does not get at least a 40% discount? c. What is the probability that a customer gets a 10% or 20% discount? d. What is the probability that two customers in a row get a 20% discount?

Answer: a. 0 25 (Solution: 3/12 = 0.25) b. 0.75 (Solution: 1 - 0.25 = 0.75 by the Complement Rule) c. 0 .75 (Solution: 6/12 + 3/12 = 9/12 = 0.75 by the Addition Rule for mutually exclusive events) d. 0.0625 (Solution: 3/12 × 3/12 = 0.0625 by the Multiplication Rule) L.O.: 2 2) Suppose you visit Stickler's bicycle shop in the hopes of getting a 100% discount on your purchases. As you wait your turn in line, there are three gold winners in a row. The two customers in line behind you begin to discuss what's happened. One believes that the streak of three gold winners has killed anyone else's chances of getting a 100% discount, while the other says just the opposite… that the wheel's "hot streak" increases their chances of getting a 100% discount. Comment on these opinions.

Answer: The spins are independent, so if the wheel is fair, the three gold winners in a row have no effect on the next person's chances.

L.O.: 1

1 .

3) SamaraCom is a communications and media company. It operates in the field of wireless communications, cable TV, telephone, and Internet connectivity. A recent survey showed that 64% of the SamaraCom clients are subscribed to Internet service, 28% are TV customers, and 22% are subscribed to a bundle (both, Internet and TV services). a. What is the probability that a client is subscribed to TV service or Internet? b. What is the probability that a SamaraCom client is subscribed to neither TV service nor Internet? c. Are the events of T = {TV service subscription} and I = {Internet service subscription} disjoint (or mutually exclusive)? Explain.

Answer: a. 0 .70 (Solution: 0.64 + 0.28 - 0.22 = 0.70 by the General Addition Rule) b. 0.30 (Solution: 1 - 0.70 = 0.30 by the Complement Rule) c. No. The probability of the intersection of these two events is equal to 0.22, not zero; a customer can have a bundle (both TV and Internet service).

L.O.: 2, 3 4) A small manufacturing company recently instituted Six Sigma training for its employees. Two methods of training were offered: online and traditional classroom. Management was interested in whether the division (Sales, Quality, Operations) in which employees worked affected their choice of method. Below is a table summarizing the data.

Traditional Online Total

Sales 16 35 51

Quality 10 23 33

Operations 8 44 52

Total 34 102 136

a. What is the probability that an employee chose online training? b. What is the probability that an employee is in the Quality division and chose online training? c. What is the probability that an employee chose online training given that he/she is in the Sales division?

Answer: a. 0.75 (Solution: 102/136 = 0.75) b. 0.17 (Solution: 23/136 = 0.17) c. 0.69 (Solution: 35/51 = 0.69) L.O.: 2 5) Does it appear that choice of instructional method (traditional or online) and division (Sales, Quality or Operations) are independent? Explain.

Answer: Since the marginal probability of choosing online training (0.75) does not equal the conditional probability of choosing online training given the employee is in the Sales division (0.69), the choice of instructional method is not independent of division.

L.O.: 3

2 .

6) One explanation put forth for the scarcity of women CEOs in the high tech industry is that there is a lack of mentoring opportunities for women. A recent survey of CEOs in this industry found that 80% were men. Moreover, 75% of those who were surveyed had been mentored, but only 15% were mentored women. a. Construct the contingency table. b. Are two events W = {a randomly selected CEO is a woman} and N = {a randomly selected CEO has not been mentored} independent? Explain.

Answer: a.

Mentored Not Mentored Total

Men 0.60 0.20 0.80

Women 0.15 0.05 0.20

Total 0.75 0.25 1.00

b. Yes, the events are independent. The conditional probability P(N∣W) = 0.05 / 0.20 = 0.25 equals the marginal probability P(N) = 0.25.

L.O.: 3 Short Answer - Quiz B 1) As an incentive to get new customers, the local branch of a bank launched "bouncing for bucks." During this week-long event, any customer opening a new chequing account with the bank would have the opportunity to throw a bouncy rubber ball into a large box divided into squares. Each square was labeled with a dollar amount that would be deposited into his/her new chequing account. The way the box was labeled is shown below.

10 30 10 30 10 20 10 50 10 20 a. What is the probability that a customer gets $20 or more? b. What is the probability that a customer gets less than $20? c. What is the probability that a customer gets $20 or $30? d. What is the probability that two customers in a row get $50?

Answer: a. 0.50 (Solution: 5/10 = 0.50) b. 0.50 (Solution: 1 - 0.50 = 0.50 by the Complement Rule) c. 0 .40 (Solution: 2/10 + 2/10 = 0.40 by the Addition Rule for mutually exclusive events) d. 0.01 (Solution: 1/10 × 1/10 = 0.01 by the Multiplication Rule) L.O.: 2

3 .

2) As you enter the bank, you watch four persons in front of you all win $50. The local branch manager tells you how lucky you are to be throwing the ball while it is on a hot streak but the friend with you says that you're unlucky because the streak can't continue. Comment on their statements.

Answer: The tosses are independent. So if the box and ball are fair, the four winners of $50 have no effect on the next person's chances of winning $50.

L.O.: 1 3) A major airline keeps track of data on how their passengers redeem frequent flyer miles. They found that in the last year 58% of passengers redeemed them to purchase tickets for domestic travel, 44% redeemed them to purchase tickets for international travel, and that 16% redeemed them to purchase tickets for both domestic and international travel. a. What is the probability that a passenger redeemed frequent flyer miles to purchase a ticket for domestic or international travel? b. What is the probability that a passenger did not redeem frequent flyer miles to purchase a ticket for domestic or international travel? c. Are two events D ={redeeming miles to purchase a ticket for domestic travel} and I ={redeeming miles to purchase a ticket for international travel} disjoint (or mutually exclusive)?

Explain.

Answer: a. 0.86 (Solution: 0.58 + 0.44 - 0.16 = 0.86 by the General Addition Rule) b. 0.14 (Solution: 1 - 0.86 = 0.14 by the Complement Rule) c. No, the probability of the intersection of these two events is equal to 0.16, not zero; a passenger could purchase tickets for both domestic and international travel.

L.O.: 2, 3 4) The option to buy extended warranties is commonplace with most electronics purchases. Does the type of purchase affect a consumer's willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table.

a. What is the probability that a consumer purchases an extended warranty? b. What is the probability that a consumer purchases a digital camera and an extended warranty? c. What is the probability that a consumer purchases an extended warranty given that he/she has purchased a digital camera?

Answer: a. 0.42 (Solution: 175/420 = 0.42) b. 0.07 (Solution: 30/420 = 0.07) c. 0.42 (Solution: 30/72 = 0.42) L.O.: 2 4 .

5) Does it appear that the decision to purchase an extended warranty and the type of electronics purchased (digital camera or laptop computer) are independent? Explain.

Answer: Since the marginal probability of purchasing an extended warranty (0.42) does equal the conditional probability of purchasing an extended warranty given the consumer purchased a digital camera (0.42), the decision to purchase an extended warranty is independent of type of electronics (digital camera or laptop computer) purchased.

L.O.: 3 6) It has been reported that men are more likely than women to participate in online auctions. A recent study found that 52% of Internet shoppers are women and that 35% of Internet shoppers have participated in online auctions. Moreover, 25% of online shoppers were men and had participated in online auctions. a. Construct the contingency table. b. Are gender and participation in online auctions independent? Explain.

Hint: Compare two events M = {a randomly selected shopper is a man} and A = {a randomly selected shopper has participated in online auctions} Answer: a.

Men Women Total Yes Online 0.25 0.10 0.35 Auction No Online 0.23 0.42 0.65 Auction Total 0.48 0.52 1.00 b. The conditional probability P (A∣M) = 0.25 / 0.48 = 0.52 does not equal the marginal probability P(A) = 0.35. Therefore participation in online auctions is not independent of gender.

L.O.: 2, 3

5 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: During its grand opening week, Stickler's bicycle shop offers a "wheel of discount savings."

After customers select the items they wish to purchase, they spin the wheel to determine the discount they will receive. The wheel is divided into 12 slices. Six slices are red and award a 10% discount, three slices are white and award a 20% discount, and two slices are blue and award a 40% discount. The remaining slice is gold and awards a 100% discount!

1) The probability that a customer gets at least a 40% discount is A) 3/12.

B) 2/12.

C) 0.0625.

D) 9/12.

E) 10/12.

Answer: A L.O.: 2 2) The probability that a customer gets a 10% or 20% discount is A) 3/12.

B) 2/12.

C) 0.0625.

D) 9/12.

E) 10/12.

Answer: D L.O.: 2 3) The probability that two customers in a row get a 20% discount is A) 3/12.

B) 2/12.

C) 0.0625.

D) 9/12.

E) 10/12.

Answer: C L.O.: 2 6 .

Consider the following to answer the question(s) below: SamaraCom is a communications and media company. It operates in the field of wireless communications, cable TV, telephone, and Internet connectivity. A recent survey showed that 64% of the SamaraCom clients are subscribed to Internet service, 28% are TV customers, and 22% are subscribed to a bundle (both, Internet and TV services).

4) What is the probability that a client is subscribed to TV service or Internet?

A) 0.22 B) 0.70 C) 0.92 D) 0.30 E) 0.08 Answer: B L.O.: 2 5) The probability that a SamaraCom client is subscribed to neither TV service nor Internet is A) 0.22.

B) 0.70.

C) 0.92.

D) 0.30.

E) 0.08.

Answer: D L.O.: 2 6) Which of the following statements about TV service subscription is true?

A) TV service subscription and having Internet from SamaraCom are disjoint events.

B) The probability of intersection of two events T = {TV service subscription} and I = {Internet service subscription} is equal to zero.

C) T = {TV service subscription} and I = {Internet service subscription} are independent events.

D) TV service subscription and having Internet from SamaraCom are mutually exclusive events.

E) TV service subscription and having Internet from SamaraCom are not mutually exclusive events.

Answer: E L.O.: 3

7 .

Consider the following to answer the question(s) below: The option to buy extended warranties is commonplace with most electronics purchases. Does the type of purchase affect a consumer's willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table.

7) The probability that a consumer does not purchase an extended warranty is A) 0.07.

B) 0.42.

C) 0.58.

D) 0.17.

E) 0.83.

Answer: C L.O.: 2 8) The probability that a consumer purchases a digital camera and an extended warranty is A) 0.07.

B) 0.42.

C) 0.58.

D) 0.17.

E) 0.83.

Answer: A L.O.: 2 9) The probability that a consumer purchases an extended warranty given that he/she has purchased a digital camera is A) 0.07.

B) 0.42.

C) 0.58.

D) 0.17.

E) 0.83.

Answer: B L.O.: 2

8 .

10) Which of the following statements is true?

A) The decision to purchase an extended warranty and the type of electronics (digital camera or laptop computer) purchased are independent.

B) The decision to purchase an extended warranty and the type of electronics (digital camera or laptop computer) purchased are mutually exclusive.

C) The decision to purchase an extended warranty and the type of electronics (digital camera or laptop computer) purchased are disjoint events.

D) The decision to purchase an extended warranty and the type of electronics (digital camera or laptop computer) purchased are not independent.

E) The decision to purchase an extended warranty and the type of electronics (digital camera or laptop computer) purchased are related.

Answer: A L.O.: 3 Consider the following to answer the question(s) below: The following table represents information about investments of 200 randomly selected residents of Etobicoke.

Age 50 or Younger Mutual Funds 30 Stocks 45 Bonds 20 Total 95

Over Age 50 35 45 25 105

Total 65 90 45 200

11) The probability that a client is over age 50 and is holding bonds is A) 0.125.

B) 0.15.

C) 0.225.

D) 0.010.

E) 0.175.

Answer: A L.O.: 2 12) The probability that a client is over age 50 and is not holding bonds is A) 0.40.

B) 0.225.

C) 0.525.

D) 0.175.

E) 0.325.

Answer: A L.O.: 2

9 .

13) The probability that a client is holding mutual funds given that he/she is age 50 or younger is A) 0.316.

B) 0.461.

C) 0.857.

D) 0.15.

E) 0.475.

Answer: A L.O.: 2 14) The probability that a client only holds bonds is A) 0.225.

B) 0.45.

C) 0.475.

D) 0.125.

E) 0.10.

Answer: A L.O.: 2 15) Which of the following statements is true?

A) The decision to purchase stocks and the age of the client are not independent.

B) The decision to purchase stocks and the age of the client are independent.

C) The decision to purchase stocks and the age of the client are mutually exclusive.

D) The decision to purchase stocks and the age of the client are unrelated.

E) The decision to purchase stocks and the age of the client are disjoint events.

Answer: A L.O.: 3 16) When a customer enters a store there are three outcomes that can occur: buy nothing, buy a small amount, or buy a large amount. It is the case that if a customer buys a large amount, he or she cannot also buy a small amount or buy nothing. We say that these events are A) disjoint.

B) independent.

C) all inclusive.

D) related.

E) unrelated.

Answer: A L.O.: 3

10 .

17) Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the purchases of customers are independent of one another, the probability that the next customer will purchase a computer is A) 0.50.

B) 1.00.

C) 0.25.

D) 0.0625.

E) 0.75.

Answer: C L.O.: 2, 3 Consider the following to answer the question(s) below: Harrison Water Sports has three retail outlets: Vancouver, Victoria, and Nanaimo. The Vancouver store does 50 percent of the total sales in a year, while the Victoria store does 35 percent of the total sales, and Nanaimo the remainder. Further analysis indicates that of the sales in Vancouver, 20 percent are in boat accessories. The percentage of boat accessories at the Victoria store is 30 and the percentage at the Nanaimo store is 25.

18) If a sale is recorded as a boat accessory, the probability that the sale was made at the Victoria store is A) 0.433.

B) 0.35.

C) 0.30.

D) 0.2425.

E) 0.105.

Answer: A L.O.: 5 19) Overall, the probability that a sale by Harrison Water Sports will be for a boat accessory is A) 0.2425.

B) 0.105.

C) 0.10.

D) 0.375.

E) 0.30.

Answer: A L.O.: 5 20) If a sale is recorded as a boat accessory, the probability that the sale was made at the Nanaimo store is A) 0.155.

B) 0.375.

C) 0.2245.

D) 0.25.

E) 0.15.

Answer: A L.O.: 5 11 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 9: Random Variables and Probability Distributions Short Answer - Quiz A 1) At a local manufacturing plant, employees must complete new machine set-ups within 30 minutes. New machine set-up times can be described by a Normal model with a mean of 22 minutes and a standard deviation of four minutes. a. What percent of new machine set-ups take more than 30 minutes? b. The typical worker needs five minutes to adjust to their surroundings before beginning their duties. What percent of new machine set-ups are completed within 25 minutes to allow for this?

Answer: a. P(x > 30) = P

= P(z > 2.00) = 0.0228 = 2.28%

b. P(x ≤ 25) = P

= P(z ≤ 0.75) = 0.7734

L.O.: 4 2) The owner of a pet store is trying to decide whether to discontinue selling specialty clothes for pets. She suspects that only 4% of the customers buy specialty clothes for their pets and thinks that she might be able to replace the clothes with more profitable items. Before making a final decision, she decides to keep track of the total number of customers for a day and whether they purchase specialty clothes. a. The owner had 275 customers that day. Assuming this was a typical day for her store, what would be the mean and standard deviation of the number of customers who buy specialty clothes for their pet each day? b. Surprised by the high number of customers who purchased specialty pet clothing that day, the owner decided that her 4% estimate must have been too low. How many clothing sales would it have taken to convince you? Justify your answer.

Answer: a. Using the Binomial model, Mean: μ = np = (275)(0.04) = 11 Standard deviation: σ = = = 3.25 b. Since np = 11 and nq = 264, we expect at least 10 successes and at least 10 failures. The sample size is large enough to apply a Normal model. It would be unusual to see the number of customers who purchased specialty pet clothing more than 2 or 3 standard deviations above the mean. Since the standard deviation is 3.25, it would be unusual to see more than 18 (11 + 2(3.25) = 17.5) customers who purchased specialty clothing. So, I would conclude that her 4% estimate must have been too low if more than 18 customers purchased specialty clothing for their pet.

L.O.: 3

1 .

3) A shareholder believes that in one year, there is a 20% chance that his stock will be worth $75, a 50% chance that it will be worth $100, and a 30% chance that it will be worth $140. a. Find the stock's expected value in one year. b. Find the standard deviation of the stock's worth in one year.

Answer: a. E(X) = Σ xP(x) = $75(0.20) + $100(0.50) + $140(0.30) = $107 b. σ = SD(X) =

, Var(X) = Σ (x - μ)2 P(x) Var(X) = Σ(x - μ)2 P(x) = (75 - 107)2(0.20) + (100 - 107)2(0.50) + (140 - 107)2(0.30) = 556 σ = SD(X) = = = $23.58 L.O.: 1 4) The number of plants that are found in a field averages 2 per square metre and follows a Poisson distribution. Based on this, a. What is the expected value? b. What is the probability that a 1-square metre section will contain less than 3 plants?

Answer: a. The expected value of the Poisson distribution is E(X) = λ = 2. b. P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = e-2

= 0.6767

L.O.: 3 Short Answer - Quiz B 1) A company's manufacturing process uses 500 litres of water at a time. A "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake. To meet federal regulations the treated water must not contain more than 80 parts per million (ppm) of the chemical. Because there is a fine charged if regulations are not met, the company sets the machine to attain an average of 75 ppm in the treated water. The machine's output can be described by a Normal model with a standard deviation 4.2 ppm. a. What percent of the batches of water discharged exceed the 80 ppm standard? b. The company's lawyers insist that not more than 2% of the treated water should be over the limit. In order to achieve this, to what mean should the company set the scrubbing machine?

Assume the standard deviation does not change.

Answer: a. P (x > 80) = 1 - P (x ≤ 80) = 1 - P

= 1 - P (z ≤ 1.19) = 1 - 0.8830 = 0.117 =

11.7% b. The z-score that has 1 - 0.02 = 0.98 ≈ 0.9798 area to the left of it is z = 2.05. = 2.05 μ = mean = 71.39 ppm L.O.: 4

2 .

2) The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy magazines and thinks that he might be able to sell something more profitable. Before making a final decision, he keeps track of the number of customers who buy magazines on a given day. a. On one day, he had 280 customers. Assuming this day was typical, what would be the mean and standard deviation of the number of customers who buy magazines each day? b. Surprised by the high number of customers who purchased magazines that day, the owner decided that his 5% estimate must have been too low. How many magazine sales would it have taken to convince you? Justify your answer.

Answer: a. Using the Binomial model, Mean: μ = np = (280)(0.05) = 14 Standard deviation: σ = = = 3.65 b. Since np = 14 and nq = 266, we expect at least 10 successes and at least 10 failures. The sample size is large enough to apply a Normal model. It would be unusual to see sales more than 2 (or 3) standard deviations above the anticipated mean. Since 14 + 2(3.65) = 21.3, I would conclude the 5% estimate was probably too low if 22 customers or more bought magazines.

L.O.: 3 3) A company believes that there is a 25% chance of making a daily profit of $500, a 35% chance that it will be $1000 and 40% chance that it will be $1500. a. Find the expected value. b. Find the standard deviation.

Answer: a. E(X) = Σ xP(x) = $500(0.25) + $1000(0.35) + $1,500(0.40) = $1,075 b. σ = SD(X) = , Var(X) = Σ (x - μ)2 P(x) Var(X) = Σ(x - μ)2 P(x) = (500 - 1,075)2(0.25) + (1,000 - 1,075)2(0.35) + (1,500 - 1,075)2(0.40) = 156,875 σ= = $396.07 L.O.: 1 4) The number of calls received by a call centre follows the Poisson distribution with an average of 5 calls per minute. For a 1 minute period, a. Find the expected value. b. Find the probability of receiving no more than 2 calls.

Answer: a. Expected value = E(X) = λ = 5 b. P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = e-5 L.O.: 3

3 .

= 0.1247

Multiple Choice - Quiz C Consider the following to answer the question(s) below: At a local manufacturing plant, employees must complete new machine set-ups within 30 minutes. New machine set-up times can be described by a Normal model with a mean of 22 minutes and a standard deviation of four minutes.

1) What percent of new machine set-ups take more than 30 minutes?

A) 97.72% B) 47.72% C) 2.28% D) 52.28% E) 50% Answer: C L.O.: 4 2) The typical worker needs five minutes to adjust to their surroundings before beginning their duties. What percent of new machine set-ups are completed within 25 minutes to allow for this?

A) 77.3% B) 27.3% C) 22.7% D) 72.7% E) 0.75% Answer: A L.O.: 4 Consider the following to answer the question(s) below: A company's manufacturing process uses 500 litres of water at a time. A "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake. To meet federal regulations the treated water must not contain more than 80 parts per million (ppm) of the chemical. Because there is a fine charged if regulations are not met, the company sets the machine to attain an average of 75 ppm in the treated water. The machine's output can be described by a Normal model with a standard deviation 4.2 ppm.

3) What percent of the batches of water discharged exceed the 80 ppm standard?

A) 88.3% B) 11.7% C) 61.7% D) 38.3% E) -11.7% Answer: B L.O.: 4

4 .

4) The company's lawyers insist that not more than 2% of the treated water should be over the limit. In order to achieve this, to what mean should the company set the scrubbing machine?

Assume the standard deviation does not change.

A) 75 ppm B) 78.63 ppm C) 71.39 ppm D) 80 ppm E) 60 ppm Answer: C L.O.: 4 Consider the following to answer the question(s) below: A company believes that there will be a 50% chance of making a profit of $1,000, a 30% chance of making a profit of $1500 and a 20% chance of making a profit of $2,000.

5) What is the expected profit?

A) $1,000 B) $300 C) $2,000 D) $1,350 E) $4,500 Answer: D L.O.: 1 6) Find the standard deviation for the company's profit?

A) $390.51 B) $152,498 C) $350 D) $18.71 E) $1,350 Answer: A L.O.: 1 Consider the following to answer the question(s) below: The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5 minute period, 7) Find the expected value.

A) 2 B) 1.41 C) 3.16 D) 10 E) 2.24 Answer: D L.O.: 1, 3 5 .

8) What is the probability that no more than 2 customers will arrive in a 5 minute period?

A) 0.0005 B) 0.1246 C) 0.0028 D) 0.6767 E) 0.1353 Answer: C L.O.: 3 Consider the following to answer the question(s) below: An airline has found that its flights between Toronto and Vancouver can take anywhere from 4.5 to 7.5 hours, with any time between this range being equally likely.

9) What is the standard deviation?

A) 0.75 hours B) 0.87 hours C) 6 hours D) 0.33 hours E) 0.5 hours Answer: B L.O.: 3 10) What is the probability that the flight will take more than 7 hours?

A) 0.83 B) 0.33 C) 0.67 D) 0.17 E) 0.99 Answer: D L.O.: 3 Consider the following to answer the question(s) below: A courier service claims that only 5 % of all of its deliveries arrive late. Assuming deliveries are independent, a sample of 10 deliveries is randomly selected.

11) What is the probability that exactly 2 of the sample deliveries arrive late?

A) 0.0746 B) 0.9884 C) 0.2347 D) 0.0439 E) 0.1125 Answer: A L.O.: 3 6 .

12) What is the probability that more than 2 of the sample deliveries arrive late?

A) 0.0115 B) 0.0105 C) 0.0862 D) 0.0746 E) 0.0439 Answer: A L.O.: 3 13) Cars arrive randomly and independently at a drive through service centre at a rate of 10 per hour. What is the probability that no cars will arrive in a 15 minute period?

A) 0.0821 B) 0.0067 C) 0.0250 D) 0.00 E) 0.1353 Answer: A L.O.: 3 14) Cars arrive randomly and independently at a drive through service centre at a rate of 10 per hour. What is the probability that 2 or 3 cars will arrive in a 15 minute period?

A) 0.4703 B) 0.0131 C) 0.0099 D) 0.2873 E) 0.0053 Answer: A L.O.: 3 15) The probability model for random variable X is specified as: P (X = x) =

The expected value of X is A) 2.00.

B) 0.50.

C) 0.333.

D) 2.333.

E) 0.167.

Answer: D L.O.: 1

7 .

16) The manager of a computer help desk operation in Moncton has collected enough data to conclude that the time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. Based on this, what is the probability that a call will last longer than 13 minutes?

A) 0.0125 B) 0.4875 C) 0.5125 D) 0.9875 E) .0224 Answer: A L.O.: 4 17) The manager of a computer help desk operation in Moncton has collected enough data to conclude that the time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. The manager wants to set the time limit that only 8% of all calls will exceed this limit. The time limit should be A) about 11.23 minutes.

B) about 5.25 minutes.

C) about 14.58 minutes.

D) about 10.35 minutes.

E) about 20.29 minutes.

Answer: A L.O.: 4 18) The manager of a computer help desk operation in Moncton has collected enough data to conclude that the time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. What is the probability that three randomly monitored calls will each be completed in 4 minutes or less?

A) about 0.00001 B) about 0.4756 C) about 0.0244 D) about 0.0732 E) about 0.1076 Answer: A L.O.: 4 19) The city of Halifax has determined that the time between arrivals at a toll booth at the Angus L. Macdonald Bridge is exponentially distributed with λ = 4 cars per minute. Based on this information, what is the probability that the time between any two cars arriving will exceed 11 seconds?

A) about 0.48 B) about 0.52 C) about 0.96 D) about 0.06 E) about 1.0 Answer: A L.O.: 4 8 .

20) It is assumed that the time between failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures. Based on this information, what is the probability that a randomly selected part will fail in less than 10 hours?

A) about 0.18 B) about 0.82 C) about 0.20 D) about 0.002 E) about 0.33 Answer: A L.O.: 4

9 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 10: Sampling Distributions Short Answer - Quiz A 1) What are the two assumptions and three conditions of the Central Limit Theorem? Explain each of them.

Answer: Independence Assumption: The sampled values must be independent of each other.

Sample Size Assumption: The sample size must be sufficiently large. We can't check these directly, but we can think about whether the Independence Assumption is plausible.

Randomization Condition: The data values must be sampled randomly, or the concept of a sampling distribution makes no sense.

10% Condition: When the sample is drawn without replacement (as is usually the case), the sample size, n, should be no more than 10% of the population.

Large-Enough Sample Condition: The CLT doesn't tell us how large a sample we need. The truth is, it depends on the shape of the original data distribution; there's no one-size-fits-all rule. For highly skewed distributions, it may require samples of several hundred, not 30 or 50 observations (as usually recommended).

L.O.: 3 2) It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic tests on 128 new cars on the lot. a. Describe the sampling distribution of the sample proportion by naming the model and telling its mean and standard deviation. b. What is the probability that in this group over 18% of the new cars will be found to have electrical problems?

Answer: a. We can assume these cars are a representative sample of all new cars, and certainly less than 10% of them. We expect np = 0.14 × 128 = 17.92 successes (electrical problems) and nq = .86 × 128 = 110.08 failures (no problems) so the sample is large enough to use the sampling model N(0.14, 0.031). b.

P ( > 0.18) = P

= P (z > 1.29) = 1 - 0.9015 = 0.0985 ≈ 10%

L.O.: 2

1 .

3) In a metal fabrication process, metal rods are produced that have an average length of 20.5 metres with a standard deviation of 2.3 metres. A quality control specialist collects a random sample of 30 rods and measures their lengths. a. Describe the sampling distribution of the sample mean by naming the model and telling its mean and standard deviation. b. Suppose the resulting sample mean is 19.5 metres. Do you think that this sample result is unusually small? Explain.

Answer: a. With a sample size of 30, the CLT says that the approximate sampling model for sample means will be the Normal model N(20.5, 0.42). b. We have a random sample of metal rods drawn from a much larger population. A sample mean of only 19.5 metres is about 2.38 standard deviations below what we expect. The sample mean of 19.5 metres is unusually small.

L.O.: 3 4) Suppose that it is believed that 40% of adults have a company pension. If 100 adults are surveyed, a. What is the probability of finding a sample with less than 30 adults having a company pension? b. What is the probability of finding no more than 45 adults having a company pension?

Answer: a. Since SD ( ) = P

=P

b. Since SD ( ) = P

=P

0.04899, we have = P (z < -2.04) = 0.0207 = 2.07%

0.04899, we have = P (z < 1.02) = 0.8461 = 84.61%

L.O.: 2

2 .

Short Answer - Quiz B 1) What are the two assumptions and three conditions for the distribution of sample proportions?

Explain each of them.

Answer: Independence Assumption: The sampled values must be independent of each other.

Sample Size Assumption: The sample size, n, must be large enough.

Randomization Condition: If your data come from an experiment, subjects should have been randomly assigned to treatments.

10% Condition: The sample size, n, must be no larger than 10% of the population.

Success/Failure Condition: The Success/Failure Condition says that the sample size must be big enough so that both the number of "successes," np, and the number of "failures," nq, are expected to be at least 10.

L.O.: 2 2) Suppose that the mean income of people in a region is $35,000 with a standard deviation of $6,000. It is known that the population is unimodal and symmetric. For a sample of size 25, a. Describe the sampling distribution of the sample mean. b. What is the probability of obtaining from a sample of 25 people an average income that is above $37,000?

Answer: a. Since the population is unimodal and symmetric, then we can use the Normal model with mean of $35,000 and standard deviation of b. Since SD ( ) =

= $1200.

= $1200,

P ( > 37,000) = P

= P (z > 1.67) = 1 - 0.9525 = 0.0475 = 4.75%

L.O.: 3

3 .

3) Suppose that in a recent survey, about 33% of Canadians polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed at a local supermarket. a. Describe the sampling distribution of the sample proportion by naming the model and telling its mean and standard deviation. b. What is the probability that no more than 12 shoppers will say that they are likely to purchase reusable cloth bags for groceries?

Answer: a. 10% condition: 45 shoppers is less than 10% of all shoppers Success/failure condition: np = 45 × 0.33 = 14.85 and nq = 45 × 0.67 = 30.15, which both exceed 10. We can use the Normal model with the mean of 0.33 and the standard deviation of = 0.070.

b. Since SD ( ) = P

= 0.070, we have

= P ( < 0.267) = P

= P (z < -0.90) = 0.1841 = 18.41%

L.O.: 2 4) A small business ships specialty homemade candies to anywhere in the world. Past records indicate that orders weigh an average of 118 grams with a standard deviation of 14 grams.

Suppose a random sample of 50 current orders is selected and each weighed. a. Describe the sampling distribution of the sample mean by naming the model and telling its mean and standard deviation. b. Suppose the resulting sample mean is 110 grams. Do you think that this sample result is unusually small? Explain.

Answer: a. We have a random sample of shipments drawn from a much larger population. With a sample of size 50 the CLT says that the approximate sampling model of the sample means will be N (118, 1.98). b. A sample mean of only 110 grams is about 4 standard deviations below what we expect, a very unusual result.

L.O.: 3

4 .

Multiple Choice - Quiz C 1) Which of the following is not an assumption or condition for the distribution of sample proportions?

A) the independence assumption B) the sample size assumption C) the randomization condition D) the 10% condition E) the large enough sample condition Answer: E L.O.: 2 2) Which of the following is not an assumption or condition for the CLT? A) the independence assumption B) the sample size assumption C) the randomization condition D) the 10% condition E) the success/failure condition Answer: E L.O.: 3 3) It is believed that 40% of all medical doctors in Canada are women. Suppose that a random sample of 100 doctors is selected. Find the probability that at least 50% of this sample will be women.

A) 50% B) 47.93% C) 2.07% D) 52.07% E) 97.93% Answer: C L.O.: 2 4) It is believed that on average, households spend $150 a week on groceries with a standard deviation of $50. What is the probability that in a sample of 64 households, the average amount spent on groceries will be no more than $140 per week?

A) 44.52% B) 5.48% C) 55.48% D) 94.52% E) 19.15% Answer: B L.O.: 3

5 .

Consider the following to answer the question(s) below: The owner of a small convenience store is trying to decide whether to discontinue selling magazines. He suspects that only 5% of the customers buy magazines and thinks that he might be able to sell something more profitable. Before making a final decision, he keeps track of the number of customers who buy magazines each day. On a typical day he has 280 customers in his store.

5) On a typical day, what would be the mean number of customers who buy magazines?

A) 280 B) 0 C) 266 D) 14 E) 25 Answer: D L.O.: 2 6) On a typical day, what would be the standard deviation of the number of customers who buy magazines?

A) 3.65 B) 14 C) 13.32 D) 25 E) 5 Answer: A L.O.: 2 Consider the following to answer the question(s) below: According to a recent survey, about 33% of Canadians polled said that they would likely purchase reusable cloth bags for groceries in order to reduce plastic waste. Suppose 45 shoppers are interviewed at a local supermarket.

7) Which of the following statements is (are) false about the sampling distribution of the sample proportion?

A) The sampling distribution can be described by the Normal model.

B) The mean of the sampling distribution is 0.33.

C) The standard deviation of the sampling distribution is 0.07.

D) The 10% Condition is not satisfied.

E) We suppose that the Independence Assumption is satisfied.

Answer: D L.O.: 3

6 .

8) What is the probability that no more than 12 shoppers will say that they are likely to purchase reusable cloth bags for groceries?

A) -0.90 B) 0.90 C) 0.267 D) 0.816 E) 0.184 Answer: E L.O.: 2 Consider the following to answer the question(s) below: In a metal fabrication process, metal rods are produced that have an average length of 20.5 metres with a standard deviation of 2.3 metres. A quality control specialist collects a random sample of 30 rods and measures their lengths.

9) Which of the following statements is (are) true about the sampling distribution of the sample mean?

A) The sampling distribution follows the Normal model with a mean of 0.68 and a standard deviation of 2.3.

B) The sampling distribution follows the Normal model with a mean of 20.5 and a standard deviation of 0.42.

C) The sampling distribution follows the Normal model with a mean of 0.68 and a standard deviation of 0.077.

D) The sampling distribution follows the Normal model with a mean of 3.74 and a standard deviation of 2.3.

E) The sampling distribution follows the Normal model with a mean of 3.74 and a standard deviation of 0.077.

Answer: B L.O.: 3 10) Suppose the resulting sample mean is 19.5 metres. Which of the following statements is true?

A) This sample mean is 2.38 standard deviations above what we expect.

B) This sample mean is more than 3 standard deviations away from the population mean.

C) This sample mean is 2.38 standard deviations below what we expect.

D) This sample mean is only 1 standard deviation above the population mean.

E) This sample mean is only 1 standard deviation below the population mean.

Answer: C L.O.: 3

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11) Suppose it is known that the income distribution in a particular region is right-skewed and bimodal. If bank economists are interested in estimating the mean income, which of the following is true?

A) Provided that the sample size is sufficiently large, the sampling distribution of will be approximately Normal with a mean equal to the population mean.

B) Provided that the sample size is sufficiently large, the sampling distribution of will be approximately Normal with a standard deviation equal to the population standard deviation.

C) The sampling distribution will also be right-skewed for large sample sizes.

D) The standard deviation of the sampling distribution of will be proportionally larger than the population standard deviation, depending on the size of the sample.

E) The sampling distribution will also be bimodal for large sample sizes.

Answer: A L.O.: 3 12) A company has determined that the mean number of days it takes to collect on its accounts receivable is 36, with a standard deviation of 11 days. The company plans to select a random sample of n = 12 accounts and compute the sample mean. Which of the following statements holds true in this situation?

A) The sampling distribution may actually be approximately Normally distributed depending on what the population distribution is.

B) The sampling distribution will always have the same distribution as the population.

C) The sampling variability will be greater than if they had sampled n = 64 accounts.

D) The sampling distribution will certainly be approximately Normally distributed in this case.

