Statistics for management and economics (11e) part 1

Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Interval Nominal Ordinal Data types Wilcoxon rank sum test Section 19-1 Sign test Section 19-2 Percentiles and quartiles Section 4-3 Chi-squared test of a contingency table Section 15-2 between two proportions Section 13-5 z-test and estimator of the difference Wilcoxon signed rank sum test Section 19-2 Wilcoxon rank sum test Section 19-1 variances Section 13-4 F-test and estimator of ratio of two t-test and estimator of mean difference Section 13-3 Median Section 4-1 Chi-squared goodness-offit test Section 15-1 of a proportion Section 12-3 z-test and estimator Pie chart Section 2-2 Bar chart Section 2-2 Frequency distribution Section 2-2 Chi-squared test and estimator of a variance Section 12-2 mean Section 12-1 t-test and estimator of a Percentiles and quartiles Section 4-3 Range, variance, and standard deviation Section 4-2 Mean, median, and mode Section 4-1 Unequal-variances t-test and estimator of the difference between two means: independent samples Section 13-1 Friedman test Section 19-3 Kruskal-Wallis test Section 19-3 Chi-squared test of a contingency table Section 15-2 Friedman test Section 19-3 Kruskal-Wallis test Section 19-3 Two-factor analysis of variance Section 14-5 Two-way analysis of variance Section 14-4 Tukey’s multiple comparison method Section 14-2 Spearman rank correlation Section 19-4 Chi-squared test of a contingency table Section 15-2 Spearman rank correlation Section 19-4 Simple linear regression and correlation Chapter 16 Least squares line Section 4-4 Coefficient of determination Section 4-4 Coefficient of correlation Section 4-4 Covariance Section 4-4 LSD multiple comparison method Section 14-2 Line chart Section 3-2 Scatter diagram Section 3-3 One-way analysis of variance Section 14-1 Equal-variances t-test and estimator of the difference between two means: independent samples Section 13-1 Histogram Section 3-1 Analyze Relationship between Two Variables Compare Two or More Populations Compare Two Populations Describe a Population Problem Objectives A GUIDE TO STATISTICAL TECHNIQUES Not covered Not covered Multiple regression Chapters 17 & 18 Analyze Relationship among Two or More Variables GENERAL SOCIAL SURVEY AND SURVEY OF CONSUMER FINANCES EXERCISES Chapter 12 13 14 15 16 17 18 19 GSS Page 2.66–2.73 3.23–3.27 3.72–3.78 4.19–4.22 4.49–4.52 4.77–4.79 4.145–4.150 12.54–12.58 12.117–12.123 12.171–12.178 13.54–13.68 13.106–13.109 13.121–13.122 13.167–13.184 13.235–13.257 A13.18–A13.28 14.23–14.46 14.67–14.80 14.98–14.99 A14.19–A14.31 15.21–15.23 15.53–15.62 A15.17–A15.32 16.50–16.65 16.101–16.112 16.142–16.150 A16.17–A16.31 17.18–17.21 17.43–17.46 A17.17–A17.35 18.24–18.33 18.40–18.42 19.17–19.30 19.58–19.59 19.85–19.93 19.107–19.117 A19.26–A19.42 43 59 73 95 104 109 135 387 411 421 453 472 479 497 506 515 534 545 557 589 599 611 627 663 670 681 689 711 715 730 750 758 777 793 804 812 829 SCF Page 2.74–2.78 3.28–3.31 3.79–3.81 4.23–4.26 4.53–4.56 4.80–4.82 4.151–4.154 12.59–12.69 12.124–12.129 12.179–12.190 13.69–13.80 13.110–13.111 13.123–13.126 13.185–13.193 13.258–13.260 A13.29–A13.38 14.47–14.56 14.81–14.82 44 59 73 96 105 110 135 388 411 422 454 472 479 498 508 515 536 546 A14.32–A14.42 15.24–15.25 15.63–15.78 A15.33–A15.43 16.66–16.75 590 600 612 629 664 A16.32–A16.41 17.22–17.24 690 712 A17.36–A17.43 731 19.31–19.34 778 A19.42–A19.49 830 Application Sections Section 4.5 (Optional) Application in Finance: Market Model (illustrating using a least squares line and coefficient of determination to estimate a stock’s market-related risk and its firm-specific risk)  125 Section 7.3 (Optional) Application in Finance: Portfolio Diversification and Asset Allocation (illustrating the laws of expected value, variance, and covariance)  218 Section 12.4 (Optional) Application in Marketing: Market Segmentation (using inference about a proportion to estimate the size of a market segment)  412 Section 14.6 (Optional) Application in Operations Management: Finding and Reducing Variation (using the analysis of variance to actively experiment to find sources of variation)  570 Section 18.3 (Optional) Human Resources Management: Pay Equity (using multiple regression to determine cases of discrimination)  751 Application Subsection Section 6.4 (Optional) Application in Medicine and Medical Insurance: Medical Screening (using Bayes’s Law to calculate probabilities after a screening test)  184 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Statistics for Management and Economics 11e Gerald Keller Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Statistics for Management and Economics, Eleventh Edition Gerald Keller Vice President, General Manager, Social Science & Qualitative Business: Erin Joyner Sr Product Team Manager: Joe Sabatino Sr Product Manager: Aaron Arnsparger Content Developer: Conor Allen Product Assistant: Renee