E) The sampling distribution cannot be approximately Normally distributed in this case.

Answer: A L.O.: 3 13) Which of the following statements is consistent with the Central Limit Theorem?

A) The Central Limit Theorem indicates that the sampling distribution will be approximately Normal when the sample size is sufficiently large.

B) The Central Limit Theorem applies without regard to the size of the sample.

C) The Central Limit Theorem applies to both dependent and independent sampled values regardless of sample size.

D) The Central Limit Theorem makes sense even if samples are not randomly selected.

E) The Central Limit Theorem applies only to populations with Normal distributions.

Answer: A L.O.: 3

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14) According to the local real estate board, the average number of days that homes stay on the market before selling is 78.4, with a standard deviation equal to 11 days. A prospective seller selected a random sample of 36 homes from the multiple listing service. Above what value for the sample mean should 95 percent of all possible sample means fall?

A) about 75.4 days B) about 81.4 days C) about 96.5 days D) about 60.3 days E) about 79.3 days Answer: A L.O.: 3 15) Which of the following statements is true with respect to the sampling distribution of a proportion?

A) The mean of the sampling distribution will equal the true population proportion.

B) An increase in the sample size will result in an increase in the size of the standard deviation.

C) The sampling distribution will be approximately Normal regardless of sample size.

D) The standard deviation of the sampling distribution will equal the standard deviation of the population.

E) The mean of the sampling distribution will be smaller than the true population proportion.

Answer: A L.O.: 2 16) A claim was recently made on national television that two of every three doctors recommend a particular pain killer. Suppose a random sample of n = 300 doctors revealed that 180 said that they would recommend the painkiller. If the TV claim is correct, what is the probability of 180 or fewer in the sample agreeing?

A) 0.0071 B) 0.4929 C) 0.9929 D) 0.0142 E) 0.5071 Answer: A L.O.: 2 17) A major textbook publisher has a contract with a printing company. Part of the contract stipulates that no more than 5 percent of the pages should have any type of printing error.

Suppose that the company selects a random sample of 400 pages and finds 33 that have an error.

If the printer is meeting the standard, what is the probability that a sample of this size would have 33 or more errors?

A) 0.0014 B) 0.4986 C) 0.9986 D) 0.1245 E) 0.3755 Answer: A L.O.: 2 9 .

18) Ian's Tree Farm grows spruce trees for plant nurseries. The average annual increase in tree diameter is 7.9 centimetres with a standard deviation of 1.3 centimetres. A random sample of n = 50 trees is collected. What is the probability of the sample mean being less the 7.4 centimetres?

A) 0.0033 B) 0.4977 C) 0.5023 D) 0.9977 E) 0.9954 Answer: A L.O.: 3 19) McCain Foods (Canada) of New Brunswick produces frozen French fries. Suppose one line of fries has an average length of 7.62 centimetres with a standard deviation of 1.27 centimetres.

To make sure that the quality standard is met, they plan to select a random sample of n = 100 fries each day. Yesterday, the sample mean was 7.75 centimetres. What is the probability that the mean would be 7.75 centimetres or more if they are meeting the quality standards?

A) 0.1539 B) 0.3413 C) 0.6587 D) 0.0398 E) 0.4602 Answer: A L.O.: 3 20) A golf course in Toronto has determined that the mean time it takes for a foursome to complete an 18-hole round of golf is 4 hours 35 minutes (275 minutes) with a standard deviation of 14 minutes. The time distribution is also thought to be approximately Normal. Every month, the head pro at the course randomly selects a sample of 8 foursomes and monitors the time it takes them to play. Suppose the mean time that was observed for the sample last month was 4 hours 44 minutes (284 minutes). What is the probability of seeing a sample mean this high or higher?

A) about 0.0344 B) about 0.4656 C) about 0.9656 D) about 0.2611 E) about 0.2389 Answer: A L.O.: 3

10 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 11: Confidence Intervals for Proportions Short Answer - Quiz A Consider the following to answer the question(s) below: EU (European Union) countries report that 46% of their labour force is female. The United Nations wants to determine if the percentage of females in the Canadian labour force is the same.

Representatives from Statistics Canada plan to check a random sample of over 10,000 employment records on file to estimate the percentage of females in the Canadian labour force.

1) Statistics Canada wants to estimate the percentage of females in the Canadian labour force to within 5%, with 90% confidence. How many employment records should be sampled?

Answer: n = (1.645)2 (0.46) (0.54) / (0.05)2 = 268.87 = 269 records L.O.: 3 2) They actually select a random sample of 525 employment records, and find that 229 of the people are females. Construct the 90% confidence interval.

Answer: Confidence interval: ± 1.645 SE ( ) = 0.43619 ± 0.03560, i.e. between 0.4006 and 0.4718 L.O.: 1 3) Interpret the confidence interval in this context.

Answer: We are 90% confident that between 40.06% and 47.18% of the employees in the Canadian labour force are females.

L.O.: 1 4) Explain what 90% confidence means in this context.

Answer: If many random samples were taken, 90% of the confidence intervals produced would contain the actual percentage of all female employment records in the Canadian labour force.

L.O.: 1 5) Should representatives from Statistics Canada conclude that the percentage of females in the Canadian labour force is lower than European rate of 46%? Explain.

Answer: No. Since 46% = 0.46 lies in the confidence interval, (0.4006, 0.4718), it is possible that the percentage of females in the labour force matches European rate of 46% female in the labour force.

L.O.: 1 6) Are the assumptions and conditions for constructing a confidence interval met? Explain.

Answer: We have a random sample of less than 10% of the employment records, with 229 successes (females) and 296 failures (males), so the Normal model applies.

L.O.: 1

1 .

Short Answer - Quiz B Consider the following to answer the question(s) below: One division of a large defense contractor manufactures telecommunication equipment for the military. This division reports that 12% of non-electrical components are reworked. Management wants to determine if this percentage is the same as the percentage rework for electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions.

1) The Quality Control Department wants to estimate the true percentage of rework for electrical components to within 4%, with 99% confidence. How many components should they sample?

Answer: n = (2.576)2 (.12) (.88) / (.04)2 = 437.96 = 438 electrical components L.O.: 3 2) They actually select a random sample of 450 electrical components and find that 46 of those had to be reworked. Create the 99% confidence interval.

Answer: Confidence interval: ±2.576 SE ( ) = 0.10222±0.03679, i.e. between 0.0654 and 0.1390 L.O.: 1 3) Interpret the confidence interval in this context.

Answer: We are 99% confident that between 6.54% and 13.9% of electrical components are reworked.

L.O.: 1 4) Explain what 99% confidence means in this context.

Answer: If many random samples were taken, 99% of the confidence intervals produced would contain the actual percentage of electrical components that are reworked.

L.O.: 1 5) Should the Quality Control Department conclude that the percentage of rework for the electrical components is lower than the rate of 12% for non-electrical components? Explain.

Answer: No. Since 12% lies in the confidence interval it's possible that the percentage of electrical components that are reworked matches the percentage of non-electrical components that are reworked.

L.O.: 1 6) Are the assumptions and conditions for constructing a confidence interval met? Explain.

Answer: We have a random sample of less than 10% of all electrical components, with 46 successes (reworked) and 404 failures (not reworked), so the Normal model applies.

L.O.: 1

2 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: EU (European Union) countries report that 46% of their labour force is female. The United Nations wants to determine if the percentage of females in the Canadian labour force is the same.

Representatives from Statistics Canada plan to check a random sample of over 10,000 employment records on file to estimate the percentage of females in the Canadian labour force.

1) Statistics Canada wants to estimate the percentage of females in the Canadian labour force to within 5% with 90% confidence. How many employment records should be sampled?

A) 121 B) 269 C) 451 D) 382 E) 1000 Answer: B L.O.: 3 2) Suppose that Statistics Canada wants to be 90% confident of estimating the percentage of females in the labour force to within 2% of the true percentage. To do this they would have to A) decrease the sample size.

B) select the same number of employment records.

C) increase the sample size.

D) increase the margin of error.

E) increase the sampling error.

Answer: C L.O.: 3 3) They actually select a random sample of 525 employment records, and find that 229 of the people are females. The 90% confidence interval is A) 0.4006 to 0.4718.

B) 0.2747 to 0.5973.

C) 0.1776 to 0.6944.

D) 0.4235 to 0.5679.

E) 0.1243 to 0.7100.

Answer: A L.O.: 1 4) If Statistics Canada wishes to tighten its interval, they should A) increase the confidence level.

B) increase the sample size.

C) decrease the sample size.

D) increase the margin of error.

E) double the margin of error .

Answer: B L.O.: 2 3 .

Consider the following to answer the question(s) below: One division of a large defense contractor manufactures telecommunication equipment for the military. This division reports that 12% of non-electrical components are reworked. Management wants to determine if this percentage is the same as the percentage rework for electrical components manufactured by the entire company. The Quality Control Department plans to check a random sample of the over 10,000 electrical components manufactured across all divisions.

5) The Quality Control Department wants to estimate the true percentage of rework for electrical components to within 4%, with 99% confidence. How many components should they sample?

A) 651 B) 1000 C) 344 D) 438 E) 579 Answer: D L.O.: 3 6) They actually select a random sample of 450 electrical components and find that 46 of those had to be reworked. The 99% confidence interval is A) 0.0654 to 0.1390.

B) 0.0432 to 0.1608.

C) 0.0763 to 0.1277.

D) 0.0541 to 0.1499.

E) 0.0787 to 0.1257.

Answer: A L.O.: 1 7) The 95% confidence interval based on this data is 0.0742 to 0.1302. Which of the following is the correct interpretation?

A) The percentage of electronic components that are to be reworked is between 7.42% and 13.02%.

B) We are 95% confident that between 7.42% and 13.02% of electrical components are to be reworked.

C) The margin of error for the true percentage of electrical components that are reworked is between 7.42% and 13.02%.

D) All samples of size 450 will yield a percentage of reworked electrical components that falls within 7.42% and 13.02%.

E) The probability that the true number of electrical parts that have to be reworked is between 7.42% and 13.02% is 0.05.

Answer: B L.O.: 1

4 .

8) Based on the 95% confidence interval, should the Quality Control Department conclude that the percentage of rework for the electrical components is lower than the rate of 12% for nonelectrical components?

A) Yes, because the lower limit of the confidence interval is 7.42%.

B) Yes, because 12% is contained within the 95% confidence interval.

C) No, because 12% is contained within the 95% confidence interval.

D) Yes, because the upper limit of the confidence interval is 13.02%.

E) Yes, because 12 is larger than the width of the confidence interval.

Answer: C L.O.: 1 9) All else being equal, increasing the level of confidence desired will A) tighten the confidence interval.

B) decrease the margin of error.

C) leave the margin of error unchanged.

D) increase the margin of error.

E) increase the standard error.

Answer: D L.O.: 2 10) Which of the following is not an assumption / condition required for constructing a confidence interval for the proportion?

A) Randomization condition B) Linearity condition C) Success/Failure condition D) 10% condition E) Independence assumption Answer: B L.O.: 1 11) City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. Suppose they find they need a sample size of 15,000 people to achieve a margin of error of 0.01 percentage points with 99 % confidence. This sample is too large to be practical.

How can they reduce the sample size?

A) Use a lower confidence level.

B) Use a smaller margin of error.

C) Use a higher level of confidence.

D) Conduct a census.

E) Use a higher confidence level and a smaller margin of error.

Answer: A L.O.: 2

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12) A sample of 250 people resulted in a confidence interval estimate of between 0.14 and 0.20 for the proportion of people who believe that tax increase proposed by the federal government is justified. Based on this information, what was the confidence level used in this estimation?

A) approximately 79% B) 95% C) approximately 36.9% D) approximately 1.26% E) approximately 90% Answer: A L.O.: 1 13) A human resources manager wishes to estimate the proportion of employees in her large company who have supplemental health insurance. What sample size should she select if she wants 95% confidence and a margin of error of 0.01?

A) 9,604 B) 3,458 C) 6,765 D) 381 E) 4,096 Answer: A L.O.: 3 14) A financial analyst is interested in estimating the proportion of publicly traded companies on the Toronto Stock Exchange that have cash balances of more than 10 percent of the total assets of the company. A random sample of 100 companies shows that 13 had cash balances of more than 10 percent of assets. The 90 % confidence interval estimate is A) 0.0747 to 0.1853.

B) 0.0641 to 0.1959.

C) -0.0870 to 0.1730.

D) -0.0507 to 0.1494.

E) -0.0412 to 0.1588.

Answer: A L.O.: 1 15) City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. From previous experience they believe the proportion is not larger than 20 percent. They want to estimate the proportion to within 0.04 percentage points with 95 % confidence. The sample size they should use is A) 385.

B) 601.

C) 97.

D) 10.

E) 248.

Answer: A L.O.: 3

6 .

16) City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. They take a sample of 400 visitors and find that 100 are on a second visit. The 95% confidence interval is A) 0.2076 to 0.292.

B) 0.1942 to 0.3058.

C) 0.2144 to 0.2856.

D) 0.1996 to 0.3004.

E) 0.2222 to 0.2777.

Answer: A L.O.: 1 17) The produce manager at a local Sobeys store is interested in estimating the percentage of apples that arrive on a shipment with bruises. A random sample of 150 apples showed 14 with bruises. Based on this information, what is the margin of error for a 95% confidence interval estimate?

A) 0.0466 B) 0.0933 C) 0.0006 D) 0.0238 E) 0.0392 Answer: A L.O.: 1 18) A study was recently conducted at a major university to estimate the difference in the proportion of business school and non-business school graduates who go on to a higher degree program within five years of graduation A random sample of 400 business school graduates showed that 75 had gone to graduate school, while in a random sample of 500 non-business graduates, 137 had done so. The standard error for the difference in the proportions of the two groups is A) 0.0279.

B) 0.

C) 0.0008.

D) 0.0865.

E) 0.1875.

Answer: A L.O.: 4

7 .

19) A study was recently conducted at a major university to estimate the difference in the proportion of business school and non-business school graduates who go on to a higher degree program within five years of graduation. A random sample of 400 business school graduates showed that 75 had gone to graduate school, while in a random sample of 500 non-business graduates, 137 had done so. The 95% confidence interval is A) -0.1412 to -0.0318.

B) -2.0465 to 1.8375.

C) -0.0880 to -0.0850.

D) -0.1144 to -0.0586.

E) -0.0873 to -0.0857.

Answer: A L.O.: 4 20) City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. They take a sample of 400 visitors and find that 100 are on a second visit. The 99% confidence interval is 0.1942 to 0.3058. The correct interpretation of the interval is A) we are 99% confident that between 19.42% and 30.58% of visitors are on a second visit.

B) the proportion of repeat visitors is between 19.42% and 30.58%.

C) the probability is 5% that between 19.42% and 30.58% of visitors are on a second visit.

D) the margin of error is between 19.42% and 30.58%.

E) all samples of 400 will have between 19.42% and 30.58% of visitors on a second visit.

Answer: A L.O.: 1

8 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 12: Testing Hypotheses about Proportions Short Answer - Quiz A Consider the following to answer the question(s) below: A company manufacturing computer chips finds that 8% of all chips manufactured are defective.

Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?

1) Write the null and alternative hypotheses.

Answer: H0 : p = 0.08 and HA : p < 0.08 L.O.: 1, 2 2) What is the value of the test statistic?

Answer: z = -1.56 L.O.: 2 3) What is the associated P-value?

Answer: P-value = 0.0594 L.O.: 2 4) State your conclusion using α = 0.01.

Answer: At α = 0.01 we fail to reject the null hypothesis. At the 0.01 level of significance, we cannot conclude that the additional training significantly lowered the defect rate.

L.O.: 2 Consider the following to answer the question(s) below: A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so but in a test market so that the effectiveness of the marketing campaign may be evaluated.

5) Write the null and alternative hypotheses.

Answer: H0 : p = 0.195 and HA : p > 0.195 L.O.: 1

1 .

6) In this context, describe the Type I error possible. How might such an error impact the company?

Answer: A Type I error would be concluding that the percentage of customers purchasing the company's brand has increased, when in fact it has not. The company would waste money on a new marketing campaign that does not increase the percentage of customers buying their brand.

L.O.: 4 7) In this context, describe the Type II error possible. How might such an error impact the company?

Answer: A Type II error would be failing to detect an increase in the percentage of customers buying the company's brand, when in fact it has. The company would miss an opportunity to increase the percentage of customers buying their brand.

L.O.: 4 8) Based on data collected in the test market, the company constructed a 98% confidence interval for the proportion of all consumers who might buy their brand. The resulting interval is 16% to 28%. What conclusion should the company reach about the new marketing campaign? Explain.

Answer: The confidence interval contains the hypothesized value of 19.5%. Therefore the data do not provide convincing evidence that the marketing campaign increases the percentage of customers for the company's products.

L.O.: 3 Short Answer - Quiz B Consider the following to answer the question(s) below: Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?

1) Write the null and alternative hypotheses.

Answer: H0 : p = 0.28 and HA : p > 0.28 L.O.: 1, 2 2) What is the value of the test statistic?

Answer: z = 2.67 L.O.: 2 3) What is the associated P-value?

Answer: P-value = 0.0038 L.O.: 2

2 .

4) State your conclusion using α = 0.05.

Answer: At α = 0.05 we reject the null hypothesis. At the 0.05 level of significance, we can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is significantly higher than 28% (or that the problem is more severe).

L.O.: 2 Consider the following to answer the question(s) below: Top management of a large multinational corporation wants to create a culture of innovativeness and change. A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work. One of his recommendations for the company is to conduct seminars for employees in order to disseminate and reinforce the new corporate philosophy. This is done for a six month trial period after which its value in changing employee attitudes will be assessed.

5) Write the null and alternative hypotheses.

Answer: H0 : p = 0.15 and HA : p > 0.15 L.O.: 1, 2 6) In this context, describe the Type I error possible. How might such an error impact the company?

Answer: A Type I error would be concluding that the percentage of employees open to new ideas has increased, when in fact it has not. The company would waste money on seminars that do not increase the percentage of employees with more innovative attitudes.

L.O.: 4 7) In this context, describe the Type II error possible. How might such an error impact the company?

Answer: A Type II error would be failing to detect an increase in the percentage of employees open to new ideas, when in fact it has taken place. The company would miss an opportunity to increase the percentage of employees with more innovative attitudes.

L.O.: 4 8) Based on data collected after the trial period, the company constructed a 95% confidence interval for the proportion of all employees open to new ideas and approaches toward their work.

The resulting interval is 18% to 22%. What conclusion should the company reach about the seminars? Explain.

Answer: The confidence interval contains values that are all above the hypothesized value of 15%, so the data provide convincing evidence that the seminars improved employee's attitudes toward innovativeness and change.

L.O.: 3

3 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: A company manufacturing computer chips finds that 8% of all chips manufactured are defective.

Management is concerned that high employee turnover is partially responsible for the high defect rate. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. Was the additional training effective in lowering the defect rate?

1) Which of the following statements is true about this hypothesis test?

A) It is a two-tailed test about a proportion.

B) It is a one-tailed test about a mean.

C) It is a one-tailed test about a proportion.

D) It is a two-tailed test about a mean.

E) It is a two-tailed test about a standard deviation.

Answer: C L.O.: 1, 2 2) The correct value of the test statistic is A) z = -1.56.

B) z = 2.57.

C) z = 1.56.

D) z = 1.96.

E) z = -2.57.

Answer: A L.O.: 2 3) The P-value associated with the test statistic is A) 0.01.

B) 0.05.

C) 0.2339.

D) 0.0594.

E) 0.0075.

Answer: D L.O.: 2

4 .

4) At α = 0.01 A) we can conclude that the additional training significantly lowered the defect rate.

B) we can conclude that the additional training did not significantly lower the defect rate.

C) we can conclude that the additional training significantly increased the defect rate.

D) we can conclude that the additional training significantly affected the defect rate.

E) we can conclude that the additional training probably increased the defect rate..

Answer: B L.O.: 2 Consider the following to answer the question(s) below: Suppose that a report indicates that 28% of Canadians have experienced difficulty in making mortgage payments. Further suppose that a news organization randomly sampled 400 Canadians from 10 cities and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities?

5) The correct null and alternative hypotheses are A) H0 : p = 0.28 and HA : p > 0.28.

B) H0 : p = 0.28 and HA : p < 0.28.

C) H0 : p = 0.28 and HA : p ≠ 0.28.

D) H0 : p ≠ 0.28 and HA : p = 0.28.

E) H0 : p > 0.28 and HA : p = 0.28.

Answer: A L.O.: 1, 2 6) The correct value of the test statistic is A) z = 1.28.

B) z = -2.67.

C) z = 2.67.

D) z = 1.96.

E) z = -1.28.

Answer: C L.O.: 2 7) The P-value associated with the test statistic is A) 0.025.

B) 0.2119.

C) 136.0177.

D) 0.0522.

E) 0.0038.

Answer: E L.O.: 2

5 .

8) At α = 0.05 A) we can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is significantly higher than 28%.

B) we can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is significantly lower than 28%.

C) we can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is not significantly different from 28%.

D) we can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is equal to 28%.

E) we can conclude that the percentage of Canadians in these cities experiencing difficulty making mortgage payments is less than or equal to 28% .

Answer: A L.O.: 2 Consider the following to answer the question(s) below: A company that sells eco-friendly cleaning products is concerned that only 19.5% of people who use such products select their brand. A marketing director suggests that the company invest in new advertising and labeling to strengthen its green image. The company decides to do so but in a test market so that the effectiveness of the marketing campaign may be evaluated.

9) In this context, committing a Type I error A) occurs when they conclude that the percentage of customers purchasing the company's brand has decreased when in fact it has not.

B) occurs when they conclude that the percentage of customers purchasing the company's brand has not increased when in fact it has.

C) would result in the company spending money on a new marketing campaign that does increase the percentage of customers buying their brand.

D) occurs when they conclude that the percentage of customers purchasing the company's brand has increased when in fact it has not and would result in the company wasting money on a new. marketing campaign that does not increase the percentage of customers buying their brand E) would have absolutely no effect on the company.

Answer: D L.O.: 4

6 .

10) Based on data collected in the test market, the company constructed a 98% confidence interval for the proportion of all consumers who might buy their brand. The resulting interval is 16% to 28%. What conclusion should the company reach about the new marketing campaign?

A) The data do not provide convincing evidence that the marketing campaign increases the proportion of customers purchasing the company's products.

B) The data do provide convincing evidence that the marketing campaign increases by 2% the proportion of customers purchasing the company's products.

C) The data do provide convincing evidence that the marketing campaign increases by 12% the proportion of customers purchasing the company's products.

D) The data do provide convincing evidence that the marketing campaign decreases by 2% the proportion of customers purchasing the company's products.

E) The data do provide convincing evidence that the marketing campaign decreases by 12% the proportion of customers purchasing the company's products.

Answer: A L.O.: 3 Consider the following to answer the question(s) below: Winnipeg Pet Plus believes that it has a market share of 25 percent of the local dog food market.

They survey 100 dog owners and ask whether or not it is their regular source of dog food, and 23 people say "yes."

11) The appropriate null and alternative hypotheses are A) H0 : p = 0.25 and HA : p ≠ 0.25.

B) H0 : p = 0.25 and HA : p > 0.25.

C) H0 : p > 0.25 and HA : p = 0.25.

D) H0 : p ≠ 0.25 and HA : p = 0.25.

E) H0 : p = 0.25 and HA : p < 0.25.

Answer: A L.O.: 1, 2 12) The correct value of the test statistic is A) -0.462.

B) -0.475.

C) 0.462.

D) 0.475.

E) -0.456.

Answer: A L.O.: 2

7 .

13) The P-value associated with the test statistic is A) 0.644.

B) 0.322.

C) 0.678.

D) 0.635.

E) 0.317.

Answer: A L.O.: 2 14) At α = 0.05 A) we cannot conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly different from 25%.

B) we can conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is precisely equal to 25.00%.

C) we can conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly lower than 25%.

D) we can conclude that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly higher than 25%.

E) there is strong evidence that the percentage of customers who buy their dog food regularly at Winnipeg Pet Plus is significantly different from 25%.

Answer: A L.O.: 2 15) In this context, committing a Type I error A) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is significantly different from 25% when in fact it is not.

B) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is less than 25% when in fact it has not.

C) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is 25% when in fact it has not.

D) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is 25% when in fact it is less than that.

E) occurs when they conclude that the percentage of customers using Winnipeg Pet Plus for their dog food is more than 25% when in fact it is less than that.

Answer: A L.O.: 4

8 .

Consider the following to answer the question(s) below: After completing sales training for a large company, it is expected that a salesperson will generate a sale on more than 15 percent of the calls he or she makes. To make sure that the sales training process is working, a random sample of 400 sales calls made by sales representatives who have completed the training have been selected and the null hypothesis is to be tested at 0.05 alpha level. Suppose that a sale is made on 76 of the calls.

16) The appropriate null and alternative hypotheses are A) H0 : p = 0.15 and HA : p > 0.15.

B) H0 : p > 0.15 and HA : p = 0.15.

C) H0 : p = 0.15 and HA : p < 0.15.

D) H0 : p < 0.15 and HA : p = 0.15.

E) H0 : p = 0.15 and HA : p ≠ 0.15.

Answer: A L.O.: 1, 2 17) The correct value of the test statistic is A) 2.24.

B) 1.96.

C) -2.24.

D) 3.34.

E) -1.645.

Answer: A L.O.: 2 18) At α = 0.05 A) We can conclude that the percentage of sales after training is significantly higher than 15%.

B) We can conclude that the percentage of sales after training is significantly lower than 15%.

C) We can conclude that the percentage of sales after training is equal to 15%.

D) We can conclude that the percentage of sales after training is not significantly different from 15%.

E) We can conclude that the percentage of sales after training is not significantly higher than 15%.

Answer: A L.O.: 2

9 .

Consider the following to answer the question(s) below: An advertising agency has developed a new ad for one of the national car manufacturing companies. The agency is interested in testing whether the proportion of favourable responses to the ad is the same between male and female adults. It conducted the test using an alpha level of 0.05. A sample of 100 adults of each gender was used in the study. Each person was asked to view the ad and indicate whether they found the ad to be "pleasing" or not. The samples resulted in 57 males and 47 females that liked the ad.

19) The appropriate null and alternative hypotheses are A) H0 : p1 = p2 and HA : p1 ≠ p2.

B) H0 : p1 = p2 and HA : p1 > p2.

C) H0 : p1 > p2 and HA : p1 ≠ p2.

D) H0 : p1 ≠ p2 and HA : p1 = p2.

E) H0 : p1 = p2 and HA : p1 < p2.

Answer: A L.O.: 5 20) The correct value of the test statistic is A) 1.42.

B) 1.645.

C) 2.234.

D) 1.024.

E) -2.234.

Answer: A L.O.: 5

10 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 13: Confidence Intervals and Hypothesis Tests for Means Short Answer - Quiz A Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years.

86 75 83 84 81 77 78 79 79 81 76 85 70 76 79 81 73 74 72 83 1) Write the null and alternative hypotheses.

Answer: H0 : µ = 77 and HA : µ > 77 L.O.: 2 2) In this context, describe the Type I error possible. How might such an error impact ABI Insurance?

Answer: A Type I error would be concluding that the average life expectancy has increased, when in fact it has not. The company would change its premium structure when it was not necessary.

L.O.: 2 3) In this context, describe the Type II error possible. How might such an error impact ABI Insurance?

Answer: A Type II error would be failing to detect that the average life expectancy has increased, when in fact it has. The company would miss an opportunity to change its premium structure when it was necessary.

L.O.: 2 4) What is the value of the test statistic?

Answer: t= t = 1.597 L.O.: 1, 2

1 .

5) What is the associated P-value?

Answer: P-value = 0.063 L.O.: 2 6) State your conclusion using α = 0.05.

Answer: We fail to reject the null hypothesis H0. ABI Insurance shouldn't change their premiums because there is no evidence indicating an increase in average life expectancy.

L.O.: 2 7) For more accurate cost determination, ABI Insurance wants to estimate the average life expectancy to within one year with 95% confidence. How many randomly selected recently paid policies would they need to sample?

Answer: n = 77.1 or 78 L.O.: 3 8) Suppose ABI samples 100 recently paid policies. This sample yields a mean of 77.7 years and a standard deviation of 3.6 years. Find a 90% confidence interval and interpret.

Answer: 77.7 ± (1.660) 3.6 / 77.1 years to 78.3 years We are 90% confident that the true average life expectancy of policyholders falls between 77.1 and 78.3 years.

L.O.: 1 Short Answer - Quiz B Consider the following to answer the question(s) below: A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals reported the following number of hours: 12 13 14 14 15 15 15 16 16 16 16 16 17 17 17 18 18 18 18 19 19 19 20 21 The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours.

1) Write the null and alternative hypotheses.

Answer: H0 : µ = 15 and HA : µ > 15 L.O.: 2 2) In this context, describe the Type I error possible. How might such an error impact the 2 .

software development firm?

Answer: A Type I error would be concluding that the average number of hours volunteered by the firm's professional employees is more than 15 hours, when in fact it is not. The firm would miss an opportunity to increase community involvement among its professional employees.

L.O.: 2 3) In this context, describe the Type II error possible. How might such an error impact the software development firm?

Answer: A Type II error would be failing to detect that the average number of hours volunteered by the firm's professional employees is more than 15 hours, when in fact it is. The firm would waste money instituting an incentive program to increase community involvement among its professional employees.

L.O.: 2 4) What is the value of the test statistic?

Answer: t= t = 3.531 L.O.: 1, 2 5) What is the associated P-value?

Answer: P-value = 0.0009 L.O.: 2 6) State your conclusion using α = 0.05.

Answer: At 5% significance level we reject the null hypothesis. The firm should not institute an incentive program because the evidence indicates that professional employees volunteer an average of more than 15 hours per month in their local community.

L.O.: 2 7) For a more accurate determination, top management wants to estimate the average number of hours volunteered per month by their professional staff to within one hour with 99% confidence.

How many randomly selected professional employees would they need to sample?

Answer: n = 36.9 or 37 L.O.: 3

3 .

8) Suppose 40 professional employees are randomly selected. This sample yields a mean of 15.2 hours and a standard deviation of 1.8 hours. Find the 95% confidence interval and interpret.

Answer: 15.2 ± (2.021) 1.8 / 14.62 to 15.78 hours We are 95% confident that the true average number of hours volunteered per month by professional employees falls between 14.62 and 15.78 hours.

L.O.: 1 Multiple Choice - Quiz C Consider the following to answer the question(s) below: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years.

86 75 83 84 81 77 78 79 79 81 76 85 70 76 79 81 73 74 72 83 1) The correct null and alternative hypotheses are A) H0 : µ = 77 and HA : µ > 77.

B) H0 : µ = 77 and HA : µ < 77.

C) H0 : µ = 77 and HA : µ ≠ 77.

D) H0 : µ ≠ 77 and HA : µ = 77.

E) H0 : µ > 77 and HA : µ = 77 Answer: A L.O.: 2 2) A Type II error in this context would be A) failing to detect that the average life expectancy has increased, when in fact it has.

B) failing to detect that the average life expectancy has increased, when in fact it is unchanged.

C) detecting that the average life expectancy has increased, when in fact it hasn't.

D) failing to detect that the average life expectancy is unchanged.

E) detecting that the average life expectancy is unchanged.

Answer: A L.O.: 2

4 .

3) The correct value of the test statistic is A) t = -1.597.

B) t = 2.779.

C) t = 1.597.

D) t = 0.443.

E) t = -2.779.

Answer: C L.O.: 1, 2 4) The P-value associated with the test statistic is A) 0.025.

B) 0.228.

C) 0.01.

D) 0.05.

E) 0.063.

Answer: E L.O.: 2 5) At α = 0.05, A) we reject the null hypothesis.

B) ABI Insurance should increase their premiums because there is evidence indicating an increase in average life expectancy.

C) we fail to reject the alternative hypothesis HA : µ > 77.

D) we fail to reject the null hypothesis, and ABI Insurance should not increase their premiums because there is no evidence indicating an increase in average life expectancy.

E) we support the alternative hypothesis HA : µ > 77. ABI Insurance should increase their premiums.

Answer: D L.O.: 2

5 .

Consider the following to answer the question(s) below: A large software development firm recently relocated its facilities. Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities. They believe that the firm's professionals volunteer an average of more than 15 hours per month. If this is not the case, they will institute an incentive program to increase community involvement. A random sample of 24 professionals reported the following number of hours: 12 13 14 14 15 15 15 16 16 16 16 16 17 17 17 18 18 18 18 19 19 19 20 21 The sample has a mean of 16.6 hours and a standard deviation of 2.22 hours.

6) The correct null and alternative hypotheses are A) H0 : µ = 15 and HA : µ < 15.

B) H0 : µ = 15 and HA : µ > 15.

C) H0 : µ = 15 and HA : µ ≠ 15.

D) H0 : µ ≠ 15 and HA : µ = 15.

E) H0 : µ < 15 and HA : µ > 15.

Answer: B L.O.: 2 7) The correct value of the test statistic is A) t = 3.531.

B) t = -3.531.

C) t = 1.223.

D) t = -1.223.

E) t = 0.789.

Answer: A L.O.: 1, 2 8) At α = 0.05, A) we reject the alternative hypothesis.

B) we fail to reject the null hypothesis.

C) the firm should institute an incentive program because there is evidence indicating that professional employees volunteer less than 15 hours per month on average.

D) we reject the null hypothesis, and the firm shouldn't institute an incentive program because there is strong evidence indicating that professional employees volunteer more than 15 hours per month, on average.

E) we reject HA : µ > 15. The P-value indicates that professional employees volunteer exactly 15 hours per month.

Answer: D L.O.: 2

6 .

9) For a more accurate determination, top management wants to estimate the average number of hours volunteered per month by their professional staff to within one hour with 99% confidence.

How many randomly selected professional employees would they need to sample?

A) 56 B) 120 C) 37 D) 25 E) 90 Answer: C L.O.: 3 10) Suppose 40 professional employees are randomly selected. This sample yields a mean of 15.2 hours and a standard deviation of 1.8 hours. The 95% confidence interval is A) 12.45 to 17.85 hours.

B) 14.62 to 15.78 hours.

C) 13.88 to 14.29 hours.

D) 10.65 to 20.22 hours.

E) 11.98 to 18.02 hours.

Answer: B L.O.: 1 Consider the following to answer the question(s) below: The cost of a university education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average number of hours students work per week exceeds 20. A random sample of 20 students was selected and the following values were observed: 26 10 40 20 40

15 20 0 32 36

10 30 5 16 10

40 36 10 12 0

11) The correct null and alternative hypotheses are A) H0 : µ = 20 and HA : µ > 20.

B) H0 : µ = 20 and HA : µ ≠ 20.

C) H0 : µ = 20 and HA : µ < 20.

D) H0 : µ > 20 and HA : µ = 20.

E) H0 : µ < 20 and HA : µ > 20.

Answer: A L.O.: 2

7 .

12) The correct value of the test statistic is A) 0.1314.

B) 3.04.

C) 2.0930.

D) 1.7291.

E) 0.8968.

Answer: A L.O.: 1, 2 13) At α = 0.05 A) we fail to reject the null hypothesis, and there is no evidence to suggest that students work more than 20 hours per week.

B) we reject the null hypothesis.

C) we support the alternative hypothesis; there is strong evidence to suggest that students work more than 20 hours per week.

D) we know students work more than 20 hours per week, on average.

E) we reject the null hypothesis. The P-value = 0.4884 indicates that students work more than 20 hours per week.

Answer: A L.O.: 2 14) For a more accurate determination, the university wants to estimate the average number of hours worked per week by students to within one hour with 99% confidence. How many randomly selected students would they need to sample?

A) 1229 B) 35 C) 554 D) 24 E) 62 Answer: A L.O.: 3 15) The 95% confidence interval is A) 14.03 to 26.77 hours.

B) 11.69 to 29.11 hours.

C) 15.14 to 25.66 hours.

D) 12.67 to 28.13 hours.

E) 13.63 to 26.37 hours.

Answer: A L.O.: 1

8 .

Consider the following to answer the question(s) below: The Dispenser Right Company makes a soft drink dispensing machine used in many fast food restaurants. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by a particular machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed: 14.25 13.70 14.02 14.13 13.99 14.04 16) The 99% confidence interval is A) 13.72 to 14.32 ounces.

B) 13.83 to 14.21 ounces.

C) 13.87 to 14.71 ounces.

D) 13.70 to 14.30 ounces.

E) 13.81 to 14.19 ounces.

Answer: A L.O.: 1 17) In order to be 99% accurate to within 0.02 ounces, what sample size would be needed if the sample standard deviation is 0.18?

A) 538 B) 23 C) 11 D) 1159 E) 440 Answer: A L.O.: 3 18) The correct null and alternative hypotheses are A) H0 : µ = 14 and HA : µ ≠ 14.

B) H0 : µ ≠ 14 and HA : µ = 14.

C) H0 : µ = 14 and HA : µ > 14.

D) H0 : µ = 14 and HA : µ < 14.

E) H0 : µ < 14 and HA : µ > 14.

Answer: A L.O.: 1

9 .

19) The correct value of the test statistic is A) 0.2889.

B) -0.2889.

C) 0.1837.

D) 0.0750.

E) 0.7842.

Answer: A L.O.: 1 20) At 5%, A) we fail to reject the null hypothesis. They should not adjust the machine because there is no evidence to suggest that it is not functioning properly.

B) we reject the null hypothesis. The P-value is very low.

C) we support the alternative hypothesis because we know the machine is working properly.

D) we support the alternative hypothesis because we know the machine needs adjustment.

E) we reject the null hypothesis. The company should adjust the machine because there is strong evidence to show it is not functioning properly.

Answer: A L.O.: 2

10 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 14: Comparing Two Means Short Answer - Quiz A Consider the following to answer the question(s) below: Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.86 hours with a standard deviation of 3.29 hours. The Human Resources Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family.

1) Are the assumptions and conditions for carrying out the t-test for two means satisfied?

Explain.

Answer: • Independence Assumption: Women and men are two independent groups.

• Randomization Condition: Samples were taken by random selection.

• 10% Condition: The sample represents less than 10% of all employees in a medium sized company.

• Nearly Normal Condition: The histograms below show that both sets are unimodal and roughly symmetric.

1 .

L.O.: 1 2) Write the null and alternative hypotheses (assuming women are group 1 and men are group 2).

Answer: H0: µ1 - µ2 = 0 vs. HA: µ1 - µ2 > 0 L.O.: 1 3) What is the value of the test statistic?

Answer: t = 2.02 L.O.: 1 4) What is the associated P-value?

Answer: P-value = 0.035 L.O.: 1 5) State your conclusion using α = 0.05.

Answer: Since the P-value is low, we reject the null hypothesis. There is evidence that women take more personal time than men, on average.

L.O.: 1 6) Create and interpret a 90% confidence interval.

Answer: Using 10 degrees of freedom, the critical t-value is 1.812. The 90% confidence interval is (0.30, 5.48). We are 90% confident that, on average, women take between 0.30 and 5.48 more hours of personal time than men.

L.O.: 2

2 .

Short Answer - Quiz B Consider the following to answer the question(s) below: A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. They took a random sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged overnight and the number of hours of use before needing to be recharged was recorded. Company A toothbrushes operated for an average of 119.7 hours with a standard deviation of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a standard deviation of 1.72 hours. Do these samples indicate that Company B toothbrushes operate more hours on average than Company A toothbrushes?

1) Are the assumptions and conditions for carrying out the t-test for two means satisfied?

Explain.

Answer: Conditions: • Independence Assumption: Company A and Company B are two independent groups.

• Randomization Condition: Samples were taken by random selection.

• 10% Condition: The sample represents less than 10% of all possible toothbrushes manufactured by Company A and B. • Nearly Normal Condition: The histograms below show that both sets are unimodal and roughly symmetric.

3 .

L.O.: 1 2) Write the null and alternative hypotheses. Assume Company A is group 1 and Company B is group 2.

Answer: H0 : µ1 - µ2 = 0 vs. HA : µ1 - µ2 < 0 L.O.: 1 3) What is the value of the test statistic?

Answer: t = -1.489 L.O.: 1 4) What is the associated P-value?

Answer: P-value = 0.0735 L.O.: 1 5) State your conclusion using α = 0.05.

Answer: Since the P-value is fairly high, we fail to reject the null hypothesis. There is not enough evidence to indicate that Company B cordless toothbrushes operate longer, on average, than those of Company A. L.O.: 1 6) Create and interpret a 90% confidence interval.

Answer: Using 30 degrees of freedom, the critical t-value is 1.697. The 90% confidence interval is (-1.93, 0.13). We are 90% confident that difference between mean operating time of Company A and Company B cordless toothbrushes falls between -1.93 hours and 0.13 hours.

L.O.: 2

4 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: Data were collected on annual personal time (in hours) taken by a random sample of 16 women and 7 men employed by a medium sized company. The women took an average of 24.75 hours of personal time per year with a standard deviation of 2.84 hours. The men took an average of 21.86 hours with a standard deviation of 3.29 hours. The Human Resources Department believes that women tend to take more personal time than men because they tend to be the primary child care givers in the family.

1) The correct null and alternative hypotheses (assuming women are group 1 and men are group 2) are A) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 < 0.

B) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 ≠ 0.

C) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 > 0.

D) H0 : µ1 - µ2 > 0 and HA : µ1 - µ2 < 0.

E) H0 : µ1 - µ2 < 0 and HA : µ1 - µ2 > 0.

Answer: C L.O.: 1 2) The t-test for two means is appropriate in this situation because A) women and men are dependent samples.

B) women and men are independent samples.

C) women and men are matched samples.

D) the observations are paired.

E) the variances of the two groups are the same.

Answer: B L.O.: 1

5 .

3) The correct value of the test statistic is A) t = 2.02.

B) t = - 1.997.

C) t = 0.458.

D) t = 4.02.

E) t = - 4.02.

Answer: A L.O.: 1 4) At α = 0.05, A) we reject the alternative hypothesis.

B) we fail to reject the null hypothesis.

C) we can conclude that women take a smaller average number of hours of personal time per year compared to men.

D) we reject the null hypothesis. There is strong evidence that women take a higher average number of hours of personal time per year compared to men.

E) there is no evidence of a difference in the true average number of hours of personal time taken by women and men.

Answer: D L.O.: 1 5) Based on the data, the correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is A) 0.30 to 5.48 hours.

B) -0.50 to 3.21 hours.

C) -4.67 to -0.62 hours.

D) 1.27 to 6.89 hours.

E) -3.21 to 0.5.

Answer: A L.O.: 2

6 .

Consider the following to answer the question(s) below: A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. They took a random sample of 18 toothbrushes from Company A and 15 from Company B. Each was charged overnight and the number of hours of use before needing to be recharged was recorded. Company A toothbrushes operated for an average of 119.7 hours with a standard deviation of 1.74 hours; Company B toothbrushes operated for an average of 120.6 hours with a standard deviation of 1.72 hours. Do these samples indicate that Company B toothbrushes operate more hours on average than Company A toothbrushes?

6) Which of the following statements is true?

A) This is a one-tailed test for the difference in the means of two dependent groups.

B) This is a two-tailed test for the difference in the means of two independent groups.

C) This is a one-tailed test for the difference in the means of two independent groups.

D) These samples are matched.

E) This is a two-tailed test for the difference in the means of two dependent groups.

Answer: C L.O.: 1 7) The correct null and alternative hypotheses (assuming Company A is group 1 and Company B is group 2) are A) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 > 0.

B) H0 : µ1 - µ2 > 0 and HA : µ1 - µ2 < 0.

C) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 < 0.

D) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 ≠ 0.

E) H0 : µ1 - µ2 < 0 and HA : µ1 - µ2 > 0.

Answer: C L.O.: 1

7 .

8) The correct value of the test statistic is A) t = -1.489.

B) t = -4.421.

C) t = 2.566.

D) t = 1.488.

E) t = -2.566.

Answer: A L.O.: 1 9) At α = 0.05, A) we reject the null hypothesis.

B) we fail to reject the alternative hypothesis.

C) we can conclude that there is significant difference between the mean operating times of cordless toothbrushes manufactured by the two companies.

D) we fail to reject the null hypothesis. There is not enough evidence to indicate that Company B cordless toothbrushes operate longer, on average, than those of Company A. E) we fail to reject the alternative hypothesis. There is strong evidence indicating that Company B cordless toothbrushes operate longer on average than those of Company A. Answer: D L.O.: 1 10) Suppose that we test the hypotheses (assuming Company A is group 1 and Company B is group 2): H0 : µ1 - µ2 = 0 vs. HA : µ1 - µ2 ≠ 0. Provided that the P-value is greater than α = 0.05, we fail to reject the null hypothesis. If we want to construct a 95% confidence interval for the difference between the mean operating times of cordless toothbrushes of Company A and Company B, we will expect A) both the upper and lower limits be negative.

B) both the upper and lower limits to be positive.

C) that zero is not included in the interval.

D) that zero falls into the interval.

E) both the upper and lower limits be positive and fairly high.

Answer: D L.O.: 2

8 .

Consider the following to answer the question(s) below: A company in the golfing industry is interested in testing its new driver to see if it has greater length off the tee than the best-selling driver. To do this, it has selected a group of golfers of differing abilities and ages. Its plan is to have each player use each of the two clubs to hit five balls. It will record the average length in yards of the drives with each club for each player.

Player 1 2 3 4 5 6 7 8 9 10

New Club 236.4 202.5 245.6 257.4 223.5 205.3 266.7 240.0 278.9 211.4

Leading Club 237.2 200.4 240.8 259.3 218.9 200.6 258.9 236.5 280.5 206.5

11) The correct null and alternative hypotheses (assuming the new club is group 1, leading club is group 2, and d = group 1 value - group 2 value) are A) H0 : µd = 0 and HA : µd > 0.

B) H0 : µd = 0 and HA : µd ≠ 0.

C) H0 : µd ≠ 0 and HA : µd = 0.

D) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 < 0.

E) H0 : µ1 - µ2 < 0 and HA : µ1 - µ2 > 0.

Answer: A L.O.: 3 12) The correct value of the test statistic is A) 2.726.

B) 1.83.

C) 2.62.

D) 0.235.

E) 1.734.

Answer: A L.O.: 3 13) The correct critical value for α = 0.05 is A) 1.833.

B) 2.262.

C) 1.734.

D) 2.101.

E) 1.645.

Answer: A L.O.: 3 9 .

14) At α = 0.05, A) We reject the null hypothesis and conclude that the evidence indicates that the new driver has greater length off the tee than the best-selling driver, on average.

B) We are 95% certain that the new driver is not better than the leading driver.

C) We know the new driver has smaller length off the tee than the best-selling driver, on average.

D) We reject the alternative hypothesis.

E) We fail to reject the null hypothesis.

Answer: A L.O.: 3 15) Based on the data, the 90% confidence interval for the difference in the length off the tee is A) 0.92 to 4.70 yards.

B) 0.48 to 5.14 yards.

C) 0.04 to 5.58 yards.

D) 0.16 to 5.46 yards.

E) 1.25 to 6.75 yards.

Answer: A L.O.: 3 Consider the following to answer the question(s) below.

A recent study of two brands of golf balls was undertaken to determine whether there is a difference in the mean distance that the two golf ball brands will fly off the tee. To conduct the test, a robot which swings the club at the same speed and with the same swing pattern each time was used. The following data reflect sample data for a random sample of balls of each brand. We assume that the variances of the two groups are the same.

Brand A: 234 Brand B: 240

236 236

230 241

227 236

234 239

233 243

228 230

229 239

16) Which test would be most appropriate for testing this hypothesis?

A) the pooled t-test B) the two sample t-test C) the paired t-test D) the two proportion z-test E) the one sample t-test Answer: A L.O.: 2, 3

10 .

230 243

238 240

17) The correct null and alternative hypotheses (assuming Brand A is group 1 and Brand B is group 2) are A) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 ≠ 0.

B) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 > 0.

C) H0 : µ1 - µ2 = 0 and HA : µ1 - µ2 < 0.

D) H0 : µ1 - µ2 < 0 and HA : µ1 - µ2 > 0.

E) H0 : µ1 - µ2 ≠ 0 and HA : µ1 - µ2 = 0.

Answer: A L.O.: 2, 3 18) The correct value of the test statistic (assuming Brand A is group 1 and Brand B is group 2) is A) -4.04.

B) 4.04.

C) 1.7340.

D) 2.1009.

E) -1.7340.

Answer: A L.O.: 2 19) The correct critical value(s) at α = 0.05 (assuming Brand A is group 1 and Brand B is group 2) is(are) A) -1.734.

B) 1.734.

C) ±2.101.

D) ±1.645.

E) -1.960.

Answer: C L.O.: 2 20) At α = 0.05, A) we reject the null hypothesis and can conclude that there is a significant difference in the mean distance that the two golf ball brands will fly off the tee.

B) we reject the null alternative hypothesis.

C) we fail to reject the null hypothesis and can conclude that there is no significant difference in the mean distance that the two golf ball brands will fly off the tee.

D) we fail to reject the null hypothesis.

E) we know there is a no difference between the two brands.

Answer: A L.O.: 2

11 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 15: Design of Experiments and Analysis of Variance (ANOVA) Short Answer - Quiz A 1) Management styles differ among organizations and may potentially affect employee job satisfaction. A sample of employees was randomly selected from each of three companies with different management styles (Authoritarian, Laissez-faire and Participative) and asked to rate their level of job satisfaction on a 10-point scale (10 being the highest level of satisfaction). The data collected and partial ANOVA results appear below.

Authoritarian 3 5 4 6 5 2 4 3 4 5

Laissez- faire 7 5 6 4 8 7 5 5 6 7

Participative 9 8 10 9 8 7 10 7 8 9

1 .

a. What are the null and alternative hypotheses (in words, not symbols)? b. Are the conditions / assumptions for ANOVA met? c. Calculate the F-statistic. d. The P-value for this statistic turns out to be < .001. State the conclusion. e. Suppose that employees fall into several job categories, such as clerical, technical, or professional. How might this affect the study results? Suggest how the design for the study could have been improved.

Answer: a. H0: Mean employee job satisfaction ratings are equal across companies with different management styles.

HA: At least one mean employee job satisfaction rating is different from the others. b. Employees were randomly selected from each of the three companies. Therefore, the independence assumption holds. Boxplots of the original data indicate that the equal variance assumption is reasonable. The Normal probability plot of residuals indicates that the Nearly Normal Condition is reasonable. c. F = 35.16 d. With such a small P-value = 3.039E-08 (using technology), we can reject the null hypothesis and conclude that at least one mean employee job satisfaction rating is different from the others. e. Job category may be a confounding variable. A randomized block design using job category as the blocking variable might improve the study.

L.O.: 2, 3

2 .

2) A survey of online consumers asked respondents to indicate how much money they spent for online purchases during the most recent Christmas holiday season. These data were analyzed to see if gender (1= Female; 2 = Male) and income level (1 = Low, 2 = Middle, 3 = High) influence the amount consumers spend online for holiday shopping. The two-way ANOVA results appear below.

3 .

a. Is this an experiment or observational study? b. Are the conditions for two-way ANOVA met? c. If so, perform the hypothesis tests and state your conclusions in terms of amount spent online, gender and income level. d. Is it appropriate to interpret the main effects in this case separately? Explain.

Answer: a. Observational study. b. Boxplots of online expenditures ($) during the last holiday shopping season by both income level and gender appear to satisfy the equal variance assumption. Also, the boxplots appear fairly symmetric. We can only assume that the survey participants were selected at random. c. All P-values are very small. This indicates a significant interaction effect as well as significant main effects. d. Since the interaction effect of gender and income level on online expenditure is significant, it is not appropriate to interpret the main effects due to gender and income level separately.

L.O.: 1, 3

4 .

Short Answer - Quiz B 1) A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below.

Process 1 60 58 55 62 68 52 64 66

Process 2 45 40 35 34 52 49 48 39

Process 3 50 52 56 47 48 52 51 50

5 .

a. What are the null and alternative hypotheses (in words, not symbols)? b. Are the conditions / assumptions for ANOVA met? c. Calculate the F-statistic. d. The P-value for this statistic turns out to be < .001. State the conclusion. e. Suppose the company is concerned about whether different batches of green vegetable material would blanch differently. Suggest how the design for the study could have been improved to take this into account.

Answer: a. H0 : Mean vitamin A retention amounts are equal across the three blanching processes.

HA : At least one mean vitamin A retention amount is different from the others. b. We need to assume that the vegetable material samples were randomly assigned to the processes. Boxplots of the original data indicate that the equal variance assumption is reasonable.

The Normal probability plot of residuals indicates that the Nearly Normal Condition is reasonable. c. F = 23.27 d. With such a small P-value = 4.7088E-06 (using technology), we can reject the null hypothesis and conclude that at least one mean vitamin A retention amount is different from the others. e. A randomized block design using batch as the blocking variable could improve the study.

L.O.: 2, 3

6 .

2) An advocacy group is interested in determining if gender (1 = Female, 2 = Male) affects executive level salaries. They take a random sample of executives in three different industries: (1 = Consumer Goods, 2 = Financial, 3 = Health Care). Salary data are collected. The two-way ANOVA results appear below.

7 .

a. Is this an experiment or observational study? b. Are the conditions for two-way ANOVA met? c. If so, perform the hypothesis tests and state your conclusions in terms of amount spent online, gender, and income level. d. Is it appropriate to interpret the main effects in this case separately? Explain.

Answer: a. Observational study. b. The executives were randomly selected. Therefore the independence assumption holds.

Boxplots of salary both industry sector and gender appear to satisfy the equal variance assumption. The boxplots appear roughly symmetric. c. Based on the very small P-values for the main effects, we can conclude that mean executive salaries are not the same across the three different industry sectors and for males and females. d. Yes. The P-value for the interaction effect indicates that it is not significant. Therefore it is appropriate to interpret the main effects separately.

L.O.: 1, 3

8 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below.

Process 1 60 58 55 62 68 52 64 66

Process 2 45 40 35 34 52 49 48 39

Process 3 50 52 56 47 48 52 51 50

1) The correct null hypothesis is A) mean vitamin A retention amounts are not all equal across the three blanching processes.

B) mean vitamin A retention amounts are equal across the three blanching processes.

C) blanching process has an effect on vitamin A retention.

D) all three blanching processes are different from each other.

E) exactly two mean vitamin A retention amounts are equal across the two particular blanching processes, and one mean is different.

Answer: B L.O.: 3 2) The F-statistic value is A) F = 23.267.

B) F = 2.215.

C) F = 27.57.

D) F = 7.999.

E) F = 3.22.

Answer: A L.O.: 3

9 .

3) The P-value for this statistic turns out to be < 0.001. Therefore, at α = 0.05 A) we fail to reject the null hypothesis.

B) we reject the alternative hypothesis.

C) we conclude that mean vitamin A retention amounts are all equal across the different blanching processes.

D) we support the null hypothesis and conclude that at least two mean vitamin A retention amounts are equal.

E) we reject the null hypothesis and conclude that at least one mean vitamin A retention amount is different from the others.

Answer: E L.O.: 3 Consider the following to answer the question(s): An advocacy group is interested in determining if gender (1 = Female, 2 = Male) affects executive level salaries. They take a random sample of executives in three different industries: (1 = Consumer Goods, 2 = Financial, 3 = Health Care). Salary data are collected. The two-way ANOVA results appear below.

4) Which of the following statements is true?

A) This is an experiment.

B) This is an observational study.

C) This is a randomized block design.

D) This is an experimental study involving a randomized block design.

E) This is a completely randomized design.

Answer: B L.O.: 1, 2 5) At α = 0.05, we can conclude A) that mean executive salaries are the same across the three different industry sectors.

B) that mean executive salaries are the same for males and females.

C) that there is a significant interaction effect.

D) that mean executive salaries are not the same across the three different industry sectors and that mean executive salaries are not the same for males and females.

E) that the P-value for the interaction effect = 0.390 > 0.05. Thus, it is not appropriate to interpret the main effects separately.

Answer: D L.O.: 3

10 .

Consider the following to answer the question(s) below: Management styles differ among organizations and may potentially affect employee job satisfaction. A sample of employees was randomly selected from each of three companies with different management styles (Authoritarian, Laissez-faire and Participative) and asked to rate their level of job satisfaction on a 10-point scale (10 being the highest level of satisfaction). The data collected and partial ANOVA results appear below.

Authoritarian 3 5 4 6 5 2 4 3 4 5

Laissez- faire 7 5 6 4 8 7 5 5 6 7

Participative 9 8 10 9 8 7 10 7 8 9

6) The correct null hypothesis is A) exactly two mean employee job satisfaction ratings are equal, and one mean is different.

B) mean employee job satisfaction ratings are not all equal across companies with different management styles.

C) management style affects employee job satisfaction rating.

D) mean employee job satisfaction ratings are equal across companies with different management styles.

E) two particular management styles affect employee job satisfaction rating, and one style is not significant.

Answer: D L.O.: 3 7) The F-statistic value is A) F = 35.16.

B) F = 2.604.

C) F = 48.7.

D) F = 1.385.

E) F = 3.60.

Answer: A L.O.: 3 11 .

8) The P-value for this statistic turns out to be < 0.001. Therefore, at α = 0.05 A) we fail to reject the null hypothesis.

B) we reject the null hypothesis and conclude that at least two mean employee job satisfaction ratings are different.

C) we conclude that mean employee job satisfaction ratings are all equal across companies with different management styles.

D) we support the null hypothesis and conclude that management style does not affect employee job satisfaction rating.

E) we reject the alternative hypothesis and conclude that mean employee job satisfaction ratings are all equal across companies with different management styles.

Answer: B L.O.: 3 9) Suppose that employees fall into several job categories, such as clerical, technical, or professional. Which of the following statements is true?

A) We are sure that job category is not a confounding variable.

B) Job category may be an outlier variable.

C) A randomized block design using job category as the blocking variable cannot improve the study.

D) Job category may be a confounding variable, and a randomized block design using job category as the blocking variable might improve the study.

E) Job category is not a lurking variable, and a randomized block design using job category as the blocking variable cannot improve the study.

Answer: D L.O.: 2

12 .

10) A survey of online consumers asked respondents to indicate how much money they spent for online purchases during the most recent Christmas holiday season. These data were analyzed to see if gender and income level influence the amount consumers spend online for holiday shopping. The two-way ANOVA results appear below.

Which of the following statements is true?

A) This is an experiment.

B) This is a randomized block design.

C) Since the interaction effect of gender and income level on online expenditure is significant, it is not appropriate to interpret the main effects due to gender and income level separately.

D) Only income level is significant.

E) The interaction effect of gender and income level on online expenditure is not significant.

Answer: C L.O.: 1, 2, 3 Consider the following to answer the question(s) below: An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of users and recorded the connect time during a week period. The following is partial Excel output for the data.

11) The correct null hypothesis is A) mean weekly connect times are equal regardless of the method of connection.

B) mean weekly connect times are not all equal regardless of the method of connection.

C) two mean weekly connect times are equal, and one mean is different.

D) method of internet connection has an impact on average weekly connect times.

E) only DSL and Cable Internet are significant.

Answer: A L.O.: 3

13 .

12) The F-statistic value is A) 43.88.

B) 962.72.

C) 21.94.

D) 0.02.

E) 3.554.

Answer: A L.O.: 3 13) The P-value for this statistic is < 0.001. Therefore, at α = 0.05 A) we reject the null hypothesis and conclude that at least two of the mean weekly connect times are different.

B) we fail to reject the null hypothesis.

C) we know average connect times are the same for all connection methods.

D) we reject the alternative hypothesis and conclude that the average weekly connect times are the same for all three methods of connection.

E) we support the null hypothesis and conclude that the method of connection is not significant.

Answer: A L.O.: 3 14) In a completely randomized design, which of the following is true?

A) The mean squares due to treatments will be larger than the mean squares due to error if the null hypothesis is rejected.

B) The mean squares due to treatments will be smaller than the mean squares due to error if the null hypothesis is rejected.

C) The sum of squares due to treatments will be equal to the sum of squares due to error if the null hypothesis is rejected.

D) The populations must have equal means.

E) The sample sizes must be equal.

Answer: A L.O.: 3

14 .

Consider the following to answer the question(s) below: A national car rental company recently conducted a study in which cars with automatic and standard transmissions were rented to male and female customers. Three customers in each category were randomly selected and the number of miles driven per day was recorded as follows:

AUTOMATIC

STANDARD

MALES 124 55 78 33 108 156

FEMALES 54 88 76 88 90 15

15) Based on the design of this study, how many degrees of freedom will be associated with the mean squares for the type of transmission?

A) 1 B) 2 C) 3 D) 6 E) 8 Answer: A L.O.: 3 16) Given the following output, which of the following statements is not true at α = 0.05?

A) Since the interaction effect of gender and transmission type on miles driven is significant, it is appropriate to interpret the main effects due to gender and transmission type separately.

B) We fail to reject the null hypothesis that the mean number of miles driven per day is the same for both types of transmission.

C) We fail to reject the null hypothesis that the mean number of miles driven per day is the same for male and female customers.

D) Since the P-value is fairly high, the interaction effect of gender and transmission type on miles driven is not significant.

E) Since all P-values are fairly high, we fail to reject all three null hypotheses.

Answer: A L.O.: 3 15 .

17) Which of the following is not a principle of experimental design?

A) Balance B) Control C) Randomization D) Blocking E) Replication Answer: A L.O.: 2 Consider the following to answer the question(s) below: To test the fuel efficiency of three new car models, random samples of twenty were selected from each of the models and litres/100 kilometres data obtained. Partial output follows.

18) What is the mean square due to treatments?

A) 0.82 B) 0.57 C) 0.03 D) 1.63 E) 0.55 Answer: A L.O.: 3 19) What is the mean square due to the error?

A) 0.57 B) 0.82 C) 0.03 D) 0.55 E) 1.63 Answer: A L.O.: 3 20) The correct value of the F-statistic is A) 1.44.

B) 0.70.

C) 1.49.

D) 0.50.

E) 1.04.

Answer: A L.O.: 3 16 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 16: Inference for Counts: Chi-Square Tests Short Answer - Quiz A 1) Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.

Lemon Lime Sports Drink Purchase Frequency 159 Drink Type/Flavour

Kiwi Strawberry 198

Tropical Punch 174

Grape Sports Drink 149

a. State appropriate hypotheses to test whether the purchasing agent is correct. b. What is the value of the test statistic and its associated P-value? c. State the conclusion at α = 0.05.

Answer: a. H0: All types of drinks are equally preferred by the students.

HA: The types of drinks are not equally preferred by the students. b. Assuming that the null hypothesis is true, the expected frequencies are equal across the four drinks. Therefore, the expected frequencies are all (0.25) (680) = 170. χ2 = 8.012 P-value = 0.0458 c. The P-value is low (less than α), so we reject the null hypothesis. These data show evidence that the drink options are not equally preferred by the students.

L.O.: 1, 2 2) By examining residuals, determine which type of drink had the most impact on the test results? What are the implications for the purchasing agent?

Answer: Kiwi Strawberry has the highest standardized residual (2.148) and its χ2 component is 4.612. More students prefer Kiwi Strawberry compared to what was expected by the purchasing agent. The purchasing agent should order more Kiwi Strawberry than other drink types.

L.O.: 2

1 .

3) A manufacturing plant for recreational vehicles receives shipments from three different parts vendors. There has been a defect issue with some of the electrical wiring in the recreational vehicles manufactured at the plant. The plant manager believes that the defect issue is dependent on the parts vendor. The plant manager reviews a sample of quality assurance inspections from the last six months.

Rejected Perfect Not perfect but acceptable

Perfect Parts Co. 53 93 22

Made-4-U Co. 48 71 31

25 Hour Parts Co. 70 88 22

a. State appropriate hypotheses to test the plant manager's belief. b. What is the value of the test statistic and its associated P-value? c. State the conclusion at α = 0.05.

Answer: a. H0 : The defect issue is independent of the parts vendor.

HA : The defect issue is dependent on the parts vendor. b. Assuming that the null hypothesis is true, we find the expected frequencies for each cell by multiplying the row total by the column total and dividing by the overall total. So the expected number of rejected parts from Perfect Parts Co. is (171)(168) / 498 = 57.69.

Rejected Perfect Not perfect but acceptable

Perfect Parts Co. 53 (57.69) 93 (85.01)

Made-4-U Co. 48 (51.51) 71 (75.90)

25 Hour Parts Co. 70 (61.81) 88 (91.08)

22 (25.30)

31 (22.59)

22 (27.11)

The expected frequencies are shown in the table above next to observed frequencies. χ2 = 7.40 P-value = 0.1162 c. The P-value is rather high (greater than α), so we fail to reject the null hypothesis. There is no evidence indicating that the defect issue is dependent on the parts vendor.

L.O.: 3

2 .

Short Answer - Quiz B 1) A real estate agency, located in a metropolitan area in Canada, kept data on the various types of properties purchased in the area. Historically, 15% of purchases were for condominiums, 30% were for townhouses, 40% for single family homes, 10% for commercial properties, and 5% for land. With changing demographics, the agency wondered if the current distribution matches the historical distribution. Recent data showed the following: Type of Property Frequency

Condos 89

Townhouses 121

Homes 78

Commercial 25

Land 12

a. State appropriate hypotheses to test whether the purchasing agent is correct. b. What is the value of the test statistic and its associated P-value? c. State the conclusion at α = 0.05.

Answer: a. H0: The current distribution of property sales is the same as the historical distribution.

HA: The current distribution of property sales differs from the historical distribution. b. Assuming that the null hypothesis is true, we use the historical distribution to find the expected frequencies. For example, the expected frequency for condos is (0.15)(325) = 48.75. χ2 = 62.538 P-value < 0.0001 c. The P-value is very small (less than α), so we reject the null hypothesis. There is strong evidence that the current distribution of property sales differs from the historical distribution.

L.O.: 1, 2 2) By examining residuals, determine which type of property had the most impact on the test results? What are the implications for the real estate agency?

Answer: Condominiums type of property has the highest standardized residual (5.765) and its χ2 component is the largest (33.232). More people bought condominiums than would have been expected based on the historical distribution. The real estate agency should try and list as many condominiums as possible.

L.O.: 2

3 .

3) An online book store wants to determine if coupon redemption is independent of gender. After a special coupon broadcast to its reward members, the following data on coupon redemption at checkout were collected.

a. State appropriate hypotheses to determine whether coupon redemption is independent of gender. b. What is the value of the test statistic and its associated P-value? c. State the conclusion at α = .05.

Answer: a. H0: Online coupon redemption and gender are independent.

HA: Online coupon redemption and gender are not independent. b. Assuming that the null hypothesis is true, we find the expected frequencies for each cell by multiplying the row total by the column total and dividing by the overall total. So the expected number of males who redeemed coupons is (191) (132) / 331 = 76.17.

The expected frequencies are shown in the table above next to observed frequencies. χ2 = 5.340 P-value =0.0208 c. The P-value is small enough (less than α) to reject the null hypothesis. There is evidence of an association between gender and whether or not online coupons are redeemed.

L.O.: 3

4 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities.

The number of drinks sold from vending machines on this campus for the last six months is shown in the following table.

Lemon Lime Sports Drink Purchase Frequency 159 Drink Type/Flavour

Kiwi Strawberry 198

Tropical Punch 174

Grape Sports Drink 149

1) The correct null hypothesis to test if the purchasing agent is correct can be worded as A) the types of drinks are not equally preferred by the students buying drinks.

B) all types of drinks are equally preferred by the students.

C) the types of drinks are independent from each other.

D) the type of drink is dependent on gender of a student.

E) the type of drink is dependent on student's program.

Answer: B L.O.: 1, 2 2) What is not true about the expected frequencies?

A) Assuming that the null hypothesis is true, the expected frequencies are equal across the four types of drinks.

B) The value of an expected frequency needs not be an integer. However, in this case they all are equal to 170.

C) We use the total number of observations (680) to calculate the expected frequencies.

D) The expected frequencies are 0.234 (Lemon Lime), 0.291 (Kiwi Strawberry), 0.256 (Tropical Punch), and 0.219 (Grape).

E) The expected frequencies are all equal to (0.25) (680) = 170.

Answer: D L.O.: 2 3) Given α = 0.05. Using the χ2 table from the Appendix B, we get the critical value of A) 7.815.

B) 9.488.

C) 11.070.

D) 9.348.

E) 12.838.

Answer: A L.O.: 2

5 .

4) The correct value of the test statistic is A) χ2 = 8.012.

B) χ2 = 12.019.

C) χ2 = 0.984.

D) χ2 = 45.014.

E) χ2 = 64.192.

Answer: A L.O.: 2 5) The degrees of freedom associated with the test statistic are A) 1.

B) 2.

C) 3.

D) 4.

E) 679.

Answer: C L.O.: 2 6) At α = 0.05, A) we reject the alternative hypothesis.

B) we fail to reject the null hypothesis.

C) we conclude that the purchasing agent was correct.

D) we reject the null hypothesis and conclude that the purchasing agent was not correct. The drink options are not equally preferred by the students.

E) as the P-value is low (less than α), we conclude that all types of drinks are equally preferred by students.

Answer: D L.O.: 1, 2

6 .

Consider the following to answer the question(s) below: An online book store wants to determine if there is an association between coupon redemption and gender. After a special coupon broadcast to its reward members, the following data on coupon redemption at checkout were collected.

7) What Chi-Square test is appropriate in this situation?

A) Goodness-of-fit B) Homogeneity C) Independence D) Normal distribution E) Gosset's t Answer: C L.O.: 3 8) The correct value of the test statistic is A) χ2 = 5.340.

B) χ2 = 8.429.

C) χ2 = 0.839.

D) χ2 = 45.556.

E) χ2 = 28.505.

Answer: A L.O.: 3 9) The degrees of freedom associated with the test statistic is A) 1.

B) 2.

C) 3.

D) 4.

E) 330.

Answer: A L.O.: 3

7 .

10) At α = 0.05, A) we reject the alternative hypothesis.

B) we fail to reject the null hypothesis.

C) we cannot conclude that there is an association between coupon redemption and gender.

D) we reject the null hypothesis and conclude that online coupon redemption and gender are not independent.

E) we know that online coupon redemption and gender are independent.

Answer: D L.O.: 3 Consider the following to answer the question(s) below: A walk-in medical clinic believes that arrivals are equally distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days.

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY

FREQUENCY 25 22 19 18 16 100

11) How many degrees of freedom are appropriate to test that arrivals are equally distributed?

A) 4 B) 100 C) 5 D) 6 E) 99 Answer: A L.O.: 2 12) What is the value of the test statistic?

A) 2.50 B) 7.7794 C) 3.62 D) 2.46 E) 6.94 Answer: A L.O.: 2

8 .

13) At α = 0.05, A) we fail to reject the null hypothesis and conclude that arrivals are equally distributed based on this sample.

B) we reject the null hypothesis.

C) we fail to reject the alternative hypothesis and can conclude that arrivals are not equally distributed based on this sample.