Schnee Sr Marketing Director: Kristen Hurd © 2018, 2014 Cengage Learning® ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced or distributed in any form or by any means, except as permitted by U.S copyright law, without the prior written permission of the copyright owner For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Sr Marketing Manager: Nate Anderson Sr Content Project Manager: Martha Conway Manufacturing Planner: Ron Montgomery Production Service: SPi Global Sr Art Director: Michelle Kunkler Cover and Internal Designer: cmillerdesign Windows is a registered trademark of the Microsoft Corporation used herein under license Macintosh and Power Macintosh are registered trademarks of Apple Computer, Inc used herein under license Library of Congress Control Number: 2017932174 Cover Image: © Rawpixel.com/Shutterstock com Package: ISBN: 978-1-337-09345-3 Intellectual Property Analyst: Brittani Morgan Book Only: ISBN: 978-1-337-29694-6 Intellectual Property Project Manager: Reba Frederics Loose-leaf Edition: ISBN: 978-1-337-29876-6 Cengage Learning 20 Channel Center Street Boston, MA 02210 USA Cengage Learning is a leading provider of customized learning ­solutions with employees residing in nearly 40 different countries and sales in more than 125 countries around the world Find your local ­representative at www.cengage.com Cengage Learning products are represented in Canada by Nelson Education, Ltd To learn more about Cengage Learning Solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com Printed in the United States of America Print Number: 01 Print Year: 2017 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Brief Contents What Is Statistics?  Graphical Descriptive Techniques I  12 Graphical Descriptive Techniques II  45 Numerical Descriptive Techniques  86 Data Collection and Sampling  140 Probability 154 Random Variables and Discrete Probability Distributions  197 Continuous Probability Distributions  244 Sampling Distributions  286 10 Introduction to Estimation  310 11 Introduction to Hypothesis Testing  333 12 Inference about a Population  371 13 Inference about Comparing Two Populations  427 14 Analysis of Variance  517 15 Chi-Squared Tests  591 16 Simple Linear Regression and Correlation  631 17 Multiple Regression  692 18 Model Building  733 19 Nonparametric Statistics  762 20 Time-Series Analysis and Forecasting  831 iii Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 iv B rief C o ntents 21 Statistical Process Control  857 22 Decision Analysis  884 23 Conclusion 904 Appendix A Data File Sample Statistics  A-1 Appendix B Tables B-1 Appendix C Index Answers to Selected Even-Numbered Exercises  C-1 I-1 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Contents Introduction 1 Key Statistical Concepts  Statistical Applications in Business  Large Real Data Sets  Statistics and the Computer  Appendix Material to Download  11 1-1 1-2 1-3 1-4 Graphical Descriptive Techniques I  12 Introduction 13 2-1 Types of Data and Information  14 2-2 Describing a Set of Nominal Data  19 2-3 Describing the Relationship between Two Nominal Variables and Comparing Two or More Nominal Data Sets  34 Graphical Descriptive Techniques II  45 3-1 3-2 3-3 3-4 What Is Statistics?  Introduction 46 Graphical Techniques to Describe a Set of Interval Data  46 Describing Time-Series Data  60 Describing the Relationship between Two Interval Variables  66 Art and Science of Graphical Presentations  73 Numerical Descriptive Techniques  86 4-1 4-2 4-3 4-4 4-5 Introduction 87 Sample Statistic or Population Parameter  87 Measures of Central Location  87 Measures of Variability  96 Measures of Relative Standing  105 Measures of Linear Relationship  110 (Optional) Applications in Finance: Market Model  125 v Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 vi C o ntents 4-6 Comparing Graphical and Numerical Techniques  129 4-7 General Guidelines for Exploring Data  132 Appendix Review of Descriptive Techniques  138 Data Collection And Sampling  140 Introduction 141 5-1 Methods of Collecting Data  141 5-2 Sampling 144 5-3 Sampling Plans  146 5-4 Sampling and Nonsampling Errors  151 Probability 154 6-1 6-2 6-3 6-4 6-5 Random Variables and Discrete Probability Distributions  197 7-1 7-2 7-3 7-4 7-5 Introduction 155 Assigning Probability to Events  155 Joint, Marginal, and Conditional Probability  160 Probability Rules and Trees  172 Bayes’s Law  180 Identifying the Correct Method  191 Introduction 198 Random Variables and Probability Distributions  198 Bivariate Distributions  209 (Optional) Applications in Finance: Portfolio Diversification and Asset Allocation 218 Binomial Distribution  225 Poisson Distribution  232 Continuous Probability Distributions  244 Introduction 245 8-1 Probability Density Functions  245 8-2 Normal Distribution  251 8-3 (Optional) Exponential Distribution  268 8-4 Other Continuous Distributions  273 Sampling Distributions  286 Introduction 