D) we support the alternative hypothesis. There is strong evidence that arrivals are not the same over weekdays.

E) as the P-value = 0.645 is high, we conclude that arrivals are not equally distributed. Monday arrivals are the highest.

Answer: A L.O.: 2 Consider the following to answer the question(s) below: A local cell phone provider wants to determine if the use of text messaging is independent of age. The following data has been collected from a random sample of customers.

UNDER 21 21-39 40 AND OVER

REGULARLY USE TEXT MESSAGING 82 57 6

DO NOT USE IT REGULARLY 34 34 83

14) Based on the data above what is the expected frequency for the "under 21 and regularly use text messaging" cell?

A) 56.8 B) 120 C) 145 D) 62 E) 50 Answer: A L.O.: 3 15) To conduct the independence test the correct degrees of freedom are A) 2.

B) 3.

C) 6.

D) 5.

E) 4.

Answer: A L.O.: 3

9 .

16) The value of the test statistic is A) 92.2095.

B) 0.

C) 9.2104.

D) 11.0705.

E) 275.02.

Answer: A L.O.: 3 17) At α = 0.05, A) we reject the null hypothesis. There is no evidence that use of text messaging is independent of age. We and can conclude that there is an association between age and the use of text messaging.

B) we fail to reject the null hypothesis.

C) we fail to reject the null alternative hypothesis and can conclude that use of text messaging is independent of age.

D) as the P-value < .0001 is very low, We reject the null hypothesis.there is no association between age and the use of text messaging.

E) since χ2 = 92.2095 > χcr2 = 5.991, we support the null hypothesis and can conclude that age and use of text messaging are not related.

Answer: A L.O.: 3 Consider the following to answer the question(s) below: We want to test whether type of car owned (domestic or foreign) is independent of gender. The following are the results of a random sample of 990 car owners.

CAR DOMESTIC FOREIGN

MALE 215 110

FEMALE 400 265

18) To conduct the independence test the correct degrees of freedom are A) 1.

B) 4.

C) 2.

D) 3.

E) 5.

Answer: A L.O.: 3

10 .

19) The value of the test statistic is A) 3.34.

B) 3.54.

C) 3.84.

D) 33.44.

E) 8.54.

Answer: A L.O.: 3 20) At α = 0.05, A) we fail to reject the null hypothesis. There is no evidence that type of car owned (domestic or foreign) is dependent on gender.

B) we reject the null hypothesis and can conclude that there is an association between gender and the type of car owned (domestic or foreign).

C) as P-value = 0.0676 is fairly high, we support the alternative hypothesis.

D) we fail to reject the null alternative hypothesis. There is strong evidence that the type of car owned (domestic or foreign) is dependent on gender.

E) since χ2 = 3.34 < χcr2 = 3.841, we can conclude that gender and the type of car owned (domestic or foreign) are unrelated.

Answer: A L.O.: 3

11 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 17: Nonparametric Methods Short Answer - Quiz A 1) Suppose that 6 economists who work for the federal government and 7 university economists were asked to grade the effectiveness of the federal government's stimulus bill in terms of its ability to increase jobs over the next two years. The grades are shown below. Do the two groups differ in terms of their opinion?

Government AA B+ BB A-

University C B+ BC+ ABC

a. What nonparametric method is appropriate for analyzing these data? b. Are the assumptions satisfied for applying this method? Explain. c. State the null and alternative hypotheses. d. Perform the test and state your conclusion at α = 0.10.

Answer: a. Wilcoxon rank-sum / Mann-Whitney test. b. Yes. We can assume that the sampled observations are independent (Independence Assumption) and the two groups are independent of each other (Independent Groups Assumption). c. H0: The government and university economists have the same typical opinion.

HA: The government and university economists have different typical opinions.

1 .

d.

The ranks in the table above order all the opinions from the worst (Cs assigned rank1.5) to the best (A assigned rank 13). We get T1 = TGovernment = 55.5 and T2 = TUniversity = 35.5. The test statistic is T = min (55.5 , 35.5) = 35.5. The critical values from the table W1 are TL = 30 and TU = 54. Therefore, we fail to reject the null hypothesis. At α = 0.10, there is no evidence that the government and university economists have different typical opinions about the economic stimulus bill.

L.O.: 2

2 .

2) Consumers were asked to "rate" the taste of three popular brands of yogurt that have been modified to include fibre. The data are shown in the table below. Are there differences in the results among the three brands?

Activia 4 5 3 2 4

Yoplait 2 2 2 1 1

Dannon 5 4 3 3 4

a. What nonparametric method is appropriate for analyzing these data? b. State the null and alternative hypotheses. c. Perform the test and state your conclusion at α = 0.05. d. If these data did satisfy the assumptions for performing ANOVA, what are the disadvantages of using this nonparametric method instead?

Answer: a. Kruskal-Wallis Test b. H0: All three brands have the same distribution of customer rating.

HA: At least one brand has a different distribution from the others. c.

The test statistic is H = 8.345. The critical value is χ2 = 5.991. Therefore, at α = 0.05 we reject the null hypothesis and conclude that at least one brand has a different distribution from the others. d. ANOVA would be more powerful. Using the Kruskal-Wallis instead of ANOVA, when the assumptions for the latter are satisfied, decreases the power of the test.

L.O.: 1, 2

3 .

3) For the scatterplots shown below, indicate what about the data make nonparametric methods appropriate for measuring the association between x and y. a.

b.

Answer: a. Outlier condition is violated b. Linearity condition is violated L.O.: 1

4 .

Short Answer - Quiz B 1) Eight hybrid cars are used to determine if there is a difference in fuel consumption (l/100 km) with and without a particular additive. The data are shown below.

Hybrid Car 1 2 3 4 5 6 7 8

(l/100km) with Additive (l/100km) without Additive 11.8 13.1 10.7 11.8 9.8 11.8 9.4 9.0 8.1 10.7 9.0 10.7 11.8 10.7 8.4 9.8

a. What nonparametric method is appropriate for analyzing these data? b. Are the assumptions satisfied for applying this method? Explain. c. State the null and alternative hypotheses. d. Perform the test and state your conclusion at α = 0.10.

Answer: a. Wilcoxon signed-rank test. b. Yes. The data are appropriately paired. We assume that the cars are randomly selected and both distributions are symmetric. c. Let the difference be d = With Additive — Without Additive.

H0: The median difference in (l/100km) with and without the additive is zero.

HA: The median difference in (l/100km) with and without the additive is not zero. d.

Order 1 2 3 4 5 6 7 8

d 0.4 -1.1 1.1 -1.3 -1.4 -1.7 -2 -2.6

Rank 1 2.5 2.5 4 5 6 7 8

We get T- = 32.5 and T+ = 3.5, therefore the test statistic value is 3.5. The critical value from the table W2 is 6. We reject the null hypothesis and conclude that the median difference in (l/100 km) with and without the additive is different from zero. Thus, there is a difference in fuel consumption (l/100 km) with and without a particular additive.

L.O.: 1, 2

5 .

2) The best tasting ice creams are generally high in fat content, which gives them a creamy texture. Four brands of ice cream were tested by consumers who graded their level of creaminess (A = very creamy to F = not creamy). Each brand was rated by a different group of consumers (the data are shown below). Are there differences in perceived creaminess among the four brands?

Brand A A B AB+ A

Brand B A AB+ A A-

Brand C C C+ BC B-

Brand D BC+ C C C-

a. What nonparametric method is appropriate for analyzing these data? b. State the null and alternative hypotheses. c. Perform the test and state your conclusion at α = 0.10. d. If these data did satisfy the assumptions for performing ANOVA, what are the disadvantages of using this nonparametric method instead?

Answer: a. Kruskal-Wallis Test. b. H0: All four brands have the same distribution of perceived creaminess.

HA: At least one of the brands has a different distribution from the others.

6 .

c.

Taste rate CC C C C C+ C+ BBBB B+ B+ AAAA A A A

Rank 1 3.5 3.5 3.5 3.5 6.5 6.5 9 9 9 11 12.5 12.5 15 15 15 18.5 18.5 18.5 18.5

Brand D C C D D C D C C D A A B A B B A A B B

The test statistic is H = 14.514. The critical value is χ2 = 6.251. Therefore, at α = .10 we reject the null hypothesis and conclude that at least one brand has a different distribution from the others. Thus, there are differences in perceived creaminess among the four brands d. ANOVA would be more powerful. By using the Kruskal-Wallis test instead of ANOVA, when the assumptions for the latter are satisfied, the power of the test is decreased.

L.O.: 1, 2

7 .

3) Suppose that ten new smart phone models were evaluated by two consumer electronics magazines (Popular Electronics and Electronics Now) from 1 (best) to 10 (worst) as follows.

How strong is the agreement between the two magazines?

Model 1 2 3 4 5 6 7 8 9 10

Popular Electronics 8 3 7 4 2 1 10 5 6 9

Electronics Now 7 6 5 3 1 2 8 9 4 10

a. Why can't the Pearson correlation be used for these data? b. The Spearman's rho is 0.745. What does this tell us about the association?

Answer: a. These data are not quantitative; they are ranks and therefore are ordinal. b. There is a strong positive association between the rankings of ten new smart phones provided by the two magazines.

L.O.: 3 Multiple Choice - Quiz C 1) Which of the following statements is false regarding nonparametric methods?

A) Nonparametric methods are appropriate when we want to treat the data as ordinal.

B) Compared to the correlation coefficient r, Spearman's rho is less affected by outliers in the data.

C) The Wilcoxon rank-sum test is the nonparametric alternative to the paired t-test.

D) Spearman's rho is always between -1 and 1.

E) The Friedman test is appropriate for a randomized block design.

Answer: C L.O.: 1, 2, 3 2) A management professor was teaching a course in business leadership as part of an executive MBA program. She divided her class of 10 executives into two equal sized groups and used a different approach (case study and online interactive) to teach about various leadership styles. To compare the effectiveness of the two approaches, the appropriate nonparametric procedure is the A) Kruskal-Wallis test.

B) Spearman's rho test.

C) Wilcoxon signed-rank test.

D) Wilcoxon rank-sum test.

E) Friedman test.

Answer: D L.O.: 1, 2, 3 8 .

3) Suppose that 6 economists who work for the federal government and 7 university economists were asked to predict the percentage change in the Canada's GDP over the three year period from January 2013 to January 2016. The Wilcoxon rank-sum test was used to determine if the two groups differ in their predictions. The value of the test statistic was calculated to be 29.5. At α = 0.05, we can conclude that A) the null hypothesis should be rejected.

B) the alternative hypothesis should not be rejected.

C) there is a difference in predictions provided by the two groups of economists.

D) since TL= 28 < 29.5 < TU = 56, we can conclude that two groups of economists have different predictions.

E) the null hypothesis should not be rejected; there is no significant difference in predictions provided by the two groups of economists.

Answer: E L.O.: 2 4) The best tasting ice creams are generally high in fat content, which gives them a creamy texture. Four brands of ice cream (two national and two local) were tested by consumers who rated how "creamy" they tasted on a 5-point Likert type scale (1 = not creamy to 5 = very creamy). Each brand was rated by a different group of consumers. The appropriate nonparametric method to use for these data is the A) Kruskal-Wallis test.

B) Kendall's tau test.

C) Wilcoxon signed-rank test.

D) Wilcoxon rank-sum test.

E) Spearman's rho test.

Answer: A L.O.: 1, 2, 3 5) Consumer ratings for three popular brands of yogurt are shown below. Using the KruskalWallis test to compare ratings among brands, the calculated value for the test statistic is Activia 4 5 3 2 4

Yoplait 2 2 2 1 1

Dannon 5 4 3 3 4

A) 8.345.

B) 12.315.

C) 4.995.

D) 2.635.

E) 402.760.

Answer: A L.O.: 2 9 .

6) Suppose the Kruskal-Wallis test was used to compare four groups. If the test statistic value was found to be 9.545, using α = 0.05 we should A) reject the alternative hypothesis.

B) not reject the null hypothesis.

C) conclude that the groups are all the same.

D) reject the null hypothesis and conclude that at least one of the groups has a different distribution from the others.

E) compare test static with the critical value χ2 = 7.815 and conclude that all four groups have the same distribution.

Answer: D L.O.: 2 7) A particular additive is claimed to increase the fuel efficiency of hybrid vehicles. Eight hybrid cars are used to determine if there is a difference in fuel efficiency (l/100km) with and without the additive. The appropriate nonparametric method to use for these data is the A) Kruskal-Wallis test.

B) Kendall's tau test.

C) Wilcoxon signed-rank test.

D) Wilcoxon rank-sum test.

E) Spearman's rho test.

Answer: C L.O.: 2, 3 8) Eight hybrid cars are used to determine if there is a difference in fuel efficiency (l/100km) with and without a particular additive. Using the appropriate nonparametric method, the value of the calculated test statistic for the data shown below is Hybrid Car 1 2 3 4 5 6 7 8

(l/100km) with Additive 11.8 10.7 9.8 9.4 8.1 9.0 11.8 8.4

(l/100km) without Additive 13.1 11.8 11.8 9.0 10.7 10.7 10.7 9.8

A) 3.5.

B) 5.

C) 8.

D) 30.

E) 32.5.

Answer: A L.O.: 2

10 .

9) Suppose the Wilcoxon signed-rank test was used on ten pairs of data. If the calculated test statistic for a two-tailed test was found to be 6, at α = 0.05 we can conclude that A) the null hypothesis should be rejected and the median of the differences is not zero.

B) the null hypothesis should not be rejected and the median of the differences is zero.

C) we know that the groups are the same.

D) the alternative hypothesis should be rejected and there is no difference between the pairs.

E) all groups are the same, as T = 6 < Tcrt = 8.

Answer: A L.O.: 2 10) Suppose that ten new smart phone models were evaluated by two consumer electronics magazines from 1 (best) to 10 (worst). Spearman's rho was calculated to be - 0.45. We can say that A) there is a high level of agreement between the two magazine rankings.

B) the association between the two magazine rankings is strong and positive.

C) we use the Spearman's test as the Quantitative Variables Condition is satisfied.

D) the association between the two magazine rankings is moderate and negative.

E) as - 0.45 is roughly close to zero, there is very strong association between the two magazine ratings.

Answer: D L.O.: 3 11) The Wilcoxon signed-rank test is used to test which of the following types of hypotheses?

A) It is used to test hypotheses involving the median of paired samples.

B) It is used to test hypotheses involving three or more population medians.

C) It is used to test hypotheses involving the variances of two or more populations.

D) It is used to test hypotheses involving the variances of paired samples.

E) It is used to test hypotheses involving two or more population proportions.

Answer: A L.O.: 1, 2 12) Suppose the Wilcoxon signed-rank test was used on seven pairs of data. If the calculated test statistic for a two-tailed test was found to be 5, at α = 0.05 we can conclude that A) the null hypothesis should not be rejected and there is no evidence that the median of the differences differs from zero.

B) the null hypothesis should be rejected and that the groups are not all the same.

C) the alternative hypothesis should not be rejected and the median of the differences is not zero.

D) as T = 5 > Tcr = 2, we support the alternative hypothesis.

E) the groups are different, as T = 5 > Tcr = 2.

Answer: A L.O.: 2

11 .

13) Which of the following is not true about the Spearman's rho compared with the correlation coefficient r?

A) Spearman's rho is not sensitive to violations of the Linearity condition.

B) Spearman's rho is not significantly affected by outliers.

C) Spearman's rho can be smaller than - 1 and greater than 1.

D) Spearman's rho can be used for data with bends and outliers.

E) It can be used when only ranks are known.

Answer: C L.O.: 3 14) We use Spearman's Rank Correlation to find whether there is a strong association between two variables. We find that the Spearman's rho is equal to 0.18 for the sample size n = 7. The correct value of the test statistic to determine whether two variables are dependent on each other is A) 0.409.

B) 0.754.

C) 0.875.

D) 0.771.

E) 2.42.

Answer: A L.O.: 3 Consider the following to answer the question(s) below: A paint manufacturer is interested in determining whether there is a difference in time it takes for two different brands of paint to dry once they have been applied to a wall surface. To test this, the company has selected a random sample of 5 walls and applied Brand 1, and another 5 walls and applied Brand 2. The following data reflect the actual drying time in hours: Brand 1 3.4 3.2 2.8 3.7 2.5

Brand 2 2.0 3.0 3.0 2.2 2.1

15) The appropriate nonparametric method to use for these data is the A) Wilcoxon rank-sum test.

B) Kruskal-Wallis test.

C) Kendall's tau test.

D) Spearman's rho test.

E) Wilcoxon signed-rank test.

Answer: A L.O.: 2, 3

12 .

16) The sum of all the ranks for this test is A) 55.

B) 10.

C) 25.

D) 90.

E) 45.

Answer: A L.O.: 2 17) Using Tukey's quick test to determine whether there is a difference in the two brands we can say that A) the total of the values is 6 and we conclude there is no significant difference.

B) the total of the values is 6 and we conclude there is a significant difference.

C) the total of the values is 4 and we conclude there is no significant difference.

D) the total of the values is 4 and we conclude there is a significant difference.

E) the total of the values is 9 and we conclude there is a significant difference.

Answer: A L.O.: 2 Consider the following to answer the question(s) below: Assume that a Kruskal-Wallis test is being conducted to determine whether or not all groups come from the same distribution.

Group 1 T1 = 60 n1 = 6

Group 2 T2 = 36 n2 = 5

Group 3 T3 = 24 n3 = 4

18) What is the correct value of the test statistic?

A) 2.16 B) 7.81 C) 48.68 D) 12.59 E) 15.69 Answer: A L.O.: 2 19) What is the critical value for α = 0.05?

A) 5.991 B) 7.815 C) 7.378 D) 12.838 E) 9.348 Answer: A L.O.: 2

13 .

20) At α = 0.05, A) we fail to reject the null hypothesis and conclude the groups come from the same distribution.

B) we reject the null hypothesis and conclude that at least one group has the different distribution from the others.

C) we support the alternative hypothesis.

D) as H = 2.16 < χcrt2 = 5.991, we fail to reject the alternative hypothesis.

E) as H = 2.16 < χcrt2 = 5.991, we reject the null hypothesis and conclude the groups do not come from the same distribution.

Answer: A L.O.: 2

14 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 18: Inference for Regression Short Answer - Quiz A Consider the following to answer the question(s) below: A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and the number of units each sold last month was recorded. Relevant data appear in the table below.

College GPA 3.25 2.87 2.66 3.33 2.87 3.21 2.76 3.91 3.55 2.55 2.44 3.22 3.01 3.44 3.22

Units Sold 24 21 18 22 22 22 18 28 29 18 20 24 21 24 25

1 .

Below are the scatterplot, regression results, and residual plots for these data.

2 .

1) Are the assumptions/conditions for regression and inference satisfied? Explain.

Answer: • Linearity condition: There is no obvious bend in the original scatterplot of the data or in the plot of the residuals against the predicted values.

• Independence assumption: These data were not collected over time and there is no reason to think that one salesperson's performance affects another.

• Equal Variance assumption: Neither the original scatterplot nor the residual plot shows any changes in the spread about the line.

• Normal Population assumption: The normal probability plot of residuals does not show severe departure from normality.

L.O.: 1 3 .

2) Write the null and alternative hypothesis.

Answer: H0: There is no association between GPA and sales performance.

HA: There is an association between GPA and sales performance.

L.O.: 1 3) Is there a significant relationship between sales performance (units sold per month) and college GPA (use α = 0.05)? Give the appropriate test statistic, associated P-value, and conclusion.

Answer: The test for regression slope results in t = 6.80, P-value = 0.000 < 0.05. With such a Pvalue we would reject the null hypothesis and conclude that there is strong evidence of an association between GPA and sales performance. The extremely small P-value means that the association we see in the data is unlikely to have occurred by chance.

L.O.: 1 4) What percentage of the variability in sales performance (units sold per month) can be accounted for by college GPA? Answer: The R2 for the regression is 78.1%. GPA seems to account for about three-fourths of the variation observed in sales performance (units sold per month).

L.O.: 1 5) Predict the units sold per month for a new hire whose college GPA is 3.00.

Answer: For a GPA = 3, the regression equation predicts = -0.43 + 7.40(3) = 21.77 units sold per month.

L.O.: 3 6) The confidence interval and prediction interval for the number of units sold per month when GPA = 3.00 are shown below. Interpret both intervals in this context.

95% CI 95% PI (20.832, 22.695) (18.120, 25.407) Answer: We can be 95% confident that the number of units sold per month by a particular salesperson whose college GPA is 3.00 will be between 18.120 and 25.407.

We can be 95% confident that the average number of units sold per month by salespersons whose college GPA is 3.00 will be between 20.832 and 22.695.

All else equal, the prediction interval will always be wider than the confidence interval.

L.O.: 3

4 .

Short Answer - Quiz B Consider the following to answer the question(s) below: An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. Relevant data appear in the table below.

Hours of Training 8 10 9 7 7 5 4 5 10 11 4 4 2 8 10

Troubleshooting time (min) 15 11 16 18 19 20 26 22 12 11 22 21 28 17 12

Below are the scatterplot, regression results, and residual plots for these data.

5 .

6 .

1) Are the assumptions / conditions for regression and inference satisfied? Explain.

Answer: • Linearity condition: There is no obvious bend in the original scatterplot of the data or in the plot of the residuals against the predicted values.

• Independence assumption: These data were not collected over time and there is no reason to think that one line worker's troubleshooting time affects another.

• Equal Variance assumption: Neither the original scatterplot nor the residual plot shows any significant changes in the spread about the line.

• Normal Population assumption: A histogram of the residuals is unimodal and roughly symmetric.

L.O.: 1 7 .

2) Write the null and alternative hypothesis.

Answer: H0: There is no association between training and troubleshooting time.

HA: There is an association between training and troubleshooting time.

L.O.: 1 3) Is there a significant relationship between time it takes to troubleshoot the process (minutes) and training received (use α = 0 .05)? Give the appropriate test statistic, associated P-value, and conclusion.

Answer: The test for regression slope results in t = - 13.35, P-value = 0.000 < 0.05. With such a P-value we would reject the null hypothesis and conclude that there is strong evidence of an association between hours of training received and the time it takes for line workers to troubleshoot the process. The extremely small P-value means that the association we see in the data is unlikely to have occurred by chance.

L.O.: 1 4) What percentage of the variability in troubleshooting time can be accounted for by amount of training received?

Answer: The R2 for the regression is 93.2%. Hours of training seems to account for about ninetenths of the variation observed in troubleshooting time (min).

L.O.: 1 5) Predict the troubleshooting time for a line worker who received 8 hours of training.

Answer: For a training time of 8 hours, the regression equation predicts = 30.7 - 1.84(8) = 15.98 minutes for troubleshooting time.

L.O.: 3 6) The confidence interval and prediction interval for troubleshooting time with 8 hours of training are shown below. Interpret both intervals in this context.

95% CI (15.180, 16.903)

95% PI (12.822, 19.261)

Answer: We can be 95% confident that the average troubleshooting time by line workers receiving 8 hours of training is between 15.180 and 16.903 minutes.

We can be 95% confident that the troubleshooting time by a particular line worker who received 8 hours of training will be between 12.822 and 19.261 minutes.

All else equal, the prediction interval will always be wider than the confidence interval.

L.O.: 3

8 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: A sales manager was interested in determining if there is a relationship between college GPA and sales performance among salespeople hired within the last year. A sample of recently hired salespeople was selected and the number of units each sold last month was recorded. Relevant data appear in the table below.

College GPA 3.25 2.87 2.66 3.33 2.87 3.21 2.76 3.91 3.55 2.55 2.44 3.22 3.01 3.44 3.22

Units Sold 24 21 18 22 22 22 18 28 29 18 20 24 21 24 25

Below are the scatterplot, regression results, and residual plots for these data.

9 .

10 .

1) Which of the following assumptions and/or conditions for regression and inference is not satisfied?

A) Linearity B) Independence C) Equal Variance D) Normal Population E) Sample Size Answer: E L.O.: 1 2) The correct null hypothesis is A) there is a strong association between GPA and sales performance.

B) there is a relationship between GPA and sales performance.

C) H0: β1 ≠ 0.

D) there is no relationship between GPA and sales performance (β1 = 0.).

E) HA: β1 ≠ 0.

Answer: D L.O.: 1

11 .

3) At α = 0 .05, A) as P-value < 0.05, we reject the null hypothesis. There is strong evidence of an association between GPA and sales performance.

B) we fail to reject the null hypothesis.

C) we can conclude that there is no significant relationship between GPA and sales performance.

D) we reject the alternative hypothesis and can conclude that there is no significant association between GPA and sales performance.

E) we fail to reject the null hypothesis and can conclude that GPA and sales performance are not related.

Answer: A L.O.: 1 4) The residual standard deviation, which measures the spread of points around the estimated regression line, is A) 3.256.

B) 1.044.

C) 1.63045.

D) 34.70.

E) 2.477.

Answer: C L.O.: 1 5) The percentage of variability in sales performance (units sold per month) accounted for by college GPA is A) 50.56%.

B) 78.1%.

C) 34.70%.

D) 100%.

E) 48.9%.

Answer: B L.O.: 2

12 .

Consider the following to answer the question(s) below: An operations manager was interested in determining if there is a relationship between the amount of training received by production line workers and the time it takes for them to troubleshoot a process problem. A sample of recently trained line workers was selected. The number of hours of training time received and the time it took (in minutes) for them to troubleshoot their last process problem were captured. The data, scatterplot and regression results are shown below.

Hours of Training 8 10 9 7 7 5 4 5 10 11 4 4 2 8 10

Troubleshooting time (min) 15 11 16 18 19 20 26 22 12 11 22 21 28 17 12

13 .

6) In testing the null hypothesis H0: β1 = 0, the correct value of the test statistic is A) t = - 13.35.

B) t = 30.03.

C) s = 1.43588.

D) t = - 1.8360.

E) t = 1.8360.

Answer: A L.O.: 1 7) At α = 0.05, A) we reject the alternative hypothesis.

B) we fail to reject the null hypothesis.

C) we can conclude that there is no significant relationship between amount of training received by production line workers and the time it takes for them to troubleshoot a process problem.

D) we reject the null hypothesis and can conclude that there is a significant relationship between amount of training received by production line workers and the time it takes for them to troubleshoot a process problem.

E) we fail to support the alternative hypothesis and can conclude that amount of training received by production line workers and the time it takes for them to troubleshoot a process are not related.

Answer: D L.O.: 1

14 .

8) From the residual plot below we can say

A) that the Nearly Normal condition is not satisfied.

B) that the Normal Population assumption is not satisfied.

C) that the Equal Variance assumption is satisfied.

D) that the Linearity condition is not satisfied.

E) that the Independence assumption is not satisfied.

Answer: C L.O.: 1

15 .

9) From the histogram of residuals below we can say

A) that the Nearly Normal condition is satisfied.

B) that the Nearly Normal condition is not satisfied.

C) that the Equal Variance assumption is not satisfied.

D) that the Linearity condition is not satisfied.

E) that the Independence assumption is not satisfied.

Answer: A L.O.: 1 10) Based on the regression equation = 30.7 - 1.84x, the troubleshooting time for a line worker who receives 8 hours of training would be A) 26.77 minutes.

B) 15.98 minutes.

C) 20 minutes.

D) 10.36 minutes.

E) 10 minutes.

Answer: B L.O.: 3

16 .

Consider the following to answer the question(s) below: A study was recently performed by the Canada Revenue Agency to determine how much tip income waiters and waitresses would make based on the size of the bill at the table. A random sample of bills and resulting tips was collected. These data and regression results are as follows: Total Bill $126 $58 $86 $20 $59 $120 $14 $17 $26 $74

Tip $19 $11 $20 $3 $14 $30 $2 $4 $2 $16

17 .

11) In testing the null hypothesis H0: β1 = 0, the correct value of the test statistic is A) 7.5634.

B) 2.0202.

C) 0.0281.

D) 0.0001.

E) 0.2128.

Answer: A L.O.: 1 12) In testing the null hypothesis H0: β1 = 0, at α = 0.05 A) we reject the null hypothesis and can conclude that there is a significant relationship between the amount of the total bill and the size of the tip received by the server.

B) we fail to reject the null hypothesis.

C) we reject the alternative hypothesis.

D) we fail to reject the null hypothesis and can conclude that there is no significant relationship between amount of total bill and the size of the tip received by the server.

E) we conclude that the amount of the total bill and the size of the tip received by the server are not related.

Answer: A L.O.: 1 13) Based upon the regression equation tips if the total bill is $100?

A) $20.61 B) $26.03 C) $15.55 D) $12.88 E) $21.28 Answer: A L.O.: 3

= -0.6684 + 0.2128x, what is the predicted value for

14) The value of the correlation coefficient is A) +0.9366.

B) - 0.9366.

C) +0.8773.

D) - 0.8773.

E) +0.8620.

Answer: A L.O.: 1, 2

18 .

15) In testing the null hypothesis that the correlation coefficient, ρ, equals 0, the correct value of the test statistic is A) 7.5602.

B) 5.1702.

C) 6.7452.

D) 2.3156.

E) 3.4891.

Answer: A L.O.: 2 16) In testing the null hypothesis that the correlation coefficient, ρ, equals 0, the correct critical values at 5% significance level are A) + 2.306.

B) + 2.228.

C) + 1.860.

D) + 1.812.

E) + 2.262.

Answer: A L.O.: 2 17) In testing the null hypothesis that the correlation coefficient, ρ, equals 0, at α = 0.05 A) we reject the null hypothesis and conclude there is strong evidence that the true correlation, ρ, is not zero.

B) we fail to reject the null hypothesis and conclude there is no evidence of an association between total bill and tip.

C) we reject the alternative hypothesis.

D) we fail to support the alternative hypothesis.

E) we know tip and total bill are not related.

Answer: A L.O.: 2 18) The 95% confidence interval for the slope is A) 0.1479 to 0.2777.

B) -5.3271 to 3.9903.

C) -4.4252 to 3.0883.

D) 0.1605 to 0.2651.

E) 0.1184 to 0.3072.

Answer: A L.O.: 1

19 .

19) Which of the following is true?

A) The confidence interval for the predicted mean value of y is always narrower than the prediction interval for an individual y when both are calculated for a given value of x.

B) The prediction interval for an individual y is always narrower than the confidence interval for the predicted mean value of y, when both are calculated for a given value of x.

C) The confidence interval of the slope is the same as the confidence interval for the predicted y.

D) The confidence interval for the predicted mean value of y is the same as the prediction interval for an individual y when both are calculated for a given value of x.

E) The width of the confidence interval for the predicted mean value of y is greater than that of the prediction interval for an individual y when both are calculated for a given value of x.

Answer: A L.O.: 1, 3 20) Which of the following is true?

A) When the correlation coefficient is significant, the slope coefficient will also be significant for a given level of α.

B) When the correlation coefficient is significant, the slope coefficient will never be significant for a given level of α.

C) The test statistics for the correlation coefficient and the slope coefficient are the same.

D) When the slope coefficient is significant, the correlation will not necessarily be significant for a given level of α.

E) The significance of the correlation and slope are unrelated.

Answer: A L.O.: 1, 2

20 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 19: Understanding Regression Residuals Short Answer - Quiz A 1) A food company launches an advertising campaign for a high fibre cereal and wants to claim that high fibre cereals are lower in calories. In order to research this claim, they obtain nutritional information for 34 breakfast cereals including the amount of fibre (in grams) and the number of calories per serving. The data resulted in the following scatterplot.

a. Do you think there is a clear pattern? Describe the association between fibre and calories. b. Comment on any unusual data point or points in the data set. Explain. c. Do you think a model could accurately predict the number of calories in a serving of cereal that has 22 grams of fibre? Explain.

Answer: a. There is no clear pattern. At first glance, there appears to be a weak, negative association between grams of fibre and the number of calories in the cereals. Yet, the five points at the bottom of the graph are outside the main cluster, with extremely low numbers of calories. b. The points in the bottom left corner seem to have extremely low calorie content for cereals between zero and three grams of fibre. The points with 9, 10 and 14 grams of fibre appear to have an unusually high amount of fibre for their calorie content, making them outliers and influential points. These three points would also be leverage points, creating the impression that there is a negative association between grams of fibre and the number of calories in the cereals. c. This data contains information about cereals with fibre content between 0 and 14 grams. It would be extrapolation to try to use this data to predict the calorie content of cereals with 22 grams of fibre. The predicted value will not be trustworthy.

L.O.: 1

1 .

2) Monthly closing stock prices for a utility company were obtained from January 2014 through August 2015. A regression model was estimated to describe the trend in closing stock prices over time. a. Based on the plot of residuals versus predicted values, is the linear model appropriate?

Explain.

b. The Durbin-Watson statistic for the collected data was found to be 0.5626. What can you conclude from this statistic at the 0.01 level of significance?

Answer: a. The residual plot shows a clear pattern and curvature. It appears that a linear model would not be appropriate. b. At the 0.01 level of significance, dL = 0.95. Since 0.5626 is less than this value, we can conclude that there is evidence of positive autocorrelation.

L.O.: 1, 2

2 .

3) The following scatterplot shows the population of Canada plotted against 5 year intervals from 1970 through 2015. a. Based on the scatterplot, is the linear model appropriate? Explain.

b. A linear regression model was estimated to describe the trend in the population of Canada over time. Examine the plot of Residuals against Year shown below. Is the association between Population and Year reasonably straight?

3 .

c. Would a re-expression of the data help? If so, what would you recommend?

Answer: a. The scatterplot appears straight enough, so a linear model seems appropriate. b. The residual plot clearly shows a curved pattern not really apparent in the scatterplot. The linear model is not quite appropriate based on the residual analysis. c. Yes. A logarithmic transformation might be an appropriate re-expression of the data.

L.O.: 3 4) Data were collected for a sample of companies regarding their investment in quality improvement efforts and cost savings realized as a result (both measured as a percentage of sales revenue). Below is the scatterplot.

The correlation coefficient for these data is r = 0.913. If data were collected for individual departments within companies rather than at the company level, would you expect the correlation to be weaker, stronger or about the same? Explain.

Answer: Relationships based on averages have higher correlation coefficients than relationships based on individual data. Therefore, a scatterplot of the investment and cost savings of quality improvement efforts for individual departments would show much more scatter and a weaker correlation coefficient.

L.O.: 1

4 .

Short Answer - Quiz B 1) Data on Internet usage (per 100 inhabitants) and population were collected for a sample of 52 countries (United Nations database). The data resulted in the following scatterplot.

a. Do you think there is a clear pattern? Describe the association between Internet usage and population. b. Comment on any unusual data point or points in the data set. Explain. c. Do you think a model could accurately predict the Internet usage in India with a population of 1,339,346,874? Explain.

Answer: a. There is no clear pattern. At first glance, there appears to be a weak, negative association between Internet usage and population because of the points at the bottom right of the graph representing countries with low Internet usage and large populations. b. The points in the bottom right corner seem to have extremely low Internet usage for densely populated countries, making them outliers and influential points. These points would also be leverage points, creating the impression that there is a negative association between Internet usage and population. c. It would be extrapolation to try to use this data to predict the Internet usage in India since its population is outside the range of population values in the data set. The predicted value would hardly be trustworthy.

L.O.: 1

5 .

2) Suppose that data on labour productivity and unit labour costs were obtained for the retail industry from 1995 through 2014. A regression was estimated to describe the linear relationship between the two variables. a. Based on the plot of residuals versus predicted values, is the linear model appropriate?

Explain.

b. Would a re-expression of the data help? If so, what would you recommend?

Answer: a. The residual plot shows a clear pattern and curvature. It appears that a linear model would not be appropriate. b. Yes. A logarithmic transformation might be an appropriate re-expression of the data.