287 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 C o ntents 9-1 9-2 9-3 9-4 10 11 Introduction to Estimation  310 Introduction to Hypothesis Testing  333 11-1 11-2 11-3 11-4 12 13 Introduction 334 Concepts of Hypothesis Testing  334 Testing the Population Mean When the Population Standard Deviation Is Known 338 Calculating the Probability of a Type II Error  359 The Road Ahead  367 Inference About a Population  371 Introduction 372 12-1 Inference about a Population Mean When the Standard Deviation Is Unknown 372 12-2 Inference about a Population Variance  389 12-3 Inference about a Population Proportion  397 12-4 (Optional) Applications in Marketing: Market Segmentation  412 Sampling Distribution of the Mean  287 Sampling Distribution of a Proportion  299 Sampling Distribution of the Difference between Two Means  305 From Here to Inference  307 Introduction 311 10-1 Concepts of Estimation  311 10-2 Estimating the Population Mean When the Population Standard Deviation Is Known 315 10-3 Selecting the Sample Size  328 vii Inference about Comparing Two Populations  427 Introduction 428 13-1 Inference about the Difference between Two Means: Independent Samples 428 13-2 Observational and Experimental Data  455 13-3 Inference about the Difference between Two Means: Matched Pairs Experiment 459 13-4 Inference about the Ratio of Two Variances 472 13-5 Inference about the Difference between Two Population Proportions  479 Appendix 13 Review of Chapters 12 and 13  510 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 412 CHAPTER 12 12-4    ( O p t i o n a l ) A pp l i c at i o n s S e gm e n tat i o n in Marketing: Market Mass marketing refers to the mass production and marketing by a company of a single product for the entire market Mass marketing is especially effective for commodity goods such as gasoline, which are very difficult to differentiate from the competition, except through price and convenience of availability Generally speaking, however, mass marketing has given way to target marketing, which focuses on satisfying the demands of a particular segment of the entire market For example, the Coca-Cola Company has moved from the mass marketing of a single beverage to the production of several different beverages Among the cola products are Coca-Cola Classic, Diet Coke, and Caffeine-Free Diet Coke Each product is aimed at a different market segment Because there is no single way to segment a market, managers must consider several different variables (or characteristics) that could be used to identify segments Surveys of customers are used to gather data about various aspects of the market, and statistical techniques are applied to define the segments Market segmentation separates consumers of a product into different groups in such a way that members of each group are similar to each other, and there are differences between groups Market segmentation grew out of the realization that a single product can seldom satisfy the needs and wants of all consumers Managers must then formulate a strategy to target these profitable segments, using the four elements of the marketing mix: product, pricing, promotion, and placement There are many ways to segment a market Table 12.1 lists several different segmentation variables and their market segments For example, car manufacturers can use education levels to segment the market It is likely that high school graduates would be quite similar to others in this group and that members of this group would differ from university graduates We would expect those differences to include the types and brands of cars each group would choose to buy However, it is likely that income level would differentiate more clearly between segments Statistical techniques can be used to help determine the best way to segment the market These statistical techniques are more advanced than this textbook Consequently, we will focus our attention on other statistical applications Table 12.1  Market Segmentation Segmentation Variable Segments Geographic   Countries   Country regions Brazil, Canada, China, France, United States Midwest, Northeast, Southwest, Southeast Demographic   Age Under 5, 5–12, 13–19, 20–29, 30–50, older than 50   Education Some high school, high school graduate, some    college, college or university graduate   Income Under $20,000, $20,000−$29,999, $30,000−$49,999,   more than $50,000 Single, married, divorced, widowed   Marital status Social   Religion   Class Behavior   Media usage   Payment method Catholic, Protestant, Jewish, Muslim, Buddhist Upper class, middle class, working class, lower class TV, Internet, newspaper, magazine Cash, check, Visa, Mastercard Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 I n f erence A bout a P opu l ation 413 It is important for marketing managers to know the size of the segment because the size (among other parameters) determines its profitability Not all segments are worth pursuing In some instances, the size of the segment is too small or the costs of satisfying it may be too high The size can be determined in several ways The census provides useful information For example, we can determine the number of Americans in various age categories or the size of geographic residences For other segments, we may need to survey members of a general population and use the inferential techniques introduced in the previous section, where we showed how to estimate the total number of successes In Section 12-3, we showed how to estimate the total number of successes in a large finite population The confidence interval estimator is N q p^ ± zα/2 Å p^ (1 − p^ ) r n The following example demonstrates the use of this estimator in market segmentation e x a m p l e  12.6 DATA Xm12-06* Segmenting the Breakfast Cereal Market In segmenting the breakfast cereal market, a food manufacturer uses health and diet consciousness as the segmentation variable Four segments are developed: Concerned about eating healthy foods Concerned primarily about weight Concerned about health because of illness Unconcerned To distinguish between groups, surveys are conducted On the basis of a questionnaire, people are categorized as belonging to one of these groups A recent survey asked a random sample of 1,250 American adults (18 and older) to complete the questionnaire The categories were recorded using the codes The most recent census reveals that 244,137,873 Americans are 18 and older Estimate with 95% confidence the number of American adults who are concerned about eating healthy foods Solution: Identify The problem objective is to describe the population of American adults The data are nominal Consequently, the parameter we wish to estimate is the proportion p of American adults who classify themselves as concerned about eating healthy The confidence interval estimator we need to employ is p^ ± zα/2 Å p^ (1 − p^ ) n from which we will produce the estimate of the size of the market segment Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 414 CHAPTER 12 Compute M an u a l l y : To solve manually, we count the number of 1s in the file We find this value to be 269 Thus, p^ = 269 x = = 2152 n 1,250 The confidence level is − α = 95 It follows that α = 05, α/2 = 025, and zα/2 = z.025 = 1.96 The 95% confidence interval estimate of p is p^ (1 − p^ ) (.2152) (1 − 2152) = 2152 ± 1.96 = 2152 ± 0228 Å n Å 1,250 LCL = 1924 UCL = 2380 p^ ± zα/2 E x ce l W o r k b o o k XL S T A T Interpret We estimate that the proportion of American adults who are in group lies between 1924 and 2380 Because there are 244,137,873 adults in the population, we estimate that the number of adults who belong to group falls between LCL = N c p^ − zα/2 p^ (1 − p^ ) d = 244,137,873 1924 = 46,972,127 Å n Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 I n f erence A bout a P opu l ation 415 and UCL = N c p^ + zα/2 p^ (1 − p^ ) d = 244,137,873 2380 = 58,104,814 Å n We will return to the subject of market segmentation in other chapters where we demonstrate how statistics can be used to determine whether differences actually exist between segments E x e rc is e s The following exercises may be solved manually See Appendix A for the sample statistics of age who are in the market segment the university wishes to target 12.130 Xr12-130   A new credit card company is investigat- 12.132 Xr12-132*  The JC Penney department store chain ing various market segments to determine whether it is profitable to direct its advertising specifically at each one One of the market segments is composed of Hispanic people According to the United States census, there are 41,580,000 Hispanic adults (18 and over) people in the United States A survey of 475 Hispanics asked each how they usually pay for products that they purchase The responses are: Cash Check Visa MasterCard Other credit card Estimate with 95% confidence the number of Hispanics in the United States who usually pay by credit card 12.131 Xr12-131*   A California university is investigating expanding its evening programs It wants to target people between 25 and 55 years old who have completed high school but did not complete college or university To help determine the extent and type of offerings, the university needs to know the size of its target market A survey of 320 California adults was drawn and each person was asked to identify his or her highest educational attainment The responses are: Did not complete high school Completed high school only Some college or university College or university graduate The Public Policy Institute of California indicates that there are 16,015,493 Californians between the ages of  25 and 55 Estimate with 95% confidence the number of Californians between 25 and 55 years segments the market for women’s apparel by its identification of values The three segments are: Conservative Traditional Contemporary Questionnaires