L.O.: 3

6 .

3) Quarterly sales figures for e-commerce retail sales were obtained from the first quarter of 2009 through the fourth quarter of 2015. A regression model was estimated to describe the trend in e-commerce retail sales over time. a. Based on the plot of residuals versus predicted values, is the linear model appropriate?

Explain.

b. The Durbin-Watson statistic for this regression model was found to be 1.727. What can you conclude from this statistic at the 0.01 level of significance?

Answer: a. The residual plot shows a curvature. In addition, the plot seems to thicken. The spread of residuals increases as the fitted value increases. b. At the 0.01 level of significance, dU = 1.24. Since 1.727 is greater than upper critical value, we can conclude that there is no evidence of positive autocorrelation. Also, we get 1.727 < 4 - du = 2.76. There is no evidence of positive or negative autocorrelation.

L.O.: 1, 2

7 .

4) A regression model was developed relating average annual pay to the percentage of women employed for a sample of companies. Below is the plot of residuals versus predicted values.

a. What can you see in the plot of residuals that may not have been clear in the original scatterplot of the data? b. Would a re-expression of the data help? If so, what would you recommend?

Answer: a. The residuals show that the plot thickens. The spread in the residuals increases as the fitted value increases. b. Yes. A logarithmic transformation might be an appropriate re-expression of the data.

L.O.: 3

8 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: Monthly closing stock prices for a utility company were obtained from January 2014 through August 2015. A regression model was estimated to describe the trend in closing stock prices over time.

1) What does the plot of residuals above suggest?

A) An outlier is present in the data set.

B) The Linearity condition is not satisfied.

C) A high-leverage point is present in the data set.

D) Extrapolation was used.

E) There is no pattern. The relationship seems reasonably straight.

Answer: B L.O.: 3 2) Suppose that for the regression model estimated using the data described, the Durbin-Watson statistic was calculated as 0.5626. Using α = 0.01 we can conclude that A) there is evidence of positive autocorrelation.

B) there is evidence of negative autocorrelation.

C) there is no evidence of positive autocorrelation.

D) there is no evidence of negative autocorrelation.

E) as dL < 0.5626 < dU, the test is inconclusive.

Answer: A L.O.: 2

9 .

3) Which of the following statement is true about autocorrelation?

A) We use autocorrelation to predict values of y for values x far from the ones used to find the linear model equation.

B) When a regression model applied to autocorrelated data, the Independence assumption is satisfied.

C) When data highly correlated over time, each data point is similar to those around it. The Independence assumption is violated.

D) We use χ2 statistic to test for autocorrelation.

E) Autocorrelation occurs only if there is at least one extreme outlier.

Answer: C L.O.: 1, 3 4) Data were collected for a sample of companies regarding their investment in quality improvement efforts and cost savings realized as a result (both measured as a percentage of sales revenue). The correlation coefficient for these data is r = 0.913. If the data were collected for individual departments within companies rather than at the company level, we would expect A) a stronger correlation.

B) a weaker correlation.

C) the same correlation.

D) fewer outliers in the data.

E) the correlation coefficient of 1.

Answer: B L.O.: 1

10 .

5) Quarterly figures for e-commerce retail sales were obtained from the first quarter of 2009 through the fourth quarter of 2015. A regression model was estimated to describe the trend in ecommerce retail sales over time. What does the plot of residuals versus predicted values suggest?

A) The relationship seems reasonably straight.

B) There is no reason to be alert for autocorrelation.

C) The Equal Spread condition is satisfied.

D) The Linearity condition is satisfied.

E) The Linearity condition is not satisfied, and the Equal Spread condition is not satisfied as well.

Answer: E L.O.: 3 6) Quarterly figures for e-commerce retail sales were obtained from the first quarter of 2009 through the fourth quarter of 2015. A regression model was estimated to describe the trend in ecommerce retail sales over time. Suppose that for the regression model estimated using the data described, the Durbin-Watson statistic was calculated as 1.727. Using α = 0.01 we can conclude that A) there is evidence of positive autocorrelation.

B) there is evidence of negative autocorrelation.

C) there is no evidence of positive or negative autocorrelation.

D) since 1.727 is greater than upper critical value, there is evidence of an outlier.

E) as dL < 1.727 < dU, the test is inconclusive.

Answer: C L.O.: 2

11 .

Consider the following to answer the question(s) below: A regression model was developed relating average annual pay to the percentage of women employed for a sample of companies. Below is the plot of residuals versus predicted values.

7) What does the plot of residuals suggest?

A) The plot of residuals shows no unusual pattern. The Equal Variance assumption is satisfied.

B) The plot of residuals has no particular structure. So, the Equal Spread condition is definitely satisfied.

C) The spread in the residuals decreases as the fitted value increases.

D) The residuals show that the plot thickens. The spread in the residuals increases as the fitted value increases. The equal spread condition is not satisfied.

E) The spread in the residuals remains unchanged as the fitted value increases. The Equal Spread condition is satisfied.

Answer: D L.O.: 3 8) Which of the following re-expressions of the data would be appropriate?

A) Square the data values.

B) Cube the data values.

C) Use a logarithmic transformation.

D) Use a geometric transformation.

E) Only extrapolation would help.

Answer: C L.O.: 3

12 .

9) A food company launches an advertising campaign for a high fibre cereal and wants to claim that high fibre cereals are lower in calories. In order to research this claim, they obtain nutritional information for 34 breakfast cereals including the amount of fibre (in grams) and the number of calories per serving. The data resulted in the following scatterplot.

Which statement is true?

A) The points in the bottom right corner seem to be high-leverage points.

B) There is a strong positive association between amount of fibre and number of calories per serving.

C) As the amount of fibre increases so does the number of calories per serving.

D) There are no unusual observations.

E) Five points in the bottom part of the scatterplot have low numbers of calories. Thus, they cannot be influential points.

Answer: A L.O.: 1

13 .

Consider the following to answer the question(s) below: Consider the following scatter diagram for 24 of the top grossing movies of all time. The data include the highest grossing films for which world box office receipts and budgets were available. The top two were Avatar and Titanic.

14 .

10) Which statement is not true?

A) The scatterplot shows no unusual observations.

B) The data contain high-leverage points.

C) The data contain potential influential points.

D) The data contain points which are associated with large residuals.

E) We would consider setting aside outliers and re-running the regression.

Answer: A L.O.: 1 11) The effect of including the data for Avatar and Titanic is A) making the value of the slope of the regression line larger.

B) making the value of the slope of the regression line smaller.

C) making the correlation between the two variables negative.

D) reducing the residual standard deviation.

E) making the regression line curvier.

Answer: A L.O.: 1

15 .

12) What does the plot of the residuals and the fitted values suggest?

A) The Equal Variance assumption is not satisfied.

B) The plot does not contain any evident outliers.

C) The Linearity condition is not satisfied.

D) There may be autocorrelation.

E) The plot does not fan out. Thus, the Equal Spread condition is satisfied.

Answer: A L.O.: 1 13) The best practice for modelling this data set given the scatter plot would be A) to estimate the model both including and excluding the data for Avatar and Titanic and then to compare the two regression models to understand how they differ.

B) to include the data for Avatar and Titanic and use the model without any doubt.

C) to exclude the data for Avatar and Titanic, construct the new model and use only new one.

D) to find different data that will measure box office success and perfectly fit to the given equation.

E) to use the given regression equation and treat Avatar and Titanic as extrapolation points.

Answer: A L.O.: 1 14) A new movie is in the making which has a budget of $350 million. What would the equation in the scatter diagram predict for its box office receipts?

A) $1,693 million B) $2,388 million C) $1,010 million D) $328 million E) $3,000 million Answer: A L.O.: 1 15) A new movie is in the making which has a budget of $350 million. Using the equation in the scatter diagram to predict sales we can say A) that the prediction is based on autocorrelation.

B) that the prediction is very close to the actual value as it is based on the strong correlation.

C) that we should be cautious with a prediction such as this since it is beyond the range of the xvalues; the prediction is an extrapolation.

D) that our prediction is trustworthy E) that $350 million falls into the range of the x-values. So, we do not need to worry about extrapolation.

Answer: C L.O.: 1

16 .

Consider the following to answer the question(s) below: The average monthly residential mortgage lending rate in Canada is available monthly beginning in 1951. A scatterplot of the residuals against time for 747 months from January 1951 to March 2013 is shown below. The rate peaked in September of 1981 at 21.46%.

The Durbin-Watson statistic has a value of D = 0.01.

16) The critical values for the Durbin-Watson statistic for α = 0.05 and n = 750 are: dL= 1.87736 and dU = 1.88270.

What does this tell us about the assumption of the independence of the errors?

A) The assumption of independent errors is violated.

B) The assumption of independent errors is not violated.

C) The errors are not related to one another over time.

D) Since D falls between the critical values, the test is inconclusive. So, we suppose that the errors are independent.

E) As D is very small, the errors are independent.

Answer: A L.O.: 2

17 .

17) What conclusion about autocorrelation in the model can we draw using the value of the Durbin-Watson statistic and the critical limits, dL=1.87736 and dU=1.88270?

A) There is evidence of positive autocorrelation.

B) There is evidence of negative autocorrelation.

C) There is no evidence of positive autocorrelation.

D) There is no evidence of negative autocorrelation.

E) As D falls between the critical values, the test is inconclusive.

Answer: A L.O.: 2 Consider the following to answer the question(s) below: Suppose that data on labour productivity and unit labour costs were obtained for the retail industry from 1995 through 2014. A regression was estimated to describe the linear relationship between the two variables.

18) What does the plot of residuals suggest?

A) The plot shows curvature. So, the Equal Spread condition is not satisfied.

B) The residual plot has no clear pattern.

C) The Equal Variance assumption is met.

D) All assumption and condition for regression inference appear to be met.

E) As the given residual plot appears generally patternless, we can construct the linear regression model.

Answer: A L.O.: 1, 3

18 .

19) Which of the following re-expressions of the data would be appropriate?

A) Use a logarithmic transformation.

B) Square the data.

C) Use a geometric transformation.

D) Take the square root of the data.

E) Take the reciprocal of the data.

Answer: A L.O.: 3 20) After transforming data, a model of retail sales of furniture and fixtures in Canada on value of building permits yielded the following equation: log10 (Sales) = 2.33 + 0.57 log10 (Value of permits) What is the predicted value of retail sales if the value of building permits is $700,000?

A) $458,887.14 B) $5.66 C) $2,137.96 D) $3.33 E) $22,060.33 Answer: A L.O.: 1, 3

19 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 20: Multiple Regression Short Answer - Quiz A 1) In determining the best companies to work for, a number of variables are considered, including size, average annual pay, and turnover rate, etc. Moreover, employee surveys are conducted in order to assess aspects of the organization's culture, such as trust and openness to change. In an attempt to determine what affects turnover rate, a sample of 33 companies was randomly selected and data collected on the average annual bonus and turnover rate (%) for 2015. In addition, a questionnaire was administered to the employees of each company to arrive at a trust index (measured on a scale of 0-100). Below are the multiple regression results.

a. Write out the estimated regression equation. b. Is the regression equation significant overall? Explain. c. How much of the variability in Turnover Rate is explained by the regression equation? d. State the hypotheses for testing the regression coefficient of Trust Index. Based on the results, what do you conclude at α = .01? e. State the hypotheses for testing the regression coefficient of Average Annual Bonus. Based on the results, what do you conclude at α = .01? f. Predict the turnover rate for a company with a trust index score of 70 and an average annual bonus of $6500. g. Comment on whether the assumptions/conditions for multiple regression are satisfied based on the plots shown below.

1 .

2 .

Answer: a. The regression equation is Turnover Rate = 12.1005 - 0.07149 Trust Index - 0.0007216 Average Annual Bonus b. From the given output: F = 131.36/2.24 = 58.64 P-value < 0.001 The F-statistic and associated P-value lead us to conclude that the regression is significant overall. c. According to the output: R2 = 79.6%.

3 .

d. Let Trust Index be the first variable.

H0: β1 = 0 vs. HA: β1 ≠ 0 Test statistic: t = - 3.64 The P-value associated with the Trust Index is 0.001. Therefore, for companies with the same average annual bonuses, there is very strong evidence that trust indices are associated with turnover rate. e. Let Annual Bonus be the second variable.

H0 : β2 = 0 vs. HA : β2 ≠ 0 Test statistic: t = - 4.87 The P-value associated with Average Annual Bonus is less than 0.001. Therefore, for companies with the same trust indices, there is very strong evidence that average annual bonuses are associated with turnover rate. f. 2.41% g. Linearity: The scatterplots of turnover rate versus trust index and turnover rate versus average annual bonus appear straight enough.

Independence: We can regard the turnover rates as being independent of one another.

Randomization: The companies in the sample were selected randomly.

Equal Spread: The plot of residuals versus predicted values does not appear to widen for higher predicted values. It shows no patter. So, it seems reasonable to assume equal variance.

Normality: The histogram of residuals is somewhat skewed, but unimodal. It seems that the nearly normal condition is satisfied.

L.O.: 1, 2

4 .

Short Answer - Quiz B 1) What affects 4K Ultra HD Smart TV sales? TVs are sold through a variety of outlets such as large electronics stores, department stores, large discount chains and online. Sales figures (number of units) for the Samsung 7 Series were obtained for last quarter from a sample of 30 different stores. Also collected were data on the selling price and amount spent on advertising the Samsung 7 Series (as a percentage of total advertising expenditure in the previous quarter) at each store. Below are the multiple regression results.

a. Write out the estimated regression equation. b. Is the regression equation significant overall? Explain. c. How much of the variability in Sales is explained by the regression equation? d. State the hypotheses for testing the regression coefficient of Price. Based on the results, what do you conclude at α = .05? e. State the hypotheses for testing the regression coefficient of Advertising Expenditure. Based on the results, what do you conclude at α = .05? f. Predict the sales for a store that sells the Samsung 7 Series for $2199 and spends 10% of its advertising budget on the product. g. Comment on whether the conditions for multiple regression are satisfied based on the plots shown below.

5 .

6 .

Answer: a. The regression equation is Sales = 90.19 - 0.03055 Price + 3.0926 Advertising b. From the given output: F = 8238.7/112.5 = 73.23 P-value < 0.001 The F-statistic and associated P-value lead us to conclude that the regression is significant overall. c. According to the output: R2 = 84.4%

7 .

d. Let Price be the first variable.

H0 : β1 = 0 vs. HA : β1 ≠ 0 Test statistic: t = - 3.04 The P-value associated with Price is 0.005. Therefore, for stores with the same advertising expenditures, there is very strong evidence that price is associated with sales. e. Let Advertising be the second variable.

H0 : β2 = 0 vs. HA : β2 ≠ 0 Test statistic: t = 8.40 The P-value associated with Advertising expenditure is less than 0.001. Therefore, for stores with the same prices, there is very strong evidence that advertising expenditures are associated with sales. f. 53.94 ≈ 54 units g. Linearity: The scatterplots of sales versus price and sales versus advertising expenditure appear straight enough.

Independence: We can regard the sales figures as being independent of one another.

Randomization: We can assume that the stores in the sample were selected randomly.

Equal Variance: The plot of residuals versus predicted values does not show any pattern.

Also, the plot does not appear to widen for higher predicted values. However, there are a couple of outliers.

Normality: The normal probability plot does not indicate an extreme departure from normality, but there is bend. Thus, construction of the histogram is recommended.

L.O.: 1, 2

8 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: In determining the best companies to work for, a number of variables are considered, including size, average annual pay, and turnover rate, etc. Moreover, employee surveys are conducted in order to assess aspects of the organization's culture, such as trust and openness to change. In an attempt to determine what affects turnover rate, a sample of 33 companies was randomly selected and data collected on the average annual bonus and turnover rate (%) for 2015. In addition, a questionnaire was administered to the employees of each company to arrive at a trust index (measured on a scale of 0-100). Below are the multiple regression results.

1) How much of the variability in Turnover Rate is explained by the estimated multiple regression model?

A) 2.24% B) 79.6% C) 12.1% D) 95.4% E) 63.36%.

Answer: B L.O.: 2 2) The calculated F-statistic to determine the overall significance of the estimated multiple regression model is A) 58.64.

B) 1.497.

C) 131.36.

D) 78.3.

E) 2.24.

Answer: A L.O.: 2 9 .

3) The correct null hypotheses for testing the regression coefficient of Trust Index (suppose that it is the first variable) A) β1 ≠ 0.

B) β1 > 0.

C) β1 = 0.

D) β1 < 0.

E) The regression equation is significant.

Answer: C L.O.: 2 4) At α = 0.01, we can conclude that A) the multiple regression model is not significant overall.

B) Trust Index is not significant independent variable in explaining turnover rate.

C) there is no evidence that Average Annual Bonus is a significant independent variable in explaining turnover rate.

D) the multiple regression model is not significant overall because only Trust Index is a significant independent variable in explaining turnover rate.

E) the multiple regression model is significant overall. Also, both variables (Trust Index and Average Annual Bonus) are significant in explaining turnover rate.

Answer: E L.O.: 2 5) Based on the estimated multiple regression model, a company having a trust index score of 70 and an average annual bonus of $6500 has a predicted turnover rate of A) 3.50%.

B) 4.21%.

C) 1.90%.

D) 2.41%.

E) 4.52%.

Answer: D L.O.: 2

10 .

Consider the following to answer the question(s) below: What affects 4K Ultra HD Smart TV sales? TVs are sold through a variety of outlets. Sales figures (number of units) for the Samsung 7 Series were obtained for last quarter from a sample of 30 different stores. Also collected were data on the selling price and amount spent on advertising the Samsung 7 Series (as a percentage of total advertising expenditure in the previous quarter) at each store. Below are the results.

6) The calculated F-statistic to determine the overall significance of the estimated multiple regression model is A) 10.61.

B) 73.23.

C) 112.5.

D) 3.60.

E) 8.40.

Answer: B L.O.: 2 7) The calculated t-statistic to determine if amount spent on advertising is a significant independent variable in explaining Samsung 7 Series sales is A) 3.60.

B) - 3.04.

C) 8.40.

D) 10.61.

E) 0.3680.

Answer: C L.O.: 2

11 .

8) Which of the following statements is true at α = .05?

A) The multiple regression model is not significant overall.

B) Price is not a significant independent variable in explaining Samsung 7 Series sales.

C) There is no evidence that Advertising is a significant independent variable in explaining Samsung 7 Series sales.

D) All we can say is that the multiple regression model is significant overall and only Price is a significant independent variable in explaining Samsung 7 Series sales.

E) We can say that the multiple regression model is significant overall. Also, both variables (Price and Advertising) are significant in explaining Samsung 7 Series sales.

Answer: E L.O.: 2 9) Using the estimated multiple regression model, the number of units sold on average at a store that sells the Samsung 7 Series for $2199 and spends 10% of its advertising budget on the product is A) 53.94 ≈ 54 units.

B) 120 units.

C) 66.94 ≈ 67 units.

D) 90.34 ≈ 90 units.

E) 689 units.

Answer: A L.O.: 2

12 .

10) Below is the plot of residuals versus predicted values for this estimated multiple regression model. What does the residual plot suggest?

A) The Linearity condition is not satisfied.

B) There is an extreme departure from normality.

C) The variance changes a lot.

D) There are a couple of possible outliers.

E) The plot thickens from left to right.

Answer: D L.O.: 1

13 .

Consider the following to answer the question(s) below: National birth rates (births per 1,000) may be influenced by the average national life expectancy in years and the national literacy rate (% of population that can read and write). Data for 49 countries were obtained and the regression results follow.

11) The calculated F-statistic to determine the overall significance of the estimated multiple regression model is A) 61.07.

B) 16.58.

C) 5.23.

D) 5.47.

E) 0.8574.

Answer: A L.O.: 2 12) The calculated t-statistic to determine if Literacy Rate is a significant independent variable in explaining birth rates is A) - 5.48.

B) 5.48.

C) 5.23.

D) 61.07.

E) - 5.23.

Answer: A L.O.: 2 14 .

13) Which of the following statements best describes this model (using α = 0 .05)?

A) The regression model is significant overall, and both Life Expectancy and Literacy Rate are significant independent variables in explaining the National Birth Rate.

B) The regression model is not significant overall.

C) Life Expectancy is not a significant independent variable in explaining the National Birth Rate.

D) There is no evidence that Literacy Rate is a significant independent variable in explaining the National Birth Rate.

E) The regression model is not significant overall because only Life Expectancy is significant independent variable in explaining the National Birth Rate.

Answer: A L.O.: 2 14) How much of the variation in the National Birth Rate can be explained by the regression model?

A) 73.51% B) 0.7231 % C) 0.7351% D) 61.07% E) 85.74% Answer: A L.O.: 2 15) If an additional explanatory variable was added to the model, what would happen to R2?

A) It would stay the same or increase.

B) It would always decrease.

C) It can decrease.

D) It can become negative.

E) If the coefficient of the additional variable is negative, R2 dramatically decreases.

Answer: A L.O.: 2 16) What would the predicted National Birth Rate be in a country with a Life Expectancy of 60 years and a Literacy Rate of 75?

A) 26.76 B) 104.33 C) 35.54 D) 55.84 E) 63.52 Answer: A L.O.: 2

15 .

17) Suppose that Life Expectancy is the first variable and Literacy Rate is the second variable.

The correct alternative hypothesis for the overall significance for this model is A) HA: at least one β ≠ 0.

B) HA: β1 = β2 = 0.

C) HA: β1 = 0.

D) HA: β2 = 0.

E) HA: all β ≠ 0.

Answer: A L.O.: 2 Consider the following to answer the question(s) below: A regression was performed to predict the Selling Price of a yacht in thousands of dollars based on the number of Rooms it had, its Age (years), and its Length (feet). The R2 is 68.45%. The equation is given here.

Selling Price = 120.51 + 7.46 Rooms - 1.78 Age + 2.83 Length 18) Which of the following statements is true?

A) For a given Age and Length, every extra room is associated with an additional $7,460 in the average selling price of the yacht.

B) The model fits 68.45% of the data.

C) Every additional foot of Length causes the selling price of the yacht to increase 2.83 times.

D) The price of a yacht decreases 1.78 times with every year it ages.

E) The selling price of an individual yacht cannot be predicted with this model.

Answer: A L.O.: 2 19) What does the coefficient of Rooms mean in the context of the regression model?

A) The average selling price will increase by $7,460 for every additional room for yachts with the same length and age.

B) The average selling price will increase 7.46 times for every additional room.

C) With every additional room the selling price will increase by 7.46%, all other things being equal.

D) There is always a decrease in selling price of $7,460 for every additional room on a yacht.

E) The average selling price will increase by $120.51 for every additional room for yachts with the same length and age.

Answer: A L.O.: 2

16 .

20) If a yacht has 5 rooms, is 4 years old, and is 60 feet long, what would the model predict the selling price to be?

A) $320,490 B) $250,960 C) $332,650 D) $199,340 E) $301,490 Answer: A L.O.: 2

17 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 21: Building Multiple Regression Models Short Answer - Quiz A 1) A sample of 30 companies was randomly selected for a study investigating what factors affect the size of company bonuses. Data were collected on the number of employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). Below are the multiple regression results.

a. Write out the estimated regression equation. b. Are all of the independent variables significant in this regression equation (using α = 0 .05)?

Explain. c. Interpret the coefficient of the Union. d. Based on the scatterplot below, do you think using Union as an indicator variable in this model is appropriate? Explain.

1 .

e. An alternative multiple regression model is fit to these data and the results are shown below.

Which model is better? Explain.

f. Using the better model, predict the annual average bonus for a company with 7500 employees that are not unionized.

Answer: a. The regression equation is Average Annual Bonus = 347.9 + 0.6547 Employees + 1259.5 Union. b. Yes, the P-value associated with each t-statistic for the regression coefficients of Employees and Union is less than 0.05, therefore in each case we reject the null hypothesis. We can conclude that the regression coefficients associated with these two independent variables are significantly different from zero. c. The estimated regression coefficient for Union is 1259.5. This means that the annual average bonus is $1259.5 more for unionized companies compared to non-unionized companies of the same size (same number of employees). d. The scatterplot shows that if we consider unionized and non-unionized companies separately, we see two different slopes (the lines are not parallel). This indicates that an interaction term Employees×Union rather than the indicator variable Union might be more appropriate. e. This second model is better. All independent variables (including the interaction term) are significant. It has a higher R2 and R2Adj than the first model. It has a smaller S than the first model as well. f. The predicted value is $5413.

L.O.: 1, 3

2 .

Short Answer - Quiz B 1) A sample of firms was selected from the high tech industry (Industry = 1) and the financial services sector (Industry = 0). Data were collected on the following variables: turnover rate, job growth, number of employees, and innovative index (higher scores indicate a more innovative and creative organizational culture). Below are the multiple regression results.

a. Write out the estimated regression equation. b. Are all of the independent variables significant in this regression equation (using α = 0.05)?

Explain. c. Interpret the coefficient of the Industry. d. An alternative multiple regression model is fit to these data and the results are shown below.

Which model is better? Explain.

3 .

e. Based on the scatterplot below, is it appropriate to use Industry as an indicator variable in this regression model? Explain.

f. Using the better model, predict turnover rate for a firm in the financial services sector with 1000 employees, an innovative index of 50 and 2% job growth rate.

Answer: a. The regression equation is Turnover Rate = 9.2439 -0.02402 Innovative Index - 0.50127 Job Growth + 0.0006144 Employees 2.8329 Industry b. No. The P-values associated with the t-statistic for the regression coefficients of Innovative Index and Employees are greater than 0.05, therefore in each case we fail to reject the null hypothesis. We can conclude that the regression coefficients associated with these two independent variables (Innovative Index and Employees) are not significantly different from zero. c. The regression coefficient indicates that the turnover rate will, on average, be 2.8329% less for a firm from the high tech industry compared to the financial services sector with the same innovative index score, job growth and number of employees. d. The second model is better because it is simpler, having two instead of four independent variables; both of these independent variables are significant, and there is no decrease in explanatory power (the R2Adj is about the same). e. Yes. The scatterplot shows that if we consider high tech and financial services firms separately, we see two parallel lines (the slopes are the same). f. The predicted turnover rate is 7.69%.

L.O.: 1, 3

4 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: A sample of 30 companies was randomly selected for a study investigating what factors affect the size of company bonuses. Data were collected on the number of employees at the company and whether or not the employees were unionized (1 = yes, 0 = no). The following multiple regression model was fit to the data.

1) The estimated regression model is A) Average Annual Bonus = 347.9 + 0.6547 Employees + 1259.5 Union.

B) Average Annual Bonus = 872.2 + 0.1105 Employees + 605.8 Union.

C) Average Annual Bonus = 0.40 + 8.92 Employees + 2.08 Union.

D) Average Annual Bonus = 0.6547 Employees + 1259.5 Union.

E) Average Annual Bonus = 347.9 + 872.2 Employees + 0.40 Union.

Answer: A L.O.: 1 2) Which of the following statements is not true at α = 0.05?

A) The multiple regression model is overall significant in explaining the size of company bonuses.

B) The number of employees at the company is a significant variable in explaining the size of company bonuses.

C) Whether or not the employees are unionized is a significant variable in explaining the size of company bonuses.

D) The regression model accounts for 62.4% of the variation in average annual bonus.

E) The regression model only accounts for 59.6% of the variation in average annual bonus because Employees is not significant variable.

Answer: E L.O.: 1, 3

5 .

3) The correct interpretation of the regression coefficient of Union is A) that the annual average bonus is $605.80 less for unionized companies compared to nonunionized companies of the same size (same number of employees).

B) that the annual average bonus is $605.80 more for unionized companies compared to nonunionized companies of the same size (same number of employees).

C) that the annual average bonus is $1259.50 less for unionized companies compared to nonunionized companies of the same size (same number of employees).

D) that the annual average bonus is $1259.50 more for unionized companies compared to nonunionized companies of the same size (same number of employees).

E) that the annual average bonus is $208 more for unionized companies compared to nonunionized companies of the same size (same number of employees).

Answer: D L.O.: 1 4) What does the scatterplot of these data (shown below) suggest?

A) Using the interaction term Employees×Union rather than the indicator variable Union in the model might be more appropriate.

B) The intersection of the line confirms that using Union as an indicator variable in this model is appropriate.

C) The intersection of the line suggests that Union should not be included in the model as a variable.

D) The intersection of the line suggests that Employees should not be included in the model as a variable.

E) Using the interaction term Employees×Union in the model is definitely inappropriate.

Answer: A L.O.: 1

6 .

Consider the following to answer the question(s) below: A sample of firms was selected from the high tech industry (Industry = 1) and the financial services sector (Industry = 0). Data were collected on the following variables: turnover rate, job growth, number of employees, and innovative index (higher scores indicate a more innovative and creative organizational culture). Below are the multiple regression results.

5) Which statement is true about the estimated multiple regression model?

A) Turnover rate is the indicator variable.

B) Innovative index is the indicator variable.

C) Test results indicate that the model is overall significant in explaining Turnover rate.

D) F test results indicate that the model is not significant in explaining Turnover rate.

E) The coefficients associated with Job Growth and Industry variables are not significantly different from zero.

Answer: C L.O.: 1 6) Which of the following independent variables are significant in this regression equation at α = 0.05?

A) Only Innovative Index B) Only Employees C) Both Innovative Index and Employees D) Only Job Growth E) Both Job Growth and Industry Answer: E L.O.: 1

7 .

7) How much of the variability in Turnover Rate is explained by the multiple regression model?

A) 73.9% B) 95.6% C) 9.3% D) 50.62% E) 91.39% Answer: B L.O.: 1 Consider the following to answer the question(s) below: An alternative multiple regression model is fit to the data on the sample of firms selected from the high tech industry (Industry = 1) and the financial services sector (Industry = 0). The results are shown below.

8) Which of the following statements is true?

A) All of the independent variables in this model are significant.

B) The dependent variable is the type of industry.

C) This model does not include an indicator variable.

D) Job Growth is a significant variable, but Industry is not.

E) The regression model is not overall significant.

Answer: A L.O.: 1, 3

8 .

9) What does the scatterplot of these data (shown below) suggest?

A) Using Job Growth as an indicator variable in this model is appropriate.

B) Using the interaction term Job Growth×Industry in the model is appropriate.

C) Using Industry as an indicator variable in this model is appropriate.

D) Job Growth should not be included in the model as a variable.

E) Using Industry as an indicator variable in this model is definitely not appropriate.

Answer: C L.O.: 1 10) Using this model, the predicted turnover rate for a firm in the financial services sector with 1000 employees, an innovativeness index of 50, and 2% job growth rate is A) 8.25%.

B) 7.69%.

C) 4.56%.

D) 6.19%.

E) 37.41%.

Answer: B L.O.: 1

9 .

11) Which of the following statements is true?

A) The method used in regression analysis for incorporating a categorical variable into the model is by organizing the categorical variable into one or more indicator variables.

B) An indicator variable is a dependent variable whose value is set at either zero or one.

C) There are four possible responses listed for marital status. Based on this, four indicator variables will need to be created and incorporated into the regression model.

D) On a survey there is a question that asks whether someone lives in a house, apartment, or condominium. These three responses could be coded in an indicator variable using values of 0, 1, and 2.

E) The scatterplot can show whether using an indicator variable in the model is appropriate.

However, it gives no clue about using an interaction term.

Answer: A L.O.: 1 12) Which of the following statements about multiple regression model building methods is true?

A) There is no simple definition of the "best" model in multiple regression analysis.

B) Stepwise selection will always find the best regression model.

C) Both stepwise and best subsets methods check assumptions and conditions.

D) The best subsets method will involve trying fewer different regression models than stepwise regression.

E) There is only one criterion (value of R2) that leads to the best model.

Answer: A L.O.: 3 13) Which of the following statements describing the consequences of collinearity in a model is not true?

A) The value of the Variance Inflation Factor will be high.

B) An estimated coefficient may have an unexpected sign or size being large or small.

C) The F-statistic for the model may indicate overall significance, but most or all of the individual coefficients have t-statistics showing insignificance.

D) Collinearity occurs when two or more predictor variables are correlated.

E) When a predictor is collinear with the other predictors in the model, the standard error of its coefficient is always small and t-statistic always large.

Answer: E L.O.: 3

10 .

Consider the following to answer the question(s) below: A regression equation that predicts the price of homes in thousands of dollars is = 24.6 + 0.055x1, where x1 is a variable that represents the assessed value of the house and x2 is an indicator variable that represents whether the house is on a busy street (1 = yes, 0 = no).

14) Based on this information, which of the following statements is true?

A) On average, homes with the same assessed value that are on busy streets are worth $3600 less than homes that are not on busy streets.

B) For a given assessed value, on average, homes that are on busy streets are worth $360 less than homes that are not on busy streets.

C) For a given assessed value, on average, homes that are on busy streets are worth $3600 more than homes that are not on busy streets.

D) On average, homes with the same assessed value that are on busy streets are worth $360 more than homes that are not on busy streets.

E) For a given assessed value, on average, homes that are on busy streets are worth 24.6 - 3.6 = $19000 less than homes that are not on busy streets.

Answer: A L.O.: 1 15) The regression model mentioned above resulted in a high R2 and large F, but individual tstatistics were not significant. Which of the following statements is true?

A) We would suspect homoscedasticity in the model.

B) We would suspect autocorrelation in the model.

C) We would suspect collinearity in the model.

D) We would suspect that the model contains influential points.

E) We would suspect that the model contains high-leverage points.

Answer: C L.O.: 1, 2 16) Trying to estimate possible collinearity in the regression model we should use A) Leverage Index.

B) Variance Inflation Factor.

C) Determination Coefficient.

D) Standardized Residual.

E) Cook's Distance.

Answer: B L.O.: 3

11 .

17) Which of the following statements does not describe a point with high leverage?

A) A point may exert high leverage because it has an unusual combination of predictor values.

B) A point with high leverage is easy to see in a regression of a single predictor and response.

C) A point of high leverage may not influence the regression slope.

D) A point with zero leverage has no effect on the regression slope.

E) The leverage can be negative.

Answer: E L.O.: 2 Consider the following to answer the question(s) below: A Toronto accounting firm estimated a model to explain variation in client profitability. The dependent variable is client net profits and the predictor variables include the hours spent working on the client and indicator variables to denote the type of client-manufacturing, service, or government. The indicator variables have a value of one if the client is the type described. The following are the model results.

18) If the number of hours spent on a client is 100, and the client is in the Service industry, what is the predicted net profit?

A) The predicted net profit is $3,569.55.

B) The predicted net profit is $1,869.81.

C) The predicted net profit is $1,283.55.

D) The predicted net profit is $4,172.08.

E) The predicted net profit is $3,585.82.

Answer: A L.O.: 1

12 .

19) At α = 0.05, which of the following statements is not correct?

A) The overall regression model is significant in explaining net profits.

B) The number of hours spent on a client is not significant in explaining variation in client profitability.

C) The indicator variables for client type are significant in explaining variation in client profitability.

D) The regression model explains about 70% of the variation in client profitability.

E) The number of hours spent on a client is significant in explaining variation in client profitability.

Answer: E L.O.: 1 20) The editors of a national automotive magazine recently studied 30 different automobiles sold in the Canada with the intent of seeing whether they could develop a multiple regression model to explain the variation in highway fuel consumption. A number of different independent variables were collected. Included in these were two variables described as follows: Car Type (categorical) 1 = Four door sedan 2 = Luxury car 3 = Compact truck 4 = Full size truck 5 = Sports car

Whether Car has ABS Brakes (categorical) 1 = All wheel ABS 2 = Rear wheel ABS 3 = No ABS

If these two variables are to be included in a regression model, how many additional indicator variables will be needed?