about personal and family values are used to identify which segment a woman falls into Suppose that the questionnaire was sent to a random sample of 1,836 women Each woman was classified using the codes 1, 2, and The latest census reveals that there are 124,723,003 adult women in the United States Use a 95% confidence level a Estimate the proportion of adult American women who are classified as traditional b Estimate the size of the traditional market segment 12.133 Xr12-133   Most life insurance companies are leery about offering policies to people over 64 When they the premiums must be high enough to overcome the predicted length of life The president of one life insurance company was thinking about offering special discounts to Americans over 64 who held full-time jobs The plan was based on the belief that full-time workers over 64 are likely to be in good health and would likely live well into their eighties To help decide what to do, he organized a survey of a random sample of the 44,679,192 American adults over 64 He asked a random sample of 325  Americans over 64 whether they c­urrently hold a full-time job (1 = No and = Yes) a Estimate with 95% confidence the size of this market segment b Write a report to the executives of an insurance company detailing your statistical analysis Source: United States Census Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 416 CHAPTER 12 12.134 Xr12-134  An advertising company was awarded the contract to design advertising for Rolls Royce automobiles An executive in the firm decided to pitch the product not only to the affluent in the United States but also to those who think they are in the top 1% of income earners in the country A survey was undertaken, which among other questions asked respondents 25 and over where their annual income ranked The following responses were given = Top 1% = Top 5% but not top 1% = Top 10% but not top 5% = Top 25% but not top 10% = Bottom 75% Estimate with 90% confidence the number of Americans 25 and over who believe they are in the top 1% of income earners The number of Americans over 25 is 211,306,936 (Source: United States Census) 12.135 Xr12-135  Suppose the survey in the previous exercise also asked those who were not in the top 1% whether they believed that within years they would be in the top 1% (1 = will not be in top 1% within years and = will be in top 1% within years) Estimate with 95% confidence the number of Americans who believe that they will be in the top 1% of income earners within years C h a p t e r S u m m a ry The inferential methods presented in this chapter address the problem of describing a single population When the data are interval, the parameters of interest are the population mean μ and the population variance σ The Student t-distribution is used to test and estimate the mean when the population standard deviation is unknown The chisquared distribution is used to make inferences about a population variance When the data are nominal, the parameter to be tested and estimated is the population proportion p The sample proportion follows an approximate normal distribution, which produces the test statistic and the interval estimator We also discussed how to determine the sample size required to estimate a population proportion We introduced market segmentation and described how statistical techniques presented in this chapter can be used to estimate the size of a segment Imp o r tant T e r ms : Robust 379 Chi-squared statistic  389 t-statistic 373 Student t-distribution 373 S y mb o l s : Symbol ν χ2 p^ ~ p Pronounced nu chi squared p hat p tilde Confidence interval estimator of σ2 F o r m u l as : Test statistic for μ t= Represents Degrees of freedom Chi-squared statistic Sample proportion Wilson estimator x−μ LCL = n − s2 UCL = n − s2 s/!n Confidence interval estimator of μ s x ± tα/2 !n σ2 Test statistic for χ2 = (n − 1)s2 σ2 χ2α/2 χ21−α/2 Test statistic for p z= p^ − p !p(1 − p)/n Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 I n f erence A bout a P opu l ation Confidence interval estimator of p  onfidence interval estimator of the total of a large C finite population p^ ± zα/2"p^ (1 − p^ )/n Sample size to estimate p n= q zα/2"p^ (1 − p^ ) B Wilson estimator 417 N c x ± tα/2 r s !n d  onfidence interval estimator of the total number of C successes in a large finite population x+2 ~ p= n+4 N c p^ ± zα/2  onfidence interval estimator of p using the Wilson C estimator p^ (1 − p^ ) d Å n ~ p ± zα/2"p~ (1 − p^ )/(n + 4) C o mp u t e r O u u t and Inst r u ct i o ns : Technique Excel t-test of μ t-estimator of μ Chi-squared test of σ2 Chi-squared estimator of σ2 z-test of p z-estimator of p 375 378 392 394 400 403 We present the flowchart in Figure 12.7 as part of our ongoing effort to help you identify the appropriate statistical technique This flowchart shows the techniques introduced in this chapter only As we add new techniques in the upcoming chapters, we will expand this flowchart until it contains all the statistical inference techniques covered in this book Use the flowchart to select the correct method in the chapter exercises that follow Figure 12.7    Flowchart of Techniques: Chapter 12 Problem objective? Describe a population Data type? Interval Nominal Type of descriptive measurement? z-test and estimator of p Central location Variability t-test and estimator of m x -test and estimator of s Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 418 CHAPTER 12 C h a p t e r E x e rc i s e s The following exercises require the use of a computer and software Use a 5% significance level unless specified otherwise The National Hockey League’s Florida Panthers play in the BB&T center The cost of parking is $20 However, Lexus occasionally pays the cost by offering free parking to drivers of Lexus cars A statistician wanted to estimate the cost of this program He randomly sampled 300 cars entering the parking lot and recorded whether the car was a Lexus (2) or not (1) By counting the number of empty parking spots he discovered that there were 4850 cars parked that night Estimate with 95% confidence the amount of money Lexus had to pay the BB&T center 12.136 Xr12-136  12.137 Xr12-137  Hazardous materials are constantly being around the country To help determine how dangerous these events are a statistics practitioner recorded the distances of a random sample of trucks, trains, airplanes, and boats carrying explosives Estimate with 95% confidence the mean distance Source: Adapted from Statistical Abstract of the United States 2012, Table 1071 12.138 Xr12-138  One of the issues that came up in a recent municipal election was the high cost of housing A candidate seeking to unseat an incumbent claimed that the average family spends more than 30% of its annual income on housing A housing expert was asked to investigate the claim A random sample of 125 households was drawn, and each household was asked to report the percentage of household income spent on housing costs a Is there enough evidence to infer that the candidate is correct? b Using a confidence level of 95%, estimate the mean percentage of household income spent on housing by all households c What is the required condition for the techniques used in Parts a and b? Use a graphical technique to check whether it is satisfied 12.139 Xr12-139  There are 604,474 bridges in the United States A structural engineering team randomly SAMPLED 850 bridges and categorized each as either structurally deficient (restricted to light vehicles, require immediate rehabilitation to remain open, or are closed), functionally obsolete (load carrying capacity, clearance, or approach highway alignment, or structurally sound These three categories were recorded as 1, 2,and 3, respectively a Estimate with 99% confidence the number of American bridges that are structurally deficient b Estimate with 90% confidence the number of American bridges that are functionally obsolete Source: U.S Federal Highway Administration, Office of Bridge Technology 12.140 Xr12-140  Robots are being used with increas- ing frequency on production lines to perform mon­otonous tasks To determine whether a robot welder should replace human welders in producing automobiles, an experiment was performed The time for the robot to complete a series of welds was found to be 38 seconds A random sample of 20 workers was taken, and the time for each worker to complete the welds was measured The mean was calculated to be 38 seconds, the same as the robot’s time However, the robot’s time did not vary, whereas there was variation among the workers’ times An analysis of the production line revealed that if the variance exceeds 17 seconds2, there will be problems Perform an analysis of the data, and determine whether problems using human welders are likely 12.141 Xr12-141  According to FBI statistics, there were 354,520 robberies in the United States in 2012 (latest statistics available) A random sample of robberies was drawn and the amount of loss was recorded Estimate with 95% confidence the total loss of all the robberies in the United States in 2012 Source: Adapted from U.S Department of Justice, Federal Bureau of Investigation, Uniform Crime Reports 12.142 Xr12-142  Refer to Exercise 12.151 Also recorded was the weapon used (1 = firearm, = knife or other cutting instrument,3 = other, = no weapon) Estimate with 90% confidence the number of crimes where a firearm was not used 12.143 Xr12-143  An important factor in attempting to pre- dict the demand for new cars is the age of the cars already on the road A random sample of 650 cars was drawn and the age of each car was recorded Estimate with 99% confidence the age mean age of all American cars Source: R.L Polk and Company 12.144 Xr12-144  Refer to Exercise 12.143 A sample of 425 pickup trucks and SUVs was drawn and the age of the vehicles was