A) 6 B) 8 C) 2 D) 4 E) 5 Answer: A L.O.: 1

13 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 22: Time Series Analysis Short Answer - Quiz A 1) A large automobile parts supplier keeps track of the demand for a particular part needed by its customers, automobile manufacturers. The time series plot below shows monthly demand for this part (in thousands) for a five year period.

a. Identify the dominant time series component(s) in the data. b. Suppose that the single exponential smoothing (SES) model was applied to these data. Below are time series graphs showing SES results using two different smoothing constants (α = 0.2 and α = 0.8). In which application is a larger value of α used?

1 .

i.

ii.

c. What forecasting method may be a better choice than SES for these data? Explain.

Answer: a. Seasonal and trend components b. A curve computed using the lager α follows the original series closely. The SES model in ii. has the larger value of α. c. A model that incorporates seasonality, like a seasonal regression model, may be a better choice. Regression would also allow capture of trend. The exponential smoothing forecasts will always lag behind the actual values when seasonality / trend are present in the series.

L.O.: 2, 3 2 .

2) Annual estimates of the population in the age group 65+ in a mid-sized city from 2005 (t = 1) onward are shown in the time series graph below.

a. Identify the dominant time series component(s) in the data. b. Below are the results from fitting a linear trend model to the data. Use this model to estimate the 65+ population in this city for 2014 (t = 10).

Fitted Trend Equation , = 145,703 + 801t c. Below are the results from fitting a quadratic trend model to the data. Use this model to estimate the 65+ population in this city for 2014 (t = 10).

Fitted Trend Equation , = 148,187 - 554t + 135.5t2 d. The actual population estimate for 2014 is 157,218. Which model does better? Why? Answer: a. Trend component b. 153,713 c. 156,197 d. The quadratic trend model provided a better forecast. It captures the underlying curvature in the trend.

L.O.: 2, 5

3 .

3) The following table shows actual sales values and forecasts provided by two different methods.

Sales (1000's Units) Method 1 Forecasts Method 2 Forecasts 58 56.8065 54.0577 55 59.2452 63.0231 68 58.9961 60.0092 45 58.1969 57.0037 60 60.1575 63.6015 72 57.1260 52.4406 a. Calculate the MAD for each method. b. Calculate the MSE for each method. c. Which method forecasts better?

Answer: a. MAD (Method 1) = 7.112 MAD (Method 2) = 9.187 b. MSE (Method 1) = 82.656 MSE (Method 2) = 113.899 c. Method 1 is better because it has a lower MAD and lower MSE. L.O.: 4

4 .

4) Monthly closing stock prices, adjusted for dividends, were obtained for Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month).

The time series graph of these data is shown below.

a. Below are the results of fitting a third-order autoregressive model, AR (3). Write out the model. Are the second and third lagged values significant? Explain.

Final Estimates of Parameters Type Coef Lag 1 0.9247 Lag 2 0.0429 Lag 3 -0.0764 Constant 8.362

SE Coef T P 0.1898 4.87 0.000 0.2603 0.16 0.870 0.1959 -0.39 0.699 1.223 6.84 0.000

b. Below are the results of fitting a first-order autoregressive model, AR (1). Write out the model. Is this model typical for stock price data? Explain.

5 .

Final Estimates of Parameters Type Coef SE Coef T P Lag 1 0.9098 0.0969 9.39 0.000 Constant 6.835 1.207 5.67 0.000 Answer: Let Boeing stock price be dependent variable y. a. = 8.362 + 0.9247yt-1 + 0.0429yt-2 - 0.0764yt-3 The second and third lagged values are not significant, as can be seen by their relatively large P-values (0.870 and 0.699, respectively). b. = 6.835 + 0.9098yt-1 With a relatively large Lag 1 coefficient, this is similar to what we find with stock price data.

However, the values are monthly and not daily, so they are not as volatile and less likely to be a random walk. In addition, the estimated intercept is not close to zero.

L.O.: 3

6 .

Short Answer - Quiz B 1) Annual estimates of the population in a certain city from 2004 (t = 1) onward are shown in the time series graph below.

a. Identify the dominant time series component(s) in the data. b. Below are the results from fitting a linear trend model to the data. Use this model to estimate the population in this city for 2014 (t = 11).

Fitted Trend Equation , = 57,206 + 528t c. Below are the results from fitting a quadratic trend model to the data. Use this model to estimate the population in this city for 2014 (t = 11).

Fitted Trend Equation , = 58,159 + 52t + 43.3t2 d. The actual population estimate for 2014 is 63,828. Which model does better? Why? Answer: a. Trend component b. 63,014 c. 63,970 d. The quadratic trend model provided a better forecast. It captures the underlying curvature in the trend.

L.O.: 2, 5

7 .

2) Quarterly sales data (in $10,000) for a small company specializing in green cleaning products are shown in the time series graph below.

A seasonal regression model was fit to these data and the results are shown below.

The regression equation is Sales = 89.06 + 1.37t - 23.37Q2 - 23.91Q3 + 27.88Q4.

8 .

a. Is the seasonal regression model significant overall? Explain. b. Interpret the regression coefficients in this model. c. Use this model to provide forecasts for each of the four quarters of the next year.

Answer: a. Yes, as indicated by the F-statistic = 234.69 and associated P-value < 0.001. In addition, the t-statistics and associated P-values indicate that all dummy variables representing quarters are significant. b. The values of the coefficients indicate that sales are on average lower in the second and third quarters, and the highest in the fourth quarter for any given year. c. Q1 Sales = $1,233,100 Q2 Sales = $1,013,100 Q3 Sales = $1,021,400 Q4 Sales = $1,553,000 L.O.: 5

9 .

3) Daily closing stock prices for Kyopera Corporation were obtained from August 3, 2016 through August 23, 2016 and appear in the time series graph below.

a. Identify the dominant time series component(s) in the data. b. The method of moving averages was applied to these data. Below are time series graphs showing moving average results using two different values of L. In which application is a larger value of L used? i.

10 .

ii.

c. Suppose that the single exponential smoothing (SES) model was applied to these data. Below are time series graphs showing SES results using two different smoothing constants (α = 0.2 and α = 0.8). In which application is a larger value of α used? i.

11 .

ii.

Answer: a. Irregular component is dominant. The time series looks like random walk. b. The lager value of L is used in application ii. as the moving average with the longer length is smoother. c. The curve computed using the smaller α is smoother, and the curve computed with the lager α follows the original series closely. Thus, in application i. α = 0.2 was used, and the plot ii. was computed with α = 0.8.

L.O.: 2, 3 4) The table below shows the closing daily stock prices for Kyopera Corporation for September 2 through September 5, 2016, as well as 4-day moving average, 2-day moving average and naïve forecasts. Calculate the MAD and MSE for each of the three types of forecasts. Which is the best?

Actual Price 81.37 81.79 80.12 79.76

4-Period MA 82.68 82.59 82.46 81.67

2-Period MA 83.34 82.39 81.58 80.96

Answer: MAD (4-Period MA) = 1.59 MAD (2-Period MA) = 1.31 MAD (Naïve) = 1.12 MSE (4-Period MA) = 2.87 MSE (2-Period MA) = 1.95 MSE (Naïve) = 1.81 The Naïve method with the smallest MAD and MSE is the best.

L.O.: 3 12 .

Naïve 83.41 81.37 81.79 80.12

Multiple Choice - Quiz C 1) A large automobile parts supplier keeps track of the demand for a particular part needed by its customers, automobile manufacturers. The time series plot below shows monthly demand for this part (in thousands) for a five-year period. The dominant component(s) in this time series is(are)

A) cyclical.

B) irregular .

C) seasonal and trend.

D) cyclical and irregular.

E) No time series component is dominant. The time series is random walk.

Answer: C L.O.: 2

13 .

Consider the following to answer the question(s) below: Annual estimates of the population in a certain city from 2005 (t = 1) onward are shown in the time series graph below.

2) The dominant component in this time series is A) cyclical.

B) irregular.

C) seasonal.

D) trend.

E) No time series component is dominant. The time series is random walk.

Answer: D L.O.: 2 3) The forecasting method that will most likely be best for this time series is A) single exponential smoothing with α = 0.1.

B) quadratic trend.

C) moving average with L = 2.

D) naïve.

E) linear trend.

Answer: B L.O.: 3, 5

14 .

Consider the following to answer the question(s) below: The following table shows actual sales values and forecasts.

Sales (1000's Units) 58 55 68 45 60 72

Forecasts 56.8065 59.2452 58.9961 58.1969 60.1575 57.1260

4) The MAD for the forecasting method used is A) 7.112.

B) 9.187.

C) 82.656.

D) 113.899.

E) 8.534.

Answer: A L.O.: 4 5) The MSE for the forecasting method used is A) 7.112.

B) 9.187.

C) 82.656.

D) 113.899.

E) 99.187.

Answer: C L.O.: 4

15 .

Consider the following to answer the question(s) below: Quarterly sales data (in $10,000) for a small company specializing in green cleaning products are shown in the time series graph below.

A seasonal regression model was fit to these data and the results are shown below.

The regression equation is Sales = 89.06 + 1.37t - 23.37Q2 - 23.91Q3 + 27.88Q4.

16 .

6) Which of the following is not true?

A) The seasonal regression model is significant in explaining sales as indicated by the F-statistic and associated P-value.

B) The seasonal regression model explains 98.02% of the variation in sales.

C) The t-statistics and associated P-values indicate that all dummy variables representing quarters are significant.

D) Q1 is the quarter without dummy variable. The next year sales in Q1 is predicted to be $1,233,100.

E) The seasonal regression model is not significant overall as only Q1 is significant.

Answer: E L.O.: 5

17 .

7) The regression coefficients in the seasonal regression model indicate that A) sales are, on average, lower in the first, second and third quarters compared with the fourth quarter.

B) sales are, on average, lowest in the fourth quarter.

C) sales are, on average, higher in the first, second and third quarters compared with the fourth quarter.

D) sales are, on average, lowest in the first quarter.

E) sales are, on average, lowest in the third quarter.

Answer: A L.O.: 5 8) Annual estimates of the population in the age group 65+ in a certain city from 2005 (t = 1) onward are used to estimate the following quadratic trend model: , = 148,187 - 554t + 135.5t2 Using this model, the estimate for 2014 is A) 157,218.

B) 156,197.

C) 153,713.

D) 161,312.

E) 158,489.

Answer: B L.O.: 5 Consider the following to answer the question(s) below: A third-order autoregressive model, AR (3) was fit to monthly closing stock prices, adjusted for dividends, of Boeing Corporation from January 2006 through August 2008 (closing price on the first trading day of the month). The results are as follows: Final Estimates of Parameters Type Coef Lag 1 0.9247 Lag 2 0.0429 Lag 3 -0.0764 Constant 8.362

SE Coef T P 0.1898 4.87 0.000 0.2603 0.16 0.870 0.1959 -0.39 0.699 1.223 6.84 0.000

18 .

9) Let Boeing stock price be dependent variable y. The estimated model is A)

= 1.223 + 0.1898yt-1 + 0.2603yt-2 + 0.1959yt-3.

B)

= 8.362 - 0.0764yt-1 + 0.0429yt-2 + 0.9247yt-3.

C)

= 1.223 + 0.1959yt-1 + 0.2603yt-2 + 0.1898yt-3.

D)

= 8.362 + 0.9247yt-1 + 0.0429yt-2 - 0.0764yt-3.

E) = 0.9247yt-1 + 0.2603yt-2 - 0.39yt-3.

Answer: D L.O.: 3 10) Which of the following statements is true?

A) At α = 0.05, the first lagged variable is significant.

B) At α = 0.05, the second lagged variable is significant.

C) At α = 0.05, the third lagged variable is significant.

D) At α = 0.05, the second lagged variable is significant and at α = 0.05, the third lagged variable is significant.

E) At α = 0.05, the first lagged variable is not significant.

Answer: A L.O.: 3 11) Which of the following is true about index numbers? Index numbers are A) used to make a relative comparison of different time periods.

B) used to measure the trend component.

C) used to measure the seasonal component.

D) used to measure the cyclical component.

E) used to measure the irregular component.

Answer: A L.O.: 1 12) Assume that the year 2000 is used as the index base period and that sales were $12 million in the year 2000. If sales were $18 million in the year 2006, the simple index number for the year 2006 is A) 150.0.

B) 15.0.

C) 0.667.

D) 6 million.

E) 66.67.

Answer: A L.O.: 1

19 .

13) A company has recorded annual sales (in $thousands) for the past 14 years and found the following linear trend model: = 5.23 + 144.60 t.

This means that A) on average, sales are increasing by $144.6K per year.

B) on average, sales are increasing by $5.23K per year.

C) there is a seasonal component in the data.

D) sales in year one were $5.23K. E) there is a cyclical component in the data.

Answer: A L.O.: 5 14) Which of the following statement is true about statistical measures used to estimate and report forecast error?

A) MSE (mean square error) is in the same units as the data.

B) MAD (mean absolute deviation) can be negative.

C) If the measurements are rescaled, MAD won't change.

D) Forecast errors cannot be negative.

E) If you choose to rescale measurements, both MASE and MAD will change, but MAPE will remain the same.

Answer: E L.O.: 4

20 .

Consider the following to answer the question(s) below: A company has developed a linear trend model to forecast monthly sales. The following data show the actual sales and the "fitted" sales for months 1-12.

Month 1 2 3 4 5 6 7 8 9 10 11 12

Sales 200 260 210 340 450 230 300 500 360 600 460 700

Predicted Sales 185 221 258 294 330 366 402 438 475 511 547 583

15) Based on these data, what is the mean square error (MSE) for the linear trend model?

A) 7976.167 B) 95714 C) 81.33 D) 976 E) 8701.273 Answer: A L.O.: 4 16) Based on these data, what is the mean absolute deviation (MAD) for the linear trend model?

A) 81.33 B) 7976.167 C) 976 D) 95714 E) 115 Answer: A L.O.: 4 17) Based on these data, what is the mean absolute percentage error (MAPE) for the linear trend model?

A) 22.79 B) 81.33 C) 2.73 D) 796 E) 0.22 Answer: A L.O.: 4 21 .

18) If you suspect that your trend forecasting model may have autocorrelated forecast errors, it is appropriate to compute A) the Durbin-Watson test statistic.

B) the MAD. C) the MSE. D) the MAPE. E) the correlation coefficient.

Answer: A L.O.: 3, 4 Consider the following to answer the question(s) below: The quarterly sales of all types of bicycles sold at a small sporting goods store in Charlottetown for the 16 quarters from January 2012 to December 2015 are depicted in the time series graph below.

22 .

19) Which of the following statements do not describe this data and model?

A) The seasonal component is the most dominant.

B) All of the coefficients are significant for α = 0.05.

C) The model is additive.

D) The regression model has both trend and seasonal components.

E) The regression model has no dummy variables.

Answer: E L.O.: 2, 5

23 .

20) A time series is shown below. Perform single exponential smoothing for this data set using α = 0.2. What is the value of the forecast for period 6?

Period 1 2 3 4 5 6

y 28 32 31 35 36 40

A) 31.5 B) 33.2 C) 36 D) 40 E) 30.4 Answer: A L.O.: 3

24 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 23: Decision Making and Risk Short Answer - Quiz A Consider the following to answer the question(s) below: A landowner is considering a community development project. Even though he realizes that the current market for housing is not very favourable, he believes that there will be an influx of retirees into the area within the next five years. He is trying to decide between two alternatives: (1) building detached homes in a planned retirement community or (2) building a smaller townhouse/condominium complex. Mortgage interest rates will affect his outcomes and the applicable payoff (in $ millions) table is shown below.

1) Using the maximin approach, which action should the land owner choose?

Answer: The land owner would should choose to build townhouses/condominiums.

L.O.: 1 2) Using the maximax approach, which action should the landowner choose?

Answer: The landowner would choose to build detached homes in a planned retirement community.

L.O.: 1 3) Suppose housing analysts predict that the probabilities for future mortgage interest rates going up, staying about the same, and going down are 0.35, 0.50 and 0.15, respectively. Compute the expected value for each action. Based on these results, which action should the landowner choose?

Answer: EV(Detached Homes) = (0.35)( -5) + (0.50)(6) + (0.15)(10) = $2.75 million EV(Townhouses/Condos) = (0.35)( -2.5) + (0.50)(4.5) + (0.15)(7.5) = $2.5 million The landowner should choose to build detached homes in a planned retirement community.

L.O.: 2 4) What is the expected value of perfect information?

Answer: $3.625 million - $2.75 million = $ 0.875 million or $875,000 L.O.: 2 5) Compute the standard deviation for each action.

1 .

Answer: SD(Detached Homes) = $5.85 million SD (Townhouses/Condos) = $3.81 million L.O.: 2

= =

6) Compute the Coefficient of Variation for each action. If the landowner is risk averse, would the CV approach lead to the same choice as the expected value approach? Explain.

Answer: CV(Detached Homes) = 5.85/2.75 = 2.13 CV(Townhouses/Condos) = 3.81/2.5 = 1.52 No; the CV is lower for building townhouses/condominiums so it is a less risky choice.

L.O.: 2 Short Answer - Quiz B Consider the following to answer the question(s) below: A farm owner who grows summer vegetables (e.g. tomatoes) must decide whether to employ additional pickers this season. If he does, he could hire either migrant workers or local teenagers who need summer employment. The migrant workers are more experienced, faster, but more expensive. Although the teenagers will work for less, they are not as experienced and tend to damage plants and produce. His profits, taking into account losses from unpicked perished or damaged produce, depend on whether there is a good or bad growing season. The payoffs are shown in the table below.

1) Using the maximin approach, which action should the farm owner choose?

Answer: The farm owner should choose to do no additional hiring.

L.O.: 1 2) Using the maximax approach, which action should the farm owner choose?

Answer: The farm owner should choose to hire migrant workers.

L.O.: 1

2 .

3) Suppose the farmer's almanac predicts the probability of a good growing season this year to be 0.75. Compute the expected value for each action. Based on these results, which action should the farm owner choose?

Answer: EV(Migrant) = (0.75)($75,000) + (0.25)($25,000) = $62,500 EV(Teenagers) = (0.75)($60,000) + (0.25)($30,000) = $52,500 EV(No Hiring) = (0.75)($50,000) + (0.25)($35,000) = $46,250 The farm owner should choose to hire migrant workers.

L.O.: 2 4) What is the expected value of perfect information?

Answer: $65,000 - $62,500 = $2500 L.O.: 2 5) Compute the standard deviation for each action.

Answer: SD(Migrant) =

= $21,651

SD(Teenagers) =

= $12,990

SD(No Hiring) = L.O.: 2

= $6,495

6) Compute the Coefficient of Variation for each action. If the farm owner is risk averse, would the CV approach lead to the same choice as the expected value approach? Explain.

Answer: CV(Migrant) = 21,651/62,500 = 0.346 CV(Teenagers) = 12,990/52,500 = 0.247 CV(No Hiring) = 6,495/46,250 = 0.140 No; the CV is lowest for not hiring any additional workers indicating that this is the least risky choice.

L.O.: 2

3 .

Multiple Choice - Quiz C Consider the following to answer the question(s) below: A landowner is considering a community development project. Even though he realizes that the current market for housing is not very favourable, he believes that there will be an influx of retirees into the area within the next five years. He is trying to decide between two alternatives: (1) building detached homes in a planned retirement community or (2) building a smaller townhouse/condominium complex. Mortgage interest rates will affect his outcomes and the applicable payoff (in $ millions) table is shown below.

1) According to the maximin approach, the landowner should A) build detached homes in a planned retirement community if interest rates go down.

B) build detached homes in a planned retirement community.

C) build detached homes in a planned retirement community if interest rates go up.

D) build townhouses/condominiums.

E) build detached homes in a planned retirement community if interest rates stay about the same.

Answer: D L.O.: 1 2) Suppose housing analysts predict that the probabilities for future mortgage interest rates going up, staying about the same, and going down are 0.35, 0.50 and 0.15, respectively. The expected value for building detached homes in a planned retirement community is A) $2.5 million.

B) $3.625 million.

C) $2.75 million.

D) $875,000.

E) $46.25 million.

Answer: C L.O.: 2

4 .

3) Based on the expected value approach, the landowner should A) build townhouses/condominiums if interest rates stay about the same.

B) build detached homes in a planned retirement community.

C) build townhouses/condominiums if interest rates go down.

D) build townhouses/condominiums.

E) build townhouses/condominiums if interest rates go up.

Answer: B L.O.: 2 4) The expected value of perfect information is A) $2.5 million.

B) $3.625 million.

C) $2.75 million.

D) $875,000.

E) $40.00 million.

Answer: D L.O.: 2 5) If the landowner is risk averse he would choose the action with the lowest Coefficient of Variation (CV). Which of the following is true?

A) The CV is lower for building townhouses and condominiums.

B) The CV is lower for building detached homes in a planned retirement community.

C) Even if the landowner is risk averse, the CV leads to the same choice as the expected value approach.

D) The CV is higher for building townhouses and condominiums, and even if the landowner is risk averse, the CV leads to the same choice as the expected value approach.

E) The CV is lower for building detached homes in a planned retirement community, and even if the landowner is risk averse, the CV leads to the same choice as the expected value approach.

Answer: A L.O.: 2

5 .

Consider the following to answer the question(s) below: A farm owner who grows summer vegetables (e.g. tomatoes) must decide whether to employ additional pickers this season. If he does, he could hire either migrant workers or local teenagers who need summer employment. The migrant workers are more experienced, faster, but more expensive. Although the teenagers will work for less, they are not as experienced and tend to damage plants and produce. His profits, taking into account losses from unpicked perished or damaged produce, depend on whether there is a good or bad growing season. The payoffs are shown in the table below.

6) According to the maximin approach, the farmer should A) hire migrant workers if the growing season is good.

B) hire teenagers.

C) not do any extra hiring.

D) hire migrant workers.

E) hire teenagers if the growing season is good.

Answer: C L.O.: 1 7) Suppose the Farmers' Almanac predicts the probability of a good growing season this year to be 0.75. What is the expected value of hiring teenagers?

A) $62,500 B) $52,500 C) $46,250 D) $12,990 E) $20,313 Answer: B L.O.: 2 8) Based on the expected value approach, the farmer should A) hire teenagers if the growing season is good.

B) hire teenagers.

C) not do any extra hiring.

D) hire migrant workers.

E) not do any extra hiring if the growing season is bad.

Answer: D L.O.: 2

6 .

9) The standard deviation for hiring migrant workers is A) $21,651.

B) $12,990.

C) $5,495.

D) $2,500.

E) $147.

Answer: A L.O.: 2 10) If the farmer is risk averse, he would A) hire migrant workers.

B) hire teenagers.

C) not do any extra hiring.

D) make the same decision as he would using the expected value approach.

E) give up farming.

Answer: C L.O.: 2 Consider the following to answer the question(s) below: A group is planning a fundraising concert. They must decide whether to hold the event indoors or out. The weather, specifically, whether or not it rains that day, will affect the amount raised by the event. The payoff table is shown below: Action Hold concert indoors Hold concert outdoors

Weather Conditions Rain No Rain $10,000 $15,000 -$10,000 35,000

11) According to the maximin approach, the group should A) hold the concert indoors.

B) hold the concert outdoors.

C) hold the concert outdoors if it does not rain.

D) hold the concert indoors if it rains.

E) hold the concert indoors if it does not rain.

Answer: A L.O.: 1 12) Historically the probability of rain on the day of the planned concert is 0.20. What is the expected value of an indoor concert?

A) $14,000 B) $26,000 C) $4,000 D) $2,000 E) $10,000 Answer: A L.O.: 2 7 .

13) What is the expected value of perfect information?

A) $4,000 B) $30,000 C) $14,000 D) $26,000 E) $10,000 Answer: A L.O.: 2 14) The standard deviation for an outdoor concert is A) $18,000.

B) $14,000.

C) $2,000.

D) $26,000.

E) $10,770.

Answer: A L.O.: 2 15) If the group is risk averse, they should A) plan to hold the event indoors.

B) plan to hold the event outdoors.

C) make the same decision as they would using the expected value approach.

D) decide not to hold the event at all.

E) plan to hold the event outdoors if it does not rain.

Answer: A L.O.: 2

8 .

Consider the following to answer the question(s) below: An investor has $10,000 to invest for one year. The choices for the placement of the funds include stocks, bonds, and mutual funds. The outcome of the investment however, will depend on the economic climate during the year. The table presents the payoffs in dollars for three possible economic scenarios. Forecasts suggest that the probability of a slowdown is 0.25, of no change is 0.50, and of growth is 0.25.

Action

Stocks Bonds Mutual Funds

Economic Climate Economic Economic No change Slowdown Growth -$2,000 $300 $2,000 $500 $600 $700 $300 $400 $1,000

16) The expected value of mutual funds is A) $525.

B) $150.

C) $600.

D) $1,150.

E) $925.

Answer: A L.O.: 2 17) According to the maximax approach, the investor would place his $10,000 in A) stocks.

B) bonds.

C) mutual funds.

D) mutual funds if there is economic growth.

E) bonds if there is no change in economic climate.

Answer: A L.O.: 1 18) The expected value with perfect information is A) $925.

B) $600.

C) $525.

D) $325.

E) $150.

Answer: A L.O.: 2

9 .

19) The expected value of perfect information is A) $325.

B) $400.

C) $775.

D) $925.

E) $600.

Answer: A L.O.: 2 20) The Return to Risk Ratio for bonds is A) 8.4854.

B) 70.71.

C) 0.1055.

D) 1.8935.

E) 0.1179.

Answer: A L.O.: 2

10 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Chapter 24: Quality Control Short Answer - Quiz A 1) Machine oil is used by clothing manufacturers to lubricate and protect sewing machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is 101 cP and the process standard deviation is 1.50 cP. a. What type of chart should be used to ensure the process remains in control? b. Determine the centreline and control limits for this chart. c. Suppose that customer specifications require viscosity of the machine oil to be 100 cP ± 4.5 cP (i.e., the LSL = 95.5 cP and the USL = 104.5 cP). Calculate and interpret both the Cp and Cpk indices.

Answer: a. Control chart for individual observations (run chart) b. The centreline is μ = 101 cP The control limits are μ ± 3σ or 101 ± 3(1.5): LCL = 96.5 cP and UCL = 105.5 cP c. Cp =

=

=

=1

To find Cpk you need to find minimum of CpL and CpU CpL =

=

CpU =

=

= 1.22 = 0.78

Cpk = 0.78 The Cp value shows that if the viscosity measurements are Normally distributed and the mean is centred, about 1 in 370 batches will have viscosity that falls outside the specification limits. The mean isn't centered between the two limits and the Cpk value of 0.78 is low. The company should work to centre the mean and/or lower the standard deviation of viscosity values.

L.O.: 1, 2

1 .

2) A company that manufactures health food snacks produces low sodium rice chips. To monitor the process for sodium levels, chips are selected periodically and the amount of sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and range in sodium content is determined. The average of the means across all samples is 55 mg and the average range is 2.2 mg. a. Estimate the process standard deviation. b. Calculate the centreline and control limits for the R chart. c. Calculate the centreline and control limits for the x-bar chart.

Answer: a. σ =

=

= 0.773 mg

b. Centreline = 2.2 mg LCL = 0.299 mg and UCL = 4.101 mg c. Centreline = 55 mg LCL = 54.18 mg and UCL = 55.82 mg L.O.: 2 3) A producer of specialty products uses a variety of natural and man-made materials to make unique countertops for kitchens and baths. One product line mixes concrete and natural river stone to make countertops that are polished to a high shine revealing unique patterns.

Occasionally coarse sand will result in undesirable pitting and rough spots on surfaces.

Consequently, as part of its quality control efforts, 8 by 4 foot polished slabs are checked periodically for imperfections. For each slab inspected the number of imperfections (pits, rough spots, etc.) is recorded. a. What type of control chart should be used for these data? b. If the average number of imperfections per 8 by 4 foot polished slab is 2.6, calculate the centreline and control limits for the appropriate control chart.

Answer: a. c chart b. Centreline = 2.6 LCL = 0 and UCL = 7.44 L.O.: 3

2 .

4) An importer of decorative ceramic tile samples 50 tiles each day from incoming shipments.

Some tiles are cracked or broken before or during transit, rendering them useless scrap. Sampling from incoming shipments for 30 days reveals that a total of 250 tiles are cracked or broken. a. What type of control chart should be used by the importer in monitoring the proportion of scrap tiles? b. Calculate the centreline for this control chart. c. Calculate the control limits for this control chart.

Answer: a. p chart b. Centreline = 0.167 c. LCL = 0.009 and UCL = 0.325 L.O.: 3 Short Answer - Quiz B 1) By design, a required dimension on a part is 0.575 cm plus or minus 0.008 cm. Assume that the process producing this part is stable with a mean of 0.579 cm and standard deviation of 0.002 cm. a. What are the specification limits on this part? b. Compute the Cp index. c. Compute the Cpk index. d. Which index is a better measure of the process capability in this instance? Explain.

Answer: a. LSL = 0.567 cm and USL = 0.583 cm b. Cp =

=

=

c. CpL =

=

=2

CpU =

=

= 0.67

= 1.33

Cpk = 0.67 d. In this case the Cpk index is better. The process is off target (shifted to the right) which is not detected by computing Cp. L.O.: 2

3 .

2) An automatic filling process is used to dispense hand sanitizer into small purse size bottles.

The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml. a. Estimate the process standard deviation. b. Calculate the centreline and control limits for the R chart. c. Calculate the centreline and control limits for the x-bar chart.

Answer: a. σ =

=

= 1.34 ml

b. Centreline = 2.75 ml LCL = 0 ml and UCL = 6.276 ml c. Centreline = 72.5 ml LCL = 70.50 ml and UCL = 74.50 ml L.O.: 2 3) A manufacturer of a particular grade of copper tubing collects data on the number of flaws occurring in 500 metre coils. Suppose they sample a total of 40 coils to initiate control charting.

The average number of defects per coil is 2.5. a. What type of control chart should be used for these data? b. If the average number of defects per coil is 2.5, calculate the centreline and control limits for the appropriate control chart.

Answer: a. c chart b. Centreline = 2.5 LCL = 0 and UCL = 7.24 L.O.: 3 4) In order to achieve higher levels of customer satisfaction, a company initiates monitoring the complaint resolution process of its customer service representatives. As a first step, the company decides to collect data on the number of unanswered calls out of the first 250 incoming to its call centre made each day. At the end of monitoring 25 days, it was found that a total of 500 incoming calls went unanswered. a. What type of control chart should be used by the company in monitoring customer satisfaction at the call centre? b. Calculate the centreline for this control chart. c. Calculate the control limits for this control chart.

Answer: a. p chart b. Centreline = 0.08 c. LCL = 0.029 and UCL = 0.131 L.O.: 3

4 .

Multiple Choice - Quiz C 1) Which of the following statements is false regarding control charts?

A) If we view using a control chart as a graphical hypothesis test, the null hypothesis is that the process has not changed.

B) A type I error in control charting results in an unnecessary adjustment to the process.

C) A type II error in control charting results in an unnecessary adjustment to the process.

D) A process within which special-cause variation is present is said to be out of control.

E) A process which exhibits only common-cause variation is said to be in control.

Answer: C L.O.: 2 2) A paper products manufacturer coats paper with a thin film of wax. To initiate control charting, data are collected on the thickness of the coating (measured in mm) by taking twentyfive samples each of size five. The appropriate control chart for these data is the A) c chart.

B) p chart.

C) Cp index.

D) x-bar and R chart.

E) ARL chart.

Answer: D L.O.: 2, 3 3) By design, a required dimension of a part is 0.575 cm plus or minus 0.008 cm. Assume that the process producing this part is stable with a mean of 0.579 cm and standard deviation of 0.002 cm. The specification limits for this part are A) 0.554 to 0.596 cm.

B) 0.567 to 0.583 cm.

C) 0.576 to 0.598 cm.

D) 0.572 to 0.584 cm.

E) 0.575 to 0.578 cm.

Answer: B L.O.: 2 4) A company that manufactures health food snacks produces low sodium rice chips. To monitor the process for sodium levels, chips are selected periodically and the amount of sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and range in sodium content is determined. The average of the means across all samples is 55 mg and the average range is 2.2 mg. The estimated process standard deviation ( ) is A) 0.773 mg.

B) 2.683 mg.

C) 0.073 mg.

D) 16.176 mg.

E) 1.833 mg.

Answer: A L.O.: 2 5 .

5) A company that manufactures health food snacks produces low sodium rice chips. To monitor the process for sodium levels, chips are selected periodically and the amount of sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and range in sodium content is determined. The average of the means across all samples is 55 mg and the average range is 2.2 mg. The lower and upper control limits for the x-bar chart are A) 52.67 and 57.33 mg.

B) 51.15 and 58.85 mg.

C) 54.18 and 55.82 mg.

D) 48.89 and 57.61 mg.

E) 37.84 and 72.16 mg.

Answer: C L.O.: 2 6) A company that manufactures health food snacks produces low sodium rice chips. To monitor the process for sodium levels, chips are selected periodically and the amount of sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and range in sodium content is determined. The average of the means across all samples is 55 mg and the average range is 2.2 mg. The lower and upper control limits for the R chart are A) 0.299 and 4.101 mg.

B) 0 and 4.4088 mg.

C) 0.136 and 1.864 mg.

D) 2.1999 and 30.152 mg.

E) 0.2493 and 3.4167 mg.

Answer: A L.O.: 2 7) An importer of decorative ceramic tile samples 50 tiles each day from incoming shipments.

Some tiles are cracked or broken before or during transit, rendering them useless scrap. Sampling from incoming shipments for 30 days reveals that a total of 250 tiles are cracked or broken. The centreline on the p chart for these data is A) 0.250.

B) 1.83.

C) 2.5.

D) 0.167.

E) 6.1.

Answer: D L.O.: 3

6 .

8) An importer of decorative ceramic tile samples 50 tiles each day from incoming shipments.

Some tiles are cracked or broken before or during transit, rendering them useless scrap. Sampling from incoming shipments for 30 days reveals that a total of 250 tiles are cracked or broken. The lower and upper control limits on the p chart for these data are A) 0.067 and 0.299.

B) 0.157 and 0.177.

C) 0 and 0.299.

D) 1.314 and 10.886.

E) 0.009 and 0.325.

Answer: E L.O.: 3 9) A manufacturer of a particular grade of copper tubing collects data on the number of flaws occurring in 500 metre coils. Suppose they sample a total of 40 coils to initiate control charting.

The average number of defects per coil is 2.5. The appropriate control chart for these data is the A) R chart.

B) c chart.

C) x-bar and R chart.

D) p chart.

E) ARL chart.

Answer: B L.O.: 2, 3 10) A manufacturer of a particular grade of copper tubing collects data on the number of flaws occurring in 500 foot coils. Suppose they sample a total of 40 coils to initiate control charting.

The average number of defects per coil is 2.5. The lower and upper control limits for the appropriate control chart for these data are A) 0 and 7.24.

B) 0 and 5.66.

C) 2.24 and 8.70.

D) 2.24 and 4.08.

E) 0.80 and 8.70.

Answer: A L.O.: 3 11) A major airline is interested in monitoring customer satisfaction with its baggage handling process. To do so, each day the airline randomly selects 100 customers and surveys them to determine if they are satisfied or not with the service provided. After 20 samples, a total of 260 unsatisfied customers were counted. The appropriate control chart for these data is the A) p chart.

B) x-bar chart.

C) R chart or S-bar chart.

D) c chart.

E) R chart.

Answer: A L.O.: 2, 3 7 .