recorded Estimate with 95% confidence the mean age of trucks and SUVs Source: R.L Polk and Company 12.145 Xr12-145  Opinion Research International surveyed people whose household incomes exceed $50,000 and asked each for their top money-related new year’s resolutions The responses are: Get out of credit card debt Retire before age 65 Die broke Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 I n f erence A bout a P opu l ation Make with current finances Look for higher paying job Estimate with 90% confidence the proportion of people whose household incomes exceed $50,000 whose top money-related resolution is to get out of credit card debt 12.146 Xr12-146  In a large state university (with numer- ous campuses), the marks in an introductory statistics course are normally distributed with a mean of 68% To determine the effect of requiring students to pass a calculus test (which at present is not a prerequisite), a random sample of 50 students who have taken calculus is given a statistics course The marks out of 100 were recorded a Estimate with 95% confidence the mean statistics mark for all students who have taken calculus b Do these data provide evidence to infer that students with a calculus background would perform better in statistics than students with no calculus? 12.147 Xr12-147  A random sample of complaints about American airlines was drawn and the type of complaint was recorded (1 = Flight problems (cancellations, delays, etc.), = Customer service (unhelpful employees, inadequate means, or cabin service, treatment of delayed passengers), = Baggage, = Ticketing/boarding, = Other Estimate with 95% confidence the proportion of airline complaints that are due to customer service Source: Adapted from Statistical Abstract of the United States 2012, Table 1081 12.148 Xr12-148  There are 138,592,000 workers in the United States An economist took a random sample of 550 workers and recorded how they commuted to work (1 = drive alone, = car pool, = public transportation, = walked, = other, and = worked at home) Is there enough evidence to infer that more than 75% of workers drive alone to work? Source: Adapted from Statistical Abstract of the United States 2012, Table 1100 12.149 Xr12-149  Refer to Exercise 12.148 Estimate with 95% confidence the number of workers who carpooled to work 12.150 Xr12-150  Refer to Exercise 12.148 Also recorded was the amount of time to commute to work on an average day Estimate with 90% confidence the average commute time 12.151 Xr12-151  The routes of postal deliverers are care- fully planned so that each deliverer works between and 7.5 hours per shift The planned routes assume an average walking speed of miles per hour and no shortcuts across lawns In an experiment to examine the amount of time deliverers actually spend 419 completing their shifts, a random sample of 75 postal deliverers was secretly timed a Estimate with 99% confidence the mean shift time for all postal deliverers b Check to determine whether the required condition for this statistical inference is satisfied c Is there enough evidence at the 10% significance level to conclude that postal workers are on average spending less than hours per day doing their jobs? 12.152 Xr12-152  A national health care system was an issue in recent presidential election campaign and is likely to be a subject of debate for many years The issue arose because of the large number of Americans who have no health insurance Under the present system, free health care is available to poor people, whereas relatively well-off Americans buy their own health insurance Those who are considered working poor and who are in the lower-middle-class economic stratum appear to be most unlikely to have adequate medical insurance To investigate this problem, a statistician surveyed 250 families whose gross income last year was between $10,000 and $25,000 Family heads were asked whether they have medical insurance coverage (2 = Has medical insurance and 1  = Doesn’t have medical insurance) The statistics practitioner wanted an estimate of the fraction of all families whose incomes are in the range of $10,000 to $25,000 who have medical insurance Perform the necessary calculations to produce an interval estimate with 90% confidence 12.153 Xr12-153  The manager of a branch of a major bank wants to improve service She is thinking about giving $1 to any customer who waits in line for a period of time that is considered excessive (The bank ultimately decided that more than minutes is excessive.) However, to get a better idea about the level of current service, she undertakes a survey of customers A student is hired to measure the time spent waiting in line by a random sample of 50 customers Using a stopwatch, the student determined the amount of time between the time the customer joined the line and the time he or she reached the teller The times were recorded Construct a 90% confidence interval estimate