12) A major airline is interested in monitoring customer satisfaction with its baggage handling process. To do so, each day the airline randomly selects 100 customers and surveys them to determine if they are satisfied or not with the service provided. After 20 samples, a total of 260 unsatisfied customers were counted. The lower and upper control limits for the appropriate control chart for these data are A) 0.029 and 0.231.

B) 0 and 0.145.

C) 0.0964 and 0.1363.

D) 0 and 0.4236.

E) 0 and 0.356.

Answer: A L.O.: 3 13) The control limits in a control chart can A) describe the range of virtually all common-cause variation.

B) describe the range of virtually all special-cause variation.

C) describe any value falling within the limits as a product of high quality.

D) describe any value falling outside the limits as a product that should be rejected.

E) indicate that the data is normally distributed.

Answer: A L.O.: 2 14) Recently a shipping company took 30 samples of the delivery times of packages that it was responsible for. Each sample was of 100 packages. Out of the 3,000 total packages, 300 were delivered late. In setting up a process control chart, what would be the correct upper control limit for the appropriate control chart for these data?

A) 0.19 B) 0.03 C) 0.07 D) 0.13 E) 0.26 Answer: A L.O.: 3

8 .

Consider the following to answer the question(s) below: A company that fills 12 ounce soft drink bottles wishes to monitor the quality of their process.

To do this, the company has taken a series of samples of 4 bottles. The overall average fill is 12.03 ounces. The average range for the samples has been 0.06 ounces.

15) What is the correct estimated process standard deviation ( )?

A) 0.029 B) 0.01 C) 0.02 D) 2.059 E) 3.99 Answer: A L.O.: 2 16) Based on this information, what is the value of the upper control limit for the x-bar chart?

A) 12.074 B) 12.059 C) 0.0437 D) 12.09 E) 0.729 Answer: A L.O.: 2 17) Based on this information, what is the value of the upper control limit for the R chart?

A) 0.137 B) 2.282 C) 0 D) 0.026 E) 0.88 Answer: A L.O.: 2 18) Suppose, after developing the control chart, a subgroup of size 4 yields a sample mean of 12.09 ounces and a range of 0.08. Which of the following statements is true?

A) The process is out of control on the x-bar chart but in control on the R chart.

B) The process is in control on the x-bar chart and out of control on the R chart.

C) Since 12.09 > 12.074, the process is in control on the x-bar chart.

D) Since 0.08 < 0.137, the process is out of control on the R chart.

E) Since 12.09 > 12.03, the process is in control on the x-bar chart.

Answer: A L.O.: 2

9 .

19) A powerful tool in establishing an out-of-control action plan is A) a fishbone diagram.

B) an x-bar chart.

C) an R chart.

D) a p chart.

E) a c chart.

Answer: A L.O.: 5 20) The main cross-town transit route in a large Ontario town makes 120 trips per day. The transit authority will tolerate an average of no more than 5 late running trips per day. They wish to use a control chart to monitor the timeliness of the route. The following data were collected for 8 days. Based on this information, the values of the appropriate lower and upper control limits are Day Late running trips

1 5

2 6

3 4

4 5

5 1

A) 0 and 10.2.

B) -1.71 and 11.71.

C) 0 and 19.5.

D) -9.75 and 19.5.

E) 2.28 and 14.47.

Answer: A L.O.: 3

10 .

6 7

7 1

8 4

Business Statistics, Cdn. Ed., 4e (Sharpe) Part I: Exploring and Collecting Data Multiple Choice - Test A 1) In listing a property, real estate agencies provides information on a number of variables.

Which of the following variables related to property listings is categorical?

A) Real Estate Tax B) Number of Bedrooms C) Style of Home D) Asking Price E) Number of Bathrooms Answer: C L.O.: 2-2 2) What type of variable is the style of a home (bungalow, split level, ranch, etc.)?

A) Nominal B) Interval C) Quantitative D) Ordinal E) Numerical Answer: A L.O.: 2-2 3) Real estate agencies also keep track of housing prices in a given area. Suppose they also provide their clients with quarterly median selling prices for homes in a given area for the past three year period. These data are A) cross-sectional.

B) time series.

C) categorical.

D) nominal.

E) ordinal.

Answer: B L.O.: 2-2 4) A researcher is conducting a study on eating disorders. Using a list of recent participants in the online Weight Watchers program, she randomly selects a name from the alphabetized list. She then chooses every tenth person from that point on to include in her study. This sampling strategy is called A) systematic.

B) cluster.

C) simple random.

D) stratified.

E) convenience.

Answer: A L.O.: 3-1, 3-3 1 .

Use the following to answer the question(s) below.

A magazine that publishes product reviews conducted a survey of teenagers' preferences for cell phones. Three brands of cell phone designed specifically with teens in mind were the focus of the study. The table summarizes responses by brand and gender.

Cell Phone LG Rumour Sidekick LX BlackJack II

Male 55 99 196

Female 87 150 113

5) Which of the following charts would be appropriate for displaying the marginal distribution of brands?

A) Side-by-side bar chart B) Segmented bar chart with the horizontal axis Gender C) Pie chart D) Line graph E) Horizontal bar chart with the vertical axis Gender Answer: C L.O.: 4-1, 4-2 6) What percent of teenagers preferred LG Rumour?

A) 50.0% (350/700) B) 40.6% (142/350) C) 24.9% (87/350) D) 15.7% (55/350) E) 20.3% (142/700) Answer: E L.O.: 4-2 7) What percent of female teenagers preferred the Sidekick LX? A) 42.9% (150/350) B) 60.2% (150/249) C) 21.4% (150/700) D) 50.0% (350/700) E) 71.1% (249/350) Answer: A L.O.: 4-2 8) What percent of teenagers who preferred the BlackJack II were males?

A) 63.4% (196/309) B) 56.0% (196/350) C) 28.0% (196/700) D) 50.0% (350/700) E) 44.1% (309/700) Answer: A L.O.: 4-2 2 .

9) Which is true of the data shown in the histogram?

A) The distribution is approximately symmetric and unimodal. The mean and median are approximately equal.

B) The distribution is skewed to the right. The mean is less than the median.

C) The distribution is skewed to the left. The mean is greater than the median.

D) The distribution is right-skewed and multimodal.

E) It is better to report the median and IQR about these data than the mean and standard deviation.

Answer: A L.O.: 5-1, 5-2, 5-3

3 .

Use the following to answer the question(s) below.

Summary statistics and a histogram for certain data are shown below.

Min 7.9

Q1 10.8

Median 13.4

Q3 16.7

Max 25.8

Mean 13.9

SD 3.6

10) What is the most appropriate measure to describe the centre of these data?

A) Range B) Mean C) Standard Deviation D) Median E) IQR Answer: D L.O.: 5-2 11) The IQR for these data is A) 16.7.

B) 5.9.

C) 17.9.

D) 3.6.

E) 13.4.

Answer: B L.O.: 5-3

4 .

12) An office supply chain has stores in two locations, Toronto and Vancouver. One of these stores is to be closed within the coming year, and to help make the decision, management reviews sales data. Below are boxplots for monthly unit sales for both locations.

Which of the following statements is not correct?

A) Monthly sales are higher in Toronto compared to Vancouver.

B) The IQR for sales in Toronto is larger than that for Vancouver.

C) Monthly sales median is less in Vancouver than in Toronto.

D) Both distributions are fairly symmetric.

E) Monthly sales median is greater in Vancouver compared to Toronto.

Answer: E L.O.: 5-4

5 .

13) Below is a stem-and-leaf display of prices for a sample of homes recently sold in a metropolitan area in Canada.

Which of the following statements is true?

A) The mean would be more appropriate than the median to describe the centre of this distribution.

B) This distribution is fairly symmetric.

C) This distribution is right-skewed.

D) This distribution is left-skewed.

E) We are unable to analyze skewness of these data.

Answer: C L.O.: 5-1, 5-2 14) Suppose a sample of 60 business majors revealed that the average time spent studying per week is 22 hours with a standard deviation of 4 hours. For one student reporting that he studies 16 hours per week, the corresponding z-score is A) -1.5.

B) 1.5.

C) 2.2.

D) -2.2.

E) -3.0.

Answer: A L.O.: 5-6

6 .

Use the following to answer the question(s) below.

A manager of Kim & Lim corporate strategy department thinks that dollars spent on advertising can to some extent be a predictor of total sales dollars. As an aid in long-term planning, she analyzes the following sales and advertising numbers for 2015 (both in $millions). Information was collected from eight companies of Kim & Lim.

Mean Standard Deviation

Advertising 13.5 4.2 22.1 60.5 38.1 6.6 17.3 41.7

Sales 153 60 443 999 546 94 131 384

25.50 19.57

351.25 317.54

15) The sum of the cross-product of the deviations is found as follows:

What is the coefficient of the correlation between x (Advertising) and y (Sales)?

A) 0.817 B) 0.647 C) 0.567 D) 0.933 E) 0.206 Answer: D L.O.: 6-2

7 .

16) Use the following regression equation Total Sales = -35.017 + 15.148 Advertising to express statistical dependence of total sales on advertising expenses in the given sample (both numbers in $millions). A company with $5,900,000 advertising expenses is expected to have total sales of A) $54,356,200.

B) $89,373,165.

C) loss of $117.

D) loss of $117,244,800.

E) $5,435,620.

Answer: A L.O.: 7-2 Multiple Choice - Test B 1) Statscan compiles data on a number of variables. Which of the following Statscan variables is categorical?

A) Consumer expenditures B) Type of workplace injuries C) Wages by occupation D) Employment costs E) Productivity by industry Answer: B L.O.: 2-2 2) What type of variable is category of workplace injuries (slip and fall, stress related, etc.)?

A) Quantitative B) Interval C) Nominal D) Ordinal E) Numerical Answer: C L.O.: 2-2 3) Statscan publishes the monthly CPI (consumer price index). This index shows the change in prices paid by urban consumers for a market basket of goods and services. These data are A) cross-sectional.

B) nominal.

C) categorical.

D) time series.

E) ordinal.

Answer: D L.O.: 2-2

8 .

4) A researcher is conducting a study on Internet use. He decides to first categorize the population by education level (high school, college graduate, advanced degree, etc.) and then survey a select number from each category. This sampling strategy is called A) systematic.

B) cluster.

C) simple random.

D) convenience.

E) stratified.

Answer: E L.O.: 3-1, 3-3 5) If a parameter is computed from a set of data, which of the following statements is true?

A) The data are obtained from a census.

B) The data are obtained from a random sample.

C) The data is from a sample that is representative of the population.

D) The data are obtained from a stratified sample.

E) The data are obtained from a convenience sample.

Answer: A L.O.: 3-1, 3-3 Use the following to answer the question(s) below.

A recent survey of online shoppers asked them to indicate the primary reason they shop via the Internet. The table summarizes responses by reason and gender.

Reason for Shopping Online Convenience Better Prices Greater Selection

Male 249 110 41

Female 90 99 211

6) What percent of respondents cite Convenience as the primary reason they shop online?

A) 42.4% (339/800) B) 22.5% (90/400) C) 62.3% (249/400) D) 84.8% (339/400) E) 31.1% (249/800) Answer: A L.O.: 4-2 7) What percent of males cite Convenience as the primary reason they shop online?

A) 42.4% (339/800) B) 73.5% (249/339) C) 62.3% (249/400) D) 31.1% (249/800) E) 50.0% (400/800) Answer: C L.O.: 4-2 9 .

8) What percent of respondents who cited Greater Selection as the primary reason they shop online were females?

A) 52.8% (211/400) B) 26.4% (211/800) C) 50.0% (400/800) D) 83.7% (211/252) E) 63.0% (252/400) Answer: D L.O.: 4-2 9) Which is true for the data shown in the histogram?

A) The distribution is skewed to the right.

B) The mean is probably smaller than the median.

C) It is appropriate to summarize these data with the mean and standard deviation.

D) The distribution is left-skewed.

E) The distribution is fairly symmetric. So, we have to report the median and IQR. Answer: A L.O.: 5-1, 5-2, 5-3

10 .

Use the following to answer the question(s) below.

A consumer magazine evaluated the price and performance of 23 models of cordless phones.

Computer output gives this summary for the prices ($): Min 15

Q1 30

Median 50

Q3 110

Max 200

Mean 71.75

SD 52.08

10) Based on the summary statistics, which of the following is true?

A) The distribution is symmetric.

B) The distribution is skewed to the right.

C) The distribution is skewed to the left.

D) The mean is a better measure of centre for these data than the median.

E) The standard deviation is larger than the range.

Answer: B L.O.: 5-1, 5-2, 5-3 11) The IQR for these data is A) $80.

B) $185.

C) $21.75.

D) $60.

E) $52.08.

Answer: A L.O.: 5-3

11 .

Use the following to answer the question(s) below.

Boxplots of earnings per share (EPS) data for a sample of retail company stocks and a sample of energy company stocks are shown below.

12) Which of the following statements is correct?

A) The median EPS is higher for energy stocks compared to retail stocks.

B) The median EPS is higher for retail stocks compared to energy stocks.

C) The IQR for the EPS data is larger for retail stocks than for energy stocks.

D) The EPS data are more variable for retail stocks than for energy stocks.

E) The mean is less than the median for energy stocks, and the mean is greater than the median for retail stocks.

Answer: B L.O.: 5-4 13) Which of the following statements is true about the distributions of EPS for retail and energy stocks?

A) The distribution of EPS for retail stocks is skewed to the right.

B) The distribution of EPS for energy stocks is symmetric.

C) Both distributions of EPS are symmetric.

D) The distribution of EPS for retail stocks is skewed to the left.

E) The distribution of EPS for energy stocks is skewed to the left.

Answer: D L.O.: 5-1, 5-2

12 .

14) Suppose a sample of 60 crates has a mean weight of 12.1 kilograms and a standard deviation of 0.05 kilograms. If a crate has the weight of 12 kilograms, what is its corresponding z-score?

A) 2.0 B) -2.0 C) 1.8 D) -3.0 E) -1.8 Answer: B L.O.: 5-6 Use the following to answer the question(s) below.

Below is Excel output showing the coefficient of correlation between personal income and vacation expenses (both in $thousands) for a large sample of clients of one travel agency in Toronto.

15) Which of the following statements are false?

A) The correlation coefficient of 0.691 indicates a relatively strong positive linear association.

B) The correlation coefficient of 0.691 has no units.

C) If we swap the variables, the correlation coefficient will still be equal to 0.691.

D) Correlation is not sensitive to scaling the data. So, new scaling has no effect on the value of the correlation coefficient. It will remain unchanged.

E) If we swap the variables, the correlation coefficient will be equal to 1.447.

Answer: E L.O.: 6-2 16) What percent of the variation of vacation expenses can be explained by variation of personal income?

A) 69.1% B) 47.7% C) 83.1% D) 52.3% E) 30.9% Answer: B L.O.: 7-2

13 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Part II: Understanding Probability Distributions and Statistical Inference Multiple Choice - Test A 1) A quality assurance manager is interested in determining the likelihood that more than 20 calls come in to a particular customer service centre per hour. What method would be most appropriate for assigning this probability?

A) Personal B) Judgmental C) Subjective D) Relative Frequency (Empirical) E) Classical (Theoretical) Answer: D L.O.: 8-1 Use the following to answer the question(s) below.

A survey of investors finds that 60% use a full service brokerage firm to invest in stocks, 30% trade stocks online and 24% do both.

2) The probability that an investor selected at random uses a full service brokerage firm to invest in stocks or trades stocks online is A) 90%.

B) 66%.

C) 34%.

D) 54%.

E) 60%.

Answer: B L.O.: 8-2 3) The probability that an investor selected at random neither uses a full service brokerage firm to invest in stocks nor trades stocks online is A) 90%.

B) 66%.

C) 34%.

D) 10%.

E) 60%.

Answer: C L.O.: 8-2

1 .

Use the following to answer the question(s) below.

An advocacy group is investigating whether gender has an effect on job category in large investment firms. They surveyed a sample of firms with the following results: Job Category Clerical / Technical Professional Staff Executive / Managerial

Male 85 720 400

Female 215 480 100

4) What is the probability that a randomly selected employee's job category is executive/managerial?

A) 0.20 B) 0.80 C) 0.13 D) 0.45 E) 0.25 Answer: E L.O.: 8-2 5) What is the probability that a randomly selected employee's job category is executive/managerial, given that the employee is female?

A) 0.13 B) 0.20 C) 0.80 D) 0.05 E) 0.45 Answer: A L.O.: 8-2 6) Two events F = {a randomly selected employee is female} and S = {a randomly selected employee's job category is professional staff} are A) independent.

B) not independent.

C) mutually exclusive.

D) independent and mutually exclusive.

E) disjoint.

Answer: B L.O.: 8-2

2 .

Use the following to answer the question(s) below.

A men's clothing store has determined the following probability distribution for the number of special size orders placed per month. The distribution is as follows: Number Ordered 0 5 10 15 20

Probability 0.10 0.10 0.12 0.30 0.38

7) The number of special size orders this men's clothing store can expect per month is A) 13.8.

B) 20.

C) 15.

D) 14.2.

E) 12.5.

Answer: A L.O.: 9-1 8) The standard deviation of the number of special size orders placed per month is A) 24.516.

B) 4.95.

C) 15.345.

D) 6.60.

E) 3.88.

Answer: D L.O.: 9-1 Use the following to answer the question(s) below.

Insurance company records indicate that 10% of its policyholders file claims involving theft or robbery of personal property from their homes. Suppose a random sample of 400 policyholders is selected.

9) The standard deviation of the sampling distribution of the sample proportion of policyholders filing claims involving theft or robbery of personal property from their homes is A) 0.000225.

B) 0.25.

C) 0.0455.

D) 0.1667.

E) 0.015.

Answer: E L.O.: 10-2

3 .

10) The probability that the sample proportion of policyholders filing claims involving theft or robbery of personal property from their homes is less than 8% is A) 0.0918.

B) 0.1333.

C) 0.4082.

D) 0.0517.

E) 0.7892.

Answer: A L.O.: 10-2 11) What is probability that the sample proportion of policyholders filing claims involving theft or robbery of personal property from their homes exceeds 15%?

A) 99.96% B) 0.04% C) 42.07% D) 57.93% E) 38.21% Answer: B L.O.: 10-2 12) We have calculated a 95% confidence interval and would like our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can A) change the z* value to a smaller number.

B) take a larger sample.

C) take a smaller sample.

D) use z* = 2.576.

E) use z* = 1.645 and decrease size of sample.

Answer: B L.O.: 11-2 Use the following to answer the question(s) below.

In economic downturns companies attempt to downsize their workforces by offering early retirement incentives to older employees. A survey of 723 companies found that 195 engage in such downsizing practices.

13) The estimated proportion of companies that downsize their workforces by offering early retirement incentives is A) 0.50.

B) 0.73.

C) 0.195.

D) 0.27.

E) 0.67.

Answer: D L.O.: 11-1

4 .

14) The 99% confidence interval for the proportion of companies that downsize their workforces by offering early retirement incentives is A) 0.19 to 0.35.

B) 0.65 to 0.81.

C) 0.19 to 0.47.

D) 0.69 to 0.77.

E) 0.23 to 0.31.

Answer: E L.O.: 11-1 15) A truck company wants on-time delivery for at least 98% of the parts they order from a metal manufacturing plant. They have been ordering from Hudson Manufacturing but will switch to a new, cheaper manufacturer (Steel-R-Us) unless there is evidence that this new manufacturer cannot meet the 98% on-time goal. As a test the truck company purchases a random sample of metal parts from Steel-R-Us, and then determines if these parts were delivered on-time. Which hypotheses should they test?

A) H0: p < 0.98 HA: p > 0.98 B) H0: p > 0.98 HA: p = 0.98 C) H0: p = 0.98 HA: p < 0.98 D) H0: p < 0.98 HA: p ≠ 0.98 E) H0: p = 0.98 HA: p > 0.98 Answer: C L.O.: 12-1, 12-2 16) A P-value indicates A) the probability that the null hypothesis is true.

B) the probability that the alternative hypothesis is true.

C) the probability of the observed statistic given that the null hypothesis is true.

D) the probability of the observed statistic given that the alternative hypothesis is true.

E) the probability of the null hypothesis.

Answer: C L.O.: 12-1

5 .

17) Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts (H0: p = 0.97 and HA: p > 0.97). The test results in a Pvalue of 0.102. In reality, the machine is producing 99% good parts. What probably happens as a result of our testing?

A) We correctly fail to reject H0.

B) We correctly reject H0.

C) We reject H0, making a Type I error.

D) We fail to reject H0, making a Type I error.

E) We fail to reject H0, making a Type II error.

Answer: E L.O.: 12-2, 12-4 18) We have created a 95% confidence interval for the true proportion with the result (0.10, 0.15). What conclusion will we make if we test H0: p = 0.16 versus HA: p ≠ 0.16 at α = 0.05?

A) Reject the null hypothesis.

B) Accept the null hypothesis.

C) Fail to reject the null hypothesis.

D) Reject the alternative hypothesis.

E) Support the null hypothesis and accept the alternative hypothesis.

Answer: A L.O.: 12-3 Use the following to answer the question(s) below.

The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 108 grams with a sample standard deviation of 14 grams. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is less than 113 grams.

19) The correct null and alternative hypotheses are A) H0: µ = 113; HA: µ > 113.

B) H0: µ = 113; HA: µ < 113.

C) H0: µ > 113; HA: µ = 113.

D) H0: µ < 113; HA: µ = 113.

E) H0: µ = 113; HA: µ ≠ 113.

Answer: B L.O.: 13-2 20) The correct value of the test statistic is A) -0.4.

B) 0.4.

C) -1.38.

D) 1.38.

E) 2.79.

Answer: C L.O.: 13-1, 13-2 6 .

21) The correct conclusion at the 0.05 level of significance is A) fail to reject the null hypothesis, and there is no evidence that the true mean weight is less than 113 grams.

B) reject the null hypothesis.

C) evidence suggests that the mean weight is less than 113 grams.

D) do not reject the null hypothesis, as evidence suggests that the mean weight is less than 113 grams.

E) reject the null hypothesis, as evidence suggests that the mean weight is less than 113 grams.

Answer: A L.O.: 13-2 Use the following to answer the question(s) below.

A sample of 30-year fixed mortgage rates at 12 randomly chosen credit unions yields a mean rate of 6.65 % and a sample standard deviation of 0.39%. A sample of 30-year fixed mortgage rates at 16 randomly selected banks yields a mean rate of 7.05% and a sample standard deviation of 0.22%. Are the mean rates different between credit unions and banks? Relevant output is shown below.

22) Which of the following is true?

A) This is a paired t-test.

B) This is a test for two means from independent samples.

C) This is a one-tailed test.

D) This is a paired design and one-tailed t-test.

E) This is a pooled t-test.

Answer: B L.O.: 14-1, 14-3

7 .

23) At the 0.05 level of significance, the correct conclusion is A) reject the alternative hypothesis.

B) fail to reject the null hypothesis.

C) evidence suggests that there is no significant difference in mean mortgage rates between credit unions and banks.

D) reject the null hypothesis; evidence suggests that there is a significant difference in mean mortgage rates between credit unions and banks.

E) fail to reject the null hypothesis; evidence suggests that the mortgage rates at credit unions are lower than at banks, on average.

Answer: D L.O.: 14-1 24) A professor was interested in determining whether the prices of new textbooks in the bookstore were higher than if purchased online. She selected 6 textbooks and priced each at the bookstore and online. Which statement is true at 5% significance level?

A) There is not enough evidence to suggest that the prices of new textbooks in the bookstore were higher than if purchased online, on average.

B) There is strong evidence that the prices are higher in the bookstore.

C) We are 95% sure that the prices are higher online.

D) There is strong evidence that the prices in the bookstore and online are different.

E) We are 95% sure that the prices in the bookstore and online are exactly the same.

Answer: A L.O.: 14-1, 14-3

8 .

25) Absorption rates into the body are important factors when manufacturing a generic version of a brand-name drug. A pharmacist read that the absorption rate into the body of a new generic drug (G) is the same as its brand-name counterpart (B). She has a researcher friend of hers run a small experiment to test H0: μG - μB = 0 against the alternative HA: μG - μB ≠ 0. Which of the following would be a Type I error?

A) Deciding that the absorption rates of G are higher, when in fact they are not.

B) Deciding that the absorption rates of G are lower, when in fact they are not.

C) Deciding that the absorption rates are the same, when in fact they are not.

D) Deciding that the absorption rates are different, when in fact they are not.

E) Deciding that the absorption rates are the same, when in fact the absorption rates of G are higher.

Answer: D L.O.: 14-1, 12-4 26) Which of the following is not an assumption or condition that needs to be checked for a paired t-interval?

A) Paired Data Assumption B) Independent Groups Assumption C) Randomization Condition D) 10% Condition E) Normal Population Assumption Answer: B L.O.: 14-3

9 .

Use the following to answer the question(s) below.

Three brands of AAA batteries are compared to determine if differences in lifetime exist. Each brand is tested in four devices (TV remote, hand-held game, flashlight and digital camera). The experiment is run once for each combination of brand and device. The twelve runs are ordered randomly. The time (in minutes) that each battery lasts under continuous usage is recorded. The partial ANOVA results are as follows:

27) The F-statistic for testing whether the three brands of AAA batteries have equal mean lifetimes is A) 2.96.

B) 1654.89.

C) 0.98.

D) 827.49.

E) 54.67.

Answer: A L.O.: 15-3 28) The P-value associated with this F-statistic associated with the brands is 0.128. Based on this, we can conclude that A) we should reject the null hypothesis.

B) there is a difference in the mean lifetimes among the different brands.

C) there is no significant difference in the mean lifetimes among the different devices.

D) we should support the alternative hypothesis.

E) there is no difference in the mean lifetimes among the different brands.

Answer: E L.O.: 15-3 29) Which of the following statements is true about this design?

A) This is a completely randomized design in one factor.

B) The devices serve as blocks to account for the variability between the lengths of time batteries last in different devices.

C) We know that the interaction effect between brand of battery and type of device is significant.

D) This is no treatment in study.

E) This is a retrospective study.

Answer: B L.O.: 15-1, 15-2

10 .

30) The following plot is the best for checking

A) Equal Variance Assumption.

B) Linearity Assumption.

C) Nearly Normal Condition.

D) Non-linear Condition.

E) Dependence Condition.

Answer: C L.O.: 15-3

11 .

Use the following to answer the question(s) below.

Chris Columbus is responsible for controlling inventory levels for four types of sailboats sold by his company. Chris takes a sample of 48 boats sold over the past several months to determine if demand is the same for each type. His results are as follows: Type of Boat Pirate's Revenge Jolly Roger Sails Delight Cruiser Cove

Sales 15 11 10 12

31) The correct null hypothesis to be tested is A) type of boat and demand are related.

B) the demand differs for each type of boat.

C) the demand is the same for each type of boat.

D) the demand is dependent on the type of boat.

E) type of boat affects the demand.

Answer: C L.O.: 16-1, 16-2 32) The calculated value of the Chi-square statistic is A) 7.815.

B) 1.17.

C) 22.35.

D) -1.17.

E) 12.56.

Answer: B L.O.: 16-2 33) At the 0.05 level of significance, the correct conclusion is A) evidence suggests that the demand is the same for different types of boats.

B) evidence suggests that the demand is not the same for different types of boats.

C) reject the null hypothesis.

D) evidence suggests that the demand is dependent on the type of boat.

E) evidence suggests that type of boat affects the demand.

Answer: A L.O.: 16-2

12 .

34) Suppose that 6 economists who work for the federal government and 7 university economists were asked to grade the effectiveness of an economic stimulus bill in terms of its ability to increase jobs over the next two years. What nonparametric method is appropriate for testing if the two groups differ in terms of their opinion?

A) Wilcoxon rank-sum test B) Wilcoxon signed-rank test C) Spearman's rho test D) Kruskal-Wallis Test E) Kendall's tau test Answer: A L.O.: 17-2, 17-3 35) Suppose that 6 economists who work for the federal government and 7 university economists were asked to grade the effectiveness of an economic stimulus bill in terms of its ability to increase jobs over the next two years. The grades are shown in below. Using the appropriate nonparametric method, the calculated value of the test statistic is Government AA B+ BB A-

University C B+ BC+ ABC

A) T = TGovernment = 55.5.

B) T= 30.

C) T = 54.

D) T = TUniversity = 35.5.

E) T = 91.

Answer: D L.O.: 17-2

13 .

36) Based on the scatterplot shown below, what makes a nonparametric method more appropriate than the Pearson correlation for measuring the association between the two variables?

A) Nonlinearity B) These variables are not quantitative.

C) The presence of an outlier D) Violation of Linearity Condition and the fact that these variables are not quantitative E) There is no unusual observation, but we have to deal with a bend in the data.

Answer: C L.O.: 17-1, 17-3

14 .

37) Suppose that ten new smart phone models were evaluated by two consumer electronics magazines (Popular Electronics and Electronics Now) from 1 (best) to 10 (worst) as shown below. Why is the Spearman's rho more appropriate than the correlation coefficient for these data?

Model 1 2 3 4 5 6 7 8 9 10

Popular Electronics 8 3 7 4 2 1 10 5 6 9

Electronics Now 7 6 5 3 1 2 8 9 4 10

A) The relationship is nonlinear.

B) The data are ordinal.

C) The data are not paired.

D) There is one extreme outlier.

E) Both outliers and bends in the data make the correlation coefficient difficult to interpret.

Answer: B L.O.: 17-3, 6-2, 2-2 Multiple Choice - Test B 1) A telecommunications company is interested in determining the likelihood of a new breakthrough technology being developed in the next ten years. What type of probability would they use to estimate the likelihood?

A) Relative Frequency B) Classical (Theoretical) C) Personal (Subjective) D) Model-Based E) Empirical Answer: C L.O.: 8-1

15 .

Use the following to answer the question(s) below.

A publishing company conducted a survey of its readership and found that 60% subscribed to Food & Wine, 30% subscribed to Wine Spectator, and 25% subscribed to both.

2) The probability that a reader subscribes to Food & Wine or Wine Spectator is A) 0.90.

B) 0.65.

C) 0.25.

D) 0.50.

E) 0.85.

Answer: B L.O.: 8-2 3) The probability that a reader does not subscribe to either is A) 0.10.

B) 0.65.

C) 0.50.

D) 0.45.

E) 0.35.

Answer: E L.O.: 8-2 Use the following to answer the question(s) below.

A government agency has 6000 employees. As an alternative to the traditional five day work week, employees were asked whether they preferred a four-day work week (10 hours per day) or flexible hours. The table below shows the results by age category.

Age Category Under 30 30 - 45 Over 45

Prefers 4-Day Week Prefers Flex Hours 600 300 1200 1500 2100 300

4) What is the probability that an employee at this government agency prefers a four-day work week?

A) 0.54 B) 0.15 C) 0.50 D) 0.35 E) 0.65 Answer: E L.O.: 8-2

16 .

5) What is the probability that an employee prefers flex hours given that he/she is in the 30-45 age group?

A) 0.90 B) 0.56 C) 0.31 D) 0.80 E) 0.67 Answer: B L.O.: 8-2 6) Two events F = {a randomly selected employee prefers flex hours} and O = {a randomly selected employee is over 45 years old} are A) independent.

B) mutually exclusive.

C) not independent.

D) independent and mutually exclusive.

E) disjoint.

Answer: C L.O.: 8-2 Use the following to answer the question(s) below.

IT staff for a large corporation has developed the following probability distribution for the number of calls requiring troubleshooting problems per day.

Number of Calls 0 1 2 3 4

Probability 0.32 0.35 0.18 0.10 0.05

7) The expected number of calls per day is A) 2.77.

B) 1.56.

C) 1.21.

D) 1.31.

E) 1.0.

Answer: C L.O.: 9-1

17 .

8) The standard deviation of the number of calls per day is A) 1.31.

B) 1.14.

C) 2.77.

D) 1.56.

E) 1.21.

Answer: B L.O.: 9-1 9) If a population is normally distributed with µ = 500 and σ = 50, and a sample of size 20 is selected, the probability that the sample mean falls between 450 and 550 will be ________ the probability that an individual value falls between 450 and 550.

A) the same as B) less than C) greater than D) less than or the same as E) approximately the same as Answer: C L.O.: 10-3 10) The standard deviation of the sampling distribution of mean times is A) 0.4 minutes.

B) 2 minutes.

C) 0.08 minutes.

D) 1.6 minutes.

E) 0.12 minutes.

Answer: A L.O.: 10-3 11) What is the probability that the sample mean will be less than 7.5 minutes?

A) 0.3944 B) 0.1056 C) 0.2114 D) 0.4013 E) 0.8944 Answer: B L.O.: 10-3 12) Which is true about a 99% confidence interval based on a given sample?

A) If we increase the sample size, the width of the interval will increase.

B) The interval contains 99% of the population.

C) Results from 99% of all samples will lie in this interval.

D) The interval is wider than a 95% confidence interval would be.

E) The interval is narrower than a 95% confidence interval would be.

Answer: D L.O.: 11-1 18 .

13) After computing a confidence interval, the investigator believes that the results are meaningless because the width of the interval is too large. In reconstructing the interval, the investigator should A) decrease the sample size.

B) increase the level of confidence.

C) increase the sample size.

D) reduce the population variance.

E) increase the margin of error.

Answer: C L.O.: 11-2 14) A human resources manager at a large company wants to estimate the proportion of employees that would be interested in reimbursement for college courses. If she wishes to be 95% confident that her estimate is within 5% of the true proportion, how many employees would need to be sampled?

A) 271 B) 385 C) 543 D) 646 E) 1234 Answer: B L.O.: 11-3 15) A type I error is committed when A) we don't reject a null hypothesis that is true.

B) we reject a null hypothesis that is false.

C) we reject a null hypothesis that is true.

D) we don't reject a null hypothesis that is false.

E) the null hypothesis is not properly constructed.

Answer: C L.O.: 12-4 Use the following to answer the question(s) below.

A newspaper poll asked respondents if they trusted "eco friendly" labels on cleaning products.

Out of 1000 adults surveyed, 498 responded "yes." We would like to test if the proportion of respondents that trust these labels is at least 50%.

16) The correct alternative hypothesis is A) p = 0.50.

B) p ≤ 0.50.

C) p ≥ 0.50.

D) p > 0.50.

E) p < 0.50.

Answer: E L.O.: 12-1, 12-2 19 .

17) The calculated test statistic value is A) -0.126.

B) -2.45.

C) 1.27.

D) -1.89.

E) 0.139.

Answer: A L.O.: 12-2 18) At the 0.01 level of significance, the correct conclusion is A) do not reject the alternative hypothesis.

B) reject the null hypothesis.

C) there is no evidence that at least 50% of respondents trust "eco-friendly" labels.

D) fail to reject the null hypothesis. There is no evidence that the proportion of respondents that trust "eco-friendly" labels is less than 50%.

E) reject the null hypothesis. There is strong evidence that the proportion of respondents that trust "eco-friendly" labels is less than 50%.

Answer: D L.O.: 12-1, 12-2 Use the following to answer the question(s) below.

A manufacturer of cordless electric shavers sampled 13 from a day's production and found the mean time of continuous usage without recharging to be 410 minutes with a sample standard deviation of 30 minutes. We can assume that times are normally distributed. We wish to test if the true mean operating time without recharging is more than 400 minutes.

19) The correct null and alternative hypotheses are A) H0: µ = 400; HA: µ < 400.

B) H0: µ = 400; HA: µ > 400.

C) H0: µ > 400; HA: µ = 400.

D) H0: µ < 400; HA: µ = 400.

E) H0: µ = 400; HA: µ ≠ 400.

Answer: B L.O.: 13-2 20) The correct value of the test statistic is A) 1.20.

B) -0.333.

C) -2.52.

D) -1.20.

E) 2.79.

Answer: A L.O.: 13-1, 13-2

20 .

21) The correct conclusion at the 0.05 level of significance is A) reject the null hypothesis.

B) fail to reject the null hypothesis, and there is no evidence that true mean operating time without recharging is more than 400 minutes.

C) evidence suggests that the mean operating time is more than 400 minutes.

D) reject the null hypothesis and find that evidence suggests that the mean operating time is more than 400 minutes.

E) do not reject the alternative hypothesis and find that evidence suggests that the mean operating time is more than 400 minutes.

Answer: B L.O.: 13-2 22) An urban planning group is interested in estimating the difference in mean household income between two neighbourhoods. They obtain the following 95% confidence interval: (-5693, -4107) Which of the following is true?

A) This is a pooled t-confidence interval.

B) There is no significant difference in the mean household incomes between the two neighbourhoods.

C) There is a significant difference in the mean household incomes between the two neighbourhoods.

D) This is a paired t-confidence interval and there is no significant difference in the mean household incomes between the two neighbourhoods.

E) This is a paired t-confidence interval and the mean household income of the first neighbourhood is higher than in the second.

Answer: C L.O.: 14-1, 14-2, 14-3

21 .

Use the following to answer the question(s) below.

Shape-Up-By-Susie claims that participating in her exercise program will result in guaranteed weight loss in just 6 weeks. Five clients weighed themselves before and then again after participating in her program and the differences "weight after - weight before" were analyzed.

Below is the relevant computer output.

23) Which of the following statement is true?

A) This is a pooled t-test.

B) This is a two-tailed test.

C) This is a two-sample t-test for independent groups.

D) This is a pooled and two-tailed t-test.

E) This is a paired t-test, and it is also one-tailed.

Answer: E L.O.: 14-1, 14-3 24) At the 0.05 level of significance, the correct conclusion is A) reject the alternative hypothesis.

B) fail to reject the null hypothesis.

C) Susie's claim is not supported by the sample evidence.

D) reject the null hypothesis and find that Susie's claim is supported by the sample evidence.

E) fail to reject the null hypothesis and support the alternative hypothesis. There is strong evidence that participating in Susie's exercise program will result in guaranteed weight gain in just 6 weeks.

Answer: D L.O.: 14-3

22 .

25) A contact lens wearer read that the producer of a new contact lens boasts that their lenses are cheaper than contact lenses from another popular company. The null hypothesis H0: μold μnew = 0 is tested against the alternative HA: μold - μnew > 0. Which of the following would be a Type II error?

A) Deciding that the new lenses are more expensive, when in fact they are cheaper.

B) Deciding that, on average, the new lenses are cheaper, when in fact they are not.

C) Deciding that, on average, the new lenses are not really cheaper, when in fact they are.

D) Deciding that the prices of new lenses are exactly the same as the old ones, when in fact they are not.

E) Deciding that the prices of old lenses are exactly the same as the new ones, when in fact they are not.

Answer: C L.O.: 14-1, 12-4 26) Which of the following is not an assumption or condition that needs to be checked for a twosample t-test for the difference between two means?

A) Independence Assumption B) Randomization Condition C) 10% Condition D) Nearly Normal Condition E) 90% Condition Answer: E L.O.: 14-1

23 .

Use the following to answer the question(s) below.

Preparing wheat for use in bread and pasta products generally involves both milling and bleaching. A company that processes wheat is interested in determining the best combination of milling and bleaching that results in a desirable wheat product without sacrificing fibre content.

They vary the milling time (short, medium and long) and bleaching (no bleaching and bleaching) and measure fibre content (gms/100 grams) of the resulting wheat product. The partial ANOVA results apply.

27) The F-statistic for testing whether bleaching has an effect on fibre content is A) 17.22.

B) 19.01.

C) 1.99.

D) 1.43.

E) 45.22.

Answer: A L.O.: 15-3 28) The F-statistic for testing whether milling has an effect on fibre content is A) 17.22.

B) 19.01.

C) 1.99.

D) 1.43.

E) 45.22.

Answer: B L.O.: 15-3

24 .

29) The P-value associated with the F-statistic for the interaction effect is 0.18. Based on this we can conclude that A) there is a significant interaction effect.

B) since there is a significant interaction effect, bleaching and milling have no effect on fibre content.

C) the significance of the interaction effect will not influence the interpretation of the main effects on fibre content due to milling and bleaching.

D) there is a significant interaction effect, and it is not appropriate to interpret the main effects on fibre content due to milling and bleaching separately.

E) there is no significant interaction effect, and it is appropriate to interpret the main effects on fibre content due to milling and bleaching separately.

Answer: E L.O.: 15-3 30) Which of the following is true about this study?

A) It is an observational study.

B) It is a completely randomized design in one factor.

C) We use the one-way analysis of variance.

D) It is an experimental study.

E) This is a retrospective study.

Answer: D L.O.: 15-2 Use the following to answer the question(s) below.

A local politician was interested in determining whether income level affects opinion regarding the governments' bailout bill of the auto industry during the 2008 financial crisis. He surveyed a sample of his constituents and got the following results.

Opinion Income Level < $ 200,000 $ 50,000 to $ 200,000 > $50,000

Favor 38 30 32

Oppose 29 42 59

31) The correct null hypothesis to be tested is A) opinion regarding the governments' bailout bill of the auto industry is independent of income level.

B) there is a relationship between income level and opinion.

C) opinion depends on income level.

D) opinion and income level are not independent.

E) there is a association between income level and opinion.

Answer: A L.O.: 16-1, 16-3

25 .

32) The calculated value of the Chi-square statistic is A) 7.433.

B) 29.13.

C) 40.70.

D) 5.999.

E) 2.347.

Answer: A L.O.: 16-3 33) At the 0.01 level of significance, the correct conclusion is A) income level affects opinion.

B) there is a relationship between income level and opinion.

C) since P-value = 0.024 > 0.01, we fail to reject the null hypothesis. Opinion and income level are independent.

D) reject the null hypothesis.

E) as χ2 = 7.433 < χcr2 = 9.210, we support the alternative hypothesis and find that there is an association between income level and opinion.

Answer: C L.O.: 16-3 34) The best tasting ice creams are generally high in fat content, which gives them a creamy texture. Four brands of ice cream were tested by consumers who graded their level of creaminess (A = very creamy to F = not creamy). Each brand was rated by a different group of consumers (the data are shown below).

Brand A A B AB+ A

Brand B A AB+ A A-

Brand C C C+ BC B-

Brand D BC+ C C C-

Using the Kruskal-Wallis test, the value of H is A) 14.51.

B) 22.10.

C) 6.351.

D) 5.999.

E) 1022.

Answer: A L.O.: 17-2

26 .

35) The best tasting ice creams are generally high in fat content, which gives them a creamy texture. Four brands of ice cream (two national and two local) were tested by consumers who graded their level of creaminess (A = very creamy to F = not creamy). Each brand was rated by a different group of consumers (the data are shown below).

Brand A A B AB+ A

Brand B A AB+ A A-

Brand C C C+ BC B-

Brand D BC+ C C C-

Using the Kruskal-Wallis test, at α = 0.10 we would conclude that A) the alternative hypothesis should be rejected.

B) the null hypothesis should be accepted.

C) there is no difference in creaminess among the brands.

D) the null hypothesis should be rejected and at least one of the brands has a different distribution from the others.

E) as H = 14.514 > χ2 = 6.251, the level of creaminess is the same for all brands.

Answer: D L.O.: 17-2 36) Suppose that ten new smart phone models were evaluated by two consumer electronics magazines (Popular Electronics and Electronics Now) from 1 (best) to 10 (worst) as shown below. To determine if there is a difference in the rankings between the two magazines, the appropriate nonparametric method is Model 1 2 3 4 5 6 7 8 9 10

Popular Electronics 8 3 7 4 2 1 10 5 6 9

Electronics Now 7 6 5 3 1 2 8 9 4 10

A) Wilcoxon rank-sum test.

B) Wilcoxon signed-rank test.

C) Spearman's rho test.

D) Kruskal-Wallis test.

E) Kendall's tau test.

Answer: B L.O.: 17-2, 17-3 27 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Part III: Exploring Relationships Among Variables Multiple Choice - Test A Use the following to answer the question(s) below.

For many countries tourism is an important source of revenue. Data are collected on the number of foreign visitors to a country (in millions) and total tourism revenue (in billions of dollars) for a sample of 10 countries. Below is the regression analysis output with tourism revenue as the dependent variable.

1) The standard error of the slope for this estimated regression equation is A) 2.58307.

B) 3.462.

C) 0.07917.

D) 6.672.

E) 0.29497.

Answer: C L.O.: 18-1 2) The calculated t-statistic to test whether the regression slope is significantly different from zero is A) 6.20.

B) 13.88.

C) 0.07917.

D) 2.58307.

E) 3.73.

Answer: E L.O.: 18-1

1 .

3) At the 0.05 level of significance, A) we reject the alternative hypothesis.

B) we do not reject the null hypothesis.

C) we conclude that the number of foreign visitors is not significant in explaining tourism revenue.

D) we reject the null hypothesis, and we conclude that the number of foreign visitors is significant in explaining tourism revenue.

E) we support the null hypothesis and we conclude that the number of foreign visitors and tourism revenue are not related.

Answer: D L.O.: 18-1 4) How much of the variability in tourism revenue is accounted for by the number of foreign visitors?

A) 63.4% B) 13.8% C) 2.58 billion $ D) 21.464% E) 3.73 billion $ Answer: A L.O.: 18-1, 7-2 5) If we were interested in predicting the tourism revenue for a particular country that had 30 million foreign visitors A) we should construct a confidence interval using the equation Tourism = 0.295 + 21.5 Visitors.

B) we should construct a prediction interval using the equation Tourism = 21.5 + 0.295 Visitors.

C) we should use the equation Tourism = 0.295 + 21.5 Visitors.

D) we should use the coefficient R2 = 0.634.

E) we should use the correlation coefficient r = = 0.796.

Answer: B L.O.: 18-1, 18-3, 7-2 6) Which statement about residuals plot is true?

A) A pattern of increasing spread indicates the predicted values become less reliable as the explanatory variable increases.

B) If all of the residuals are very small, the model will not predict accurately.

C) High-leverage points always have large residuals.

D) The outliers always deserve special attention because they produce small residuals.

E) Residuals reveal data that behave differently. The plot provides clues for fixing the regression model.

Answer: E L.O.: 19-1

2 .

7) The model = 12 + 20 Diameter can be used to predict the breaking strength of a rope (in kilograms) from its diameter (in centimetres). According to this model, how much force should a rope one-half centimeter in diameter withstand?

A) 484 kg B) 16 kg C) 22 kg D) 256 kg E) 4.7 kg Answer: A L.O.: 19-3 8) The residual plot for a linear regression model is shown below.

Which of the following is true?

A) The linear model is okay because approximately the same number of points is above the line as below it.

B) The linear model is okay because the association between the two variables is fairly strong.

C) The linear model is okay because there is no extreme outlier.

D) The linear model is okay because there is no pattern.

E) The linear model is not good because of the curve in the residuals.

Answer: E L.O.: 18-1, 7-1

3 .

Use the following to answer the question(s) below.

In order to examine if there is a relationship between the size of cash bonuses and pay scale, data were obtained on the average annual cash bonus and the average annual pay for a sample of 20 companies. Below is the regression analysis output with annual cash bonus as the dependent variable.

9) What is the correlation between average annual cash bonus and average annual pay?

A) -0.223 B) 0.472 C) 0.108 D) -0.540 E) 0.245 Answer: B L.O.: 18-2, 7-2, 6-2 10) At 5% significance level, which of the following statements is true about the correlation between average annual cash bonus and average annual pay?

A) It is not significantly different from zero.

B) It is negative but not significantly different from zero.

C) It is positive and significantly different from zero.

D) It is negative and significantly different from zero.

E) We fail to reject the null hypothesis Hο : ρ = 0.

Answer: C L.O.: 18-2, 6-2

4 .

11) Below is the plot of residuals versus fitted values for this regression model.

Based on the plot, which assumption/condition is definitely violated?

A) Equal Variance B) Linearity C) Normality D) Independence E) Randomization Answer: A L.O.: 18-1

5 .

Use the following to answer the question(s) below.

Weekly commodity prices for heating oil (in cents) were obtained and regressed against time.

Below is the regression output and residual plots from fitting a linear model.

6 .

12) Based on the output and plots, which of the following statements is not true?

A) The t-test for the regression slope indicates that it is significantly different from zero.

However, histogram shows that the distribution is skewed to the right.

B) According to the regression output, the model explains 71.9% of the variability in heating oil prices. However, the residual plot shows a clear pattern and curvature.

C) The normal probability plot shows some bend and indicates that we probably cannot proceed with regression inference.

D) The residual plot suggests that the Independence assumption might be violated.

E) The histogram and plots show that all assumptions and conditions for regression inference are met.

Answer: E L.O.: 18-1, 19-1, 19-2, 7-2 7 .

13) Which of the following statement is true?

A) The normal probability plot shows no bend and indicates that Independence assumption is satisfied.

B) The residual plot has no pattern and indicates that Independence assumption is satisfied.

C) The histogram is relatively bell-shaped and indicates that Independence assumption is satisfied.

D) The t-test for the regression slope indicates that Independence assumption is satisfied.

E) The histogram and plots show that not all assumptions and conditions for regression inference are met. It looks like data are highly correlated over time. So, we should test the model for autocorrelation.

Answer: E L.O.: 19-1, 19-2 14) The Durbin-Watson statistic indicates A) that there is evidence of positive autocorrelation.

B) that there is evidence of negative autocorrelation.

C) that there is no evidence of positive autocorrelation.

D) that there is no evidence of negative autocorrelation.

E) Since the Durbin-Watson statistic falls between the critical values, the test is inconclusive.

Answer: A L.O.: 19-2

8 .

15) A forester would like to estimate the diameter of maple trees based on age. She gathers data from trees that have been cut and plots their diameters (in inches) against their ages (in years).

She fits a linear model and both the scatterplot and residual plots are shown below.

Which of the following is true?

A) If we used this model to predict the diameter of a maple tree that is 50 years old, the predicted value would be too low.

B) If we used this model to predict the diameter of a maple tree that is 50 years old, the predicted value would be quite reliable.

C) Re-expressing these data by taking the logarithm of age would not improve this model.

D) The residual plot shows no bend. We should not consider transforming data.

E) If we used this model to predict the diameter of a maple tree that is 50 years old, the predicted value would be too high; furthermore, re-expressing these data by taking the logarithm of age would improve this model.

Answer: E L.O.: 19-3

9 .

Use the following to answer the question(s) below.

A large pharmaceutical company selected a random sample of new hires and obtained their job performance ratings based on their first six months with the company. These data were used to build a multiple regression model to predict the job performance of new hires based on age, GPA and gender (female = 1 and male = 0). The results of the analysis are shown below.

16) Based on the F-statistic and associated P-value, we can conclude that at α = 0.05 A) the regression model is not significant overall.

B) all independent variables in the model are significant.

C) the regression model is significant overall.

D) none of the independent variables in the model are significant.

E) only GPA variable in the model is significant.

Answer: C L.O.: 20-2 17) How much of the variability in Job Performance is explained by the regression model?

A) 30.33% B) 77.7% C) 5.56% D) 60.76% E) 30.99% Answer: B L.O.: 20-2 18) At α = 0.05, we can conclude that A) Age is not a significant variable in predicting job performance.

B) GPA is a significant variable in predicting job performance.

C) the regression coefficient associated with GPA is significantly different from zero.

D) Gender is a significant variable in predicting job performance.

E) the regression coefficient associated with Age is not significantly different from zero.

Answer: D L.O.: 20-2 10 .

19) Which of the following is the correct interpretation for the regression coefficient of Gender?

A) The regression coefficient indicates that the job performance score for a female will, on average, be 9.06 points higher than for males of the same age and GPA. B) The regression coefficient indicates that the job performance score for a female will, on average, be 9.06 points lower than for males of the same age and GPA. C) The regression coefficient indicates that the job performance score for a female will, on average, be 9.06 times higher than for males.

D) The regression coefficient indicates that the job performance score for a female will, on average, be 9.06 times lower than for males.

E) The regression coefficient indicates that the job performance score for a female will, on average, be 2.314 times lower than for males.

Answer: A L.O.: 21-3 20) Which of the following is not true about the best regression models?

A) They definitely have more predictors than the regular models.

B) They have a relatively high R2 value.

C) They have predictors that are reliably measured and relatively unrelated to each other.

D) They have no cases with extraordinarily high leverage that might dominate and alter the model.

E) They have relatively small P-values for the F- and t-statistics.

Answer: A L.O.: 21-3 Multiple Choice - Test B

11 .

Use the following to answer the question(s) below.

Data were collected for a sample of 12 pharmacists to determine if years of experience and salary are related. Below are the regression analysis results. The dependent variable is Salary in thousands of dollars.

1) The standard error of the slope for this estimated regression equation is A) 3.381.

B) 0.2149.

C) 5.58485.

D) 82.8.

E) 1.4882.

Answer: B L.O.: 18-1 2) The calculated t-statistic to test whether the regression slope is significant is A) 10.99.

B) 47.97.

C) 31.2.

D) 6.93.

E) 5.58485.

Answer: D L.O.: 18-1 3) The P-value associated with this statistic is < 0.001. At the 0.05 level of significance A) we reject the alternative hypothesis.

B) we fail to reject the null hypothesis.

C) there is no evidence that the number of years of experience is significant in explaining pharmacists' salary.

D) we reject the null hypothesis, and we conclude that there is strong evidence of an association between years of experience and pharmacists' salary.

E) we support the null hypothesis, and we conclude that years of experience and pharmacists' salary are not related.

Answer: D L.O.: 18-1 12 .

4) How much of the variability in pharmacists' salary is accounted for by years of experience?

A) 82.8% B) 47.97% C) 5.58485 thousand dollars D) 10.99% E) 98.9% Answer: A L.O.: 18-1 5) Using the estimated regression equation to predict salary for 10 years of experience gives the following results.

Which of the following is true?

A) 95% of pharmacists with 10 years of experience earn between $38,960 and $65,130.

B) 95% of pharmacists with 10 years of experience earn between $48,010 and $56,080.

C) We are 95% confident that a particular pharmacist who has 10 years of experience earns between $38,960 and $65,130.

D) We are 95% confident that a particular pharmacist who has 10 years of experience earns between $48,010 and $56,080.

E) 52.05% of pharmacists with 10 years of experience on average earn between $48,010 and $56,080.

Answer: C L.O.: 18-1, 18-3 6) Which statement about re-expressing data is true?

A) To make unimodal distribution that is skewed to the left more symmetric we should take the square root of the variable.

B) Transforming data cannot make a scatterplot and residual plot less spread out.

C) Transforming data is based only on the logarithmic function of the response variable.

D) One goal of re-expressing may be to make the variability of the response variable more uniform.

E) Re-expressing data by the logarithms should be used only when we want make the form of the scatterplot more nearly linear.

Answer: D L.O.: 19-3

13 .

7) The model = 3.30 + 0.235 Speed can be used to predict the stopping distance (in metres) for a car traveling at a specific speed (in kph). According to this model, about how much distance will a car going 65 kph need to stop?

A) 345.0 metres B) 18.6 metres C) 27.0 metres D) 4.3 metres E) 729.0 metres Answer: A L.O.: 19-3 8) A least squares estimated regression line has been fitted to a set of data and the resulting residual plot is shown. Which is true?

A) The linear model seems appropriate.

B) The linear model is poor because some residuals are large.

C) The linear model is poor because there is a pattern.

D) The plot shows a bend, thus a curved model would be more appropriate.

E) There is one extreme outlier, a transformation of the data is recommended.

Answer: A L.O.: 18-1, 7-1

14 .

Use the following to answer the question(s) below.

Stock prices and earnings per share (EPS) data were collected for a sample of 15 companies.

Below are the regression results. The dependent variable is Stock Price.

9) What is the correlation between stock price and EPS? A) -0.975 B) 0.975 C) 0.906 D) 0.950 E) -0.950 Answer: B L.O.: 18-2, 7-2, 6-2 10) Which of the following statements is true about the correlation between stock price and EPS? A) The correlation is negative.

B) The correlation is not significantly different from zero.

C) The correlation is positive and significantly different from zero.

D) We fail to reject the null hypothesis Hο : ρ ≠ 0.

E) As t statistic for the correlation coefficient test equals 15.82 and associated P-value is very small, we fail to support the alternative hypothesis HΑ : ρ ≠ 0.

Answer: C L.O.: 18-2, 7-2, 6-2

15 .

11) Below are residual plots for this regression model.

16 .

Based on these plots, which of the following statements is true?

A) The scatterplot of the residuals against the predicted values shows patter.

B) The scatterplot of residuals against the predicted values shows no possible outlier.

C) The histogram is bell-shaped. The Nearly Normal condition is reasonably satisfied.

D) The histogram indicates that the Independence assumption is violated.

E) The normal probability plot shows no bend.

Answer: C L.O.: 18-1

17 .

Use the following to answer the question(s) below.

A linear regression model was fit to data representing technology adoption over time. The regression output and residual plot appears below.

18 .

12) Based on the output and plot, which of the following statements is not true?

A) According to the regression output, the model explains 82.5% of the variability in Technology Adoption. However, the residual plot shows a pattern and curvature.

B) The scatter plot of the residuals against the predicted values shows a pattern. A regression model applied to the data is questionable.

C) The t-test for the regression slope indicates that it is significantly different from zero, but the residual scatter plot shows that Equal Variance assumption is violated.

D) The regression model is applied to the time series data. The residual plot suggests that the Independence assumption might be violated. We have to use Durbin-Watson statistic to detect autocorrelation.

E) The plot shows that all assumptions and conditions for regression inference are met. R2 and P-value report that there is strong correlation between Technology Adoption and Time.

Answer: E L.O.: 18-1, 19-1, 19-2, 7-2 13) It is known that at 1% significance level the critical values for Durbin-Watson statistic are 0.738 and 1.038. The Durbin-Watson statistic indicates A) that the residuals are positively autocorrelated.

B) that the residuals are negatively autocorrelated.

C) that there is no positive autocorrelation.

D) that there is no negative autocorrelation.

E) that the test is inconclusive as dL < D < dU. Answer: A L.O.: 19-2

19 .

Use the following to answer the question(s) below.

A newly developed drug is tested to determine absorption levels in a patient's bloodstream. A patient is injected with the drug and the concentration (units/cc) in the patient's blood is measured every hour for seven hours. Below is the output from fitting a linear regression model.

20 .

14) Which of the following is true?

A) The linear model is absolutely perfect for estimation of the concentration level after 10 hours.

The scatterplot shows no bend.

B) This model will probably underestimate the concentration level after 10 hours. The scatterplot shows some bend and suggests that the linear model is not appropriate.

C) This model will definitely overestimate the concentration level after 10 hours, as the scatterplot shows two extreme outliers.

D) The linear model is appropriate for estimation of the concentration level after 10 hours. It explains 89.21% of the variability in blood concentration levels of the drug.

E) The linear model is not appropriate because it explains only 4.72% of the variability in blood concentration levels of the drug.

Answer: B L.O.: 18-1, 18-2, 18-3, 7-2

21 .

15) Re-expressing these data results in the following model

The residuals plotted against the fitted values for this model is shown below.

What is true about the predicted concentration level after 10 hours has elapsed?

A) The predicted value is 0.1000 units/cc.

B) This value is considered as a regular one.

C) This value is accurate because R2 = 100.0%.

D) The predicted value is 1.2589 units/cc, and this value is considered an extrapolation.

E) 10 hours falls into the range of the predictor variable Time Elapsed.

Answer: D L.O.: 19-1

22 .

Use the following to answer the questions below.

The following is output from regression analysis performed to develop a model for predicting a firm's Price-Earnings Ratio (PE) based on Growth Rate, Profit Margin, and whether or not the firm is Green (1 = Yes, 0 = No).

16) Based on the F-statistic and associated P-value, we can conclude at α = 0.05 that A) the regression model is not significant overall.

B) all independent variables in the model are significant.

C) the regression model is significant overall.

D) none of the independent variables in the model are significant.

E) only Profit Margin variable in the model is significant.

Answer: C L.O.: 20-2 17) At α = 0.05, we can conclude that A) Growth Rate is not a significant variable in predicting a firm's PE ratio.

B) Profit Margin is a significant variable in predicting a firm's PE ratio.

C) the regression coefficient associated with Growth Rate is not significantly different from zero.

D) whether or not a firm is Green is significant in predicting its PE ratio.

E) the regression coefficient associated with whether or not a firm is Green is not significantly different from zero.

Answer: D L.O.: 20-2

23 .

18) Which of the following is the correct interpretation for the regression coefficient of Green?

A) The regression coefficient indicates that the PE ratio of a firm that is green will, on average, be 2.09 points higher than a firm that is not green with the same profit growth rate and profit margin.

B) The regression coefficient indicates that the PE ratio of a firm that is green will, on average, be 2.09 points lower than a firm that is not green with the same profit growth rate and profit margin.

C) The regression coefficient indicates that the PE ratio of a firm that is green will, on average, be 2.09 times higher than a firm that is not green.

D) The regression coefficient indicates that the PE ratio of a firm that is green will, on average, be 2.09 times lower than a firm that is not green.

E) The regression coefficient is not significantly different from zero.

Answer: A L.O.: 20-2, 21-1 19) Which of the following measures is used to check for collinearity when building a multiple regression model?

A) Cook's Distance B) Variance Inflation Factor C) Determination Coefficient D) Standardized Residual E) Leverage Index Answer: B L.O.: 21-3 20) Which of the following is/are not correct about the best regression models?

A) They have relatively few predictors.

B) They have a relatively high R2 value.

C) They have predictors that are reliably measured and relatively unrelated to each other.

D) They have no cases with extraordinarily high leverage that might dominate and alter the model.

E) They can be obtained only by stepwise regression method.

Answer: E L.O.: 21-3

24 .

Business Statistics, Cdn. Ed., 4e (Sharpe) Part IV: Using Statistics for Decision Making Multiple Choice - Test A Use the following to answer the question below.

The time series graph below shows monthly sales figures for a specialty gift item sold on the Home Shopping Network (HSN).

1) The dominant time series component in these data is A) cyclical.

B) seasonal.

C) random walk.

D) irregular.

E) index numbers.

Answer: B L.O.: 22-1, 22-2

1 .

Use the following to answer the question(s) below.

The monthly returns on a social choice portfolio comprised of "green" companies are shown below for the last six months of 2015.

Month July August September October November December

Monthly Return 2.2% 2.5 1.8 1.4 1.1 1.9

2) The forecasted monthly return for January 2016 using a three-month moving average is A) 2.8.

B) 1.9.

C) 2.0.

D) 2.4.

E) 1.5.

Answer: E L.O.: 22-3 3) Use a single exponential smoothing (SES) model with α = 0.8 to forecast for January 2016.

Assume that the forecast for December 2015 was 1.18%.

A) 1.50 B) 1.18 C) 1.76 D) 1.90 E) 2.20 Answer: C L.O.: 22-3

2 .

Use the following to answer the question(s) below.

Sunny Side Condominiums recently purchased land outside of Toronto and is trying to decide the size complex it should build (large or small). The following payoff table (in thousands of dollars) considers three possible levels of demand.

4) Using the maximax approach, Sunny Side should A) build a small complex with medium demand.

B) build a large complex.

C) build a small complex with high demand.

D) build a small complex with low demand.

E) build a large complex if demand is high.

Answer: B L.O.: 23-1 5) If there is a 45% chance that the demand level will be low, 30% that it will be medium and 25% chance that it will be high, the expected value (in thousands of dollars) associated with the best action is A) $326.25.

B) $310.

C) $535.

D) $208.75.

E) $225.

Answer: A L.O.: 23-2 6) What is the expected value of perfect information?

A) $326.25 B) $310 C) $535 D) $208.75 E) $225 Answer: D L.O.: 23-2

3 .

7) The standard deviations (in thousands of dollars) for building a small and large complex are 535 and 976, respectively. Based on the resulting coefficients of variation (CV), which of the following statements would be true?

A) The CV of building a large complex is less than that of building a small complex.

B) The CV of building a small complex is less than that of building a large complex.

C) The risk averse action would be to build a large complex.

D) Since the CV of building a large complex is less than that of building a small complex, the risk averse action would be to build a large complex.

E) The CV of building a small complex is about the same as that of building a large complex.

Answer: B L.O.: 23-2 8) Machine oil is used by clothing manufacturers to lubricate and protect sewing machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is 101 cP and the process standard deviation is 1.50 cP. What type of chart should be used to ensure the process remains in control?

A) p chart B) c chart C) R chart D) Control chart for individual observations (run chart) E) ARL chart Answer: D L.O.: 24-1 9) Machine oil is used by clothing manufacturers to lubricate and protect sewing machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is 101 cP and the process standard deviation is 1.50 cP. What are the limits for a runs chart to be used to see that the process remains control?

A) 99.5 cP and 102.5 cP B) 96.5 cP and 105.5 cP C) 95.5 cP and 106.5 cP D) 92.5 cP and 110.5 cP E) 99.5 cP and 107.5 cP Answer: B L.O.: 24-1

4 .

10) Machine oil is used by clothing manufacturers to lubricate and protect sewing machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is 101 cP and the process standard deviation is 1.50 cP. What is the Cpk index if the customer specifications require viscosity of the machine oil to be 100 cP ± 4.5 cP? A) 1.0 B) 1.22 C) 0.78 D) 1.67 E) 1.28 Answer: C L.O.: 24-2, 24-4 11) By design, a required dimension on a part is 0.575 cm plus or minus 0.008 cm. Assume that the process producing this part is stable with a mean of 0.579 cm and standard deviation of 0.002 cm. What is the Cp index?

A) 1.33 B) 2.00 C) 0.67 D) 1.00 E) 0.33 Answer: A L.O.: 24-2 12) A producer of specialty products uses a variety of natural and man-made materials to make unique countertops for kitchens and baths. One product line mixes concrete and natural river stone to make countertops that are polished to a high shine revealing unique patterns.

Occasionally coarse sand will result in undesirable pitting and rough spots on surfaces.

Consequently, as part of its quality control efforts, 8 by 4 metre polished slabs are checked periodically for imperfections. For each slab inspected the number of imperfections (pits, rough spots, etc.) is recorded. What type of control chart should be used for these data?

A) Run chart B) p chart C) c chart D) x-bar and R charts E) ARL chart Answer: C L.O.: 24-1, 24-2, 24-3 13) The minimax choice A) minimizes the maximum cost.

B) maximizes the minimum cost.

C) minimizes the maximum profit.

D) minimizes the maximum revenue.

E) maximizes the maximum possible return.

Answer: A L.O.: 23-1 5 .

Multiple Choice - Test B Use the following to answer the question(s) below.

The time series graph below shows annual sales figures (in thousands of dollars) for a well known department store chain.

1) The dominant time series component in these data is A) trend.

B) seasonal.

C) random walk.

D) irregular.

E) index numbers.

Answer: A L.O.: 22-1, 22-2 2) Which model would be most appropriate for forecasting this series?

A) Moving Average using L = 3 B) Single Exponential Smoothing with α = 0.1 C) Quadratic Trend D) Linear Trend E) Seasonal Regression Answer: C L.O.: 22-3, 22-5

6 .

3) Quarterly returns were forecasted for a mutual fund made up of technology stocks. The forecast errors for the last six quarters are as follows: -0.47, 1.12, -0.85, 1.27, 0.07, and -0.05.

The MAD based on these forecast errors is A) 0.77.

B) 0.98.

C) 0.22.

D) 0.18.

E) 0.64.

Answer: E L.O.: 22-4 Use the following to answer the question(s) below.

As a result of the financial crisis in the fall of 2008, when the government intervened to help the economy, an investor was considering various strategies for her money and the estimated profits would depend on how successful the intervention would be in helping the economy. The estimated annual return for two different investment strategies are shown in the following table.

4) Using the maximax approach, the investor should A) choose 20% stocks 80% bonds.

B) choose 80% stocks 20% bonds.

C) choose 20% stocks 80% bonds if the economy rebounds.

D) choose 80% stocks 20% bonds if the economy declines.

E) choose 20% stocks 80% bonds if there is no change.

Answer: B L.O.: 23-1 5) If there is a 30% chance that the economy will decline, 50% that there will be no change and 20% chance that it will rebound, the expected value associated with the best investment strategy is A) $590.

B) -$250.

C) $1290.

D) $700.

E) -$450.

Answer: A L.O.: 23-2

7 .

6) The expected value of perfect information is A) $590.

B) -$250.

C) $1290.

D) $700.

E) -$450.

Answer: D L.O.: 23-2 7) The standard deviation associated with the investment strategy of allocating 80% to stocks and 20% to bonds is A) $4,500.

B) $2,250.

C) $3,473.

D) $2,567.

E) $1,782.

Answer: C L.O.: 23-2 8) A producer of specialty products uses a variety of natural and man-made materials to make unique countertops for kitchens and baths. One product line mixes concrete and natural river stone to make countertops that are polished to a high shine revealing unique patterns.

Occasionally coarse sand will result in undesirable pitting and rough spots on surfaces.

Consequently, as part of its quality control efforts, 8 by 4 metre polished slabs are checked periodically for imperfections. For each slab inspected the number of imperfections (pits, rough spots, etc.) is recorded. If the average number of imperfections per 8 by 4 metre polished slab is 2.6, the control limits for the appropriate control chart are A) 0 and 7.44.

B) 0.98 and 4.21.

C) 0 and 9.89.

D) 1.24 and 3.96.

E) 1.24 and 4.21.

Answer: A L.O.: 24-3

8 .

9) An automatic filling process is used to dispense hand sanitizer into small purse size bottles.

The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml. The estimated process standard deviation is A) 2.75 ml.

B) 2.44 ml.

C) 1.88 ml.

D) 1.34 ml.

E) 35.2 ml.

Answer: D L.O.: 24-2 10) An automatic filling process is used to dispense hand sanitizer into small purse size bottles.

The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml. The control limits for the R chart are A) 0 and 4.357 ml.

B) 0 and 6.276 ml.

C) 0 and 2.888 ml.

D) 2.00 and 3.50 ml.

E) 2.00 and 4.357 ml.

Answer: B L.O.: 24-2 11) An automatic filling process is used to dispense hand sanitizer into small purse size bottles.

The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml. The control limits for the x-bar chart are A) 68.48 and 76.52 ml.

B) 71.16 and 73.84 ml.

C) 70.50 and 74.50 ml.

D) 72 and 73 ml.

E) 66.84 and 78.16 ml.

Answer: C L.O.: 24-2

9 .

12) In order to achieve higher levels of customer satisfaction, a company begins monitoring the complaint resolution process of its customer service representatives. As a first step, the company decides to collect data on the number of unanswered calls out of the first 250 incoming calls to its call centre made each day. At the end of monitoring 25 days, it was found that a total of 500 incoming calls went unanswered. The control limits for the p chart of these data are A) 0.029 and 0.131.

B) 0 and 0.304.

C) 0.066 and 0.094.

D) 0.048 and 0.112.

E) 0.102 and 0.112.

Answer: A L.O.: 24-3 13) The minimin choice strategy is A) the action that minimizes the minimum possible returns across all states of nature.

B) the action that minimizes the maximum possible cost across all states of nature.

C) the action that minimizes the minimum possible cost across all states of nature.

D) the action that maximizes the minimum possible cost across all states of nature.

E) the action that maximizes the minimum possible returns across all states of nature.

Answer: C L.O.: 23-1

10 .