of the mean waiting time for the bank’s customers 12.154 Xr12-154  Obesity is defined as having a Body Mass Index (BMI = 30 grams/kilogram2) over 30 A statistics practitioner took a random sample of American adults and classified their BMI as either Under 20, 20–30, Over 30 There are 234,564,000 American adults Estimate with 95% confidence the number of Americans who are obese Source: Adapted from Statistical Abstract of the United States 2012, Table 1342 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 420 CHAPTER 12 12.155 Xr12-155  Engineers who are in charge of the ­ roduction of springs used to make car seats are p concerned about the variability in the length of the springs The springs are designed to be 500 mm long When the springs are too long, they will loosen and fall out When they are too short, they will not fit into the frames The springs that are too long and too short must be reworked at considerable additional cost The engineers have calculated that a standard deviation of mm will result in an acceptable number of springs that must be reworked A random sample of 100 springs was measured Can we infer at the 5% significance level that the number of springs requiring reworking is unacceptably large? Refer to Exercise 12.155 Suppose the engineers recoded the data so that springs that were the correct length were recorded as 1, springs that were too long were recorded as 2, and springs that were too short were recorded as Can we infer at the 10% significance level that less than 90% of the springs are the correct length? 12.156 Xr12-156  12.157 Xr12-157  An advertisement for a major home appli- ance manufacturer claims that its repair personnel are the loneliest in the world because its appliances require the smallest number of service calls To examine this claim, a researcher drew a random sample of 100 owners of 5-year-old washing machines The number of service calls made in the 5-year period were recorded Find the 90% confidence interval estimate of the mean number of service calls for all 5-year-old washing machines 12.158 Xr12-158  An oil company sends out monthly state- ments to its customers who purchased gasoline and other items using the company’s credit card Until now, the company has not included a preaddressed envelope for returning payments The average and the standard deviation of the number of days before payment is received are 9.8 and 3.2, respectively As an experiment to determine whether enclosing preaddressed envelopes speeds up payment, 150 customers selected at random were sent preaddressed envelopes with their bills The numbers of days to payment were recorded a Do the data provide sufficient evidence at the 10% level of significance to establish that enclosure of preaddressed envelopes improves the average speed of payments? b Can we conclude at the 10% significance level that the variability in payment speeds decreases when a preaddressed envelope is sent? 12.159 Xr12-159  A rock promoter is in the process of deciding whether to book a new band for a rock concert He knows that this band appeals almost exclusively to teenagers According to the latest census, there are 400,000 teenagers in the area The promoter decides to a survey to try to estimate the proportion of teenagers who will attend the concert How large a sample should be taken in order to estimate the proportion to within 02 with 99% confidence? 12.160 Xr12-160  Exercise 12.159, suppose that the pro- moter decided to draw a sample of size 600 (because of financial considerations) Each teenager was asked whether he or she would attend the concert (2 = Yes, I will attend; = No, I will not attend) Estimate with 95% confidence the number of teenagers who will attend the concert 12.161 Xr12-161  The owner of a downtown parking lot suspects that the person he hired to run the lot is stealing some money The receipts as provided by the employee indicate that the average number of cars parked in the lot is 125 per day and that, on average, each car is parked for 3.5 hours To determine whether the employee is stealing, the owner watches the lot for days On those days, the numbers of cars parked are as follows: 120  130  124  127  128 The time spent on the lot for the 629 cars that the owner observed during the days was recorded Can the owner conclude at the 1% level of significance that the employee is stealing? (Hint: Since there are two ways to steal, two tests should be performed.) 12.162 Xr12-162  Jim Cramer hosts CNBC’s “Mad Money” program Mr Cramer regularly makes suggestions about which stocks to buy and sell How well has Mr Cramer’s picks performed over the past two years (2005 to 2007)? To answer the question a random sample of Mr Cramer’s picks was selected The name of the stock, the buy price of the stock, the current or sold price and the percent return were recorded a Estimate with 95% confidence the mean return for all of Mr Cramer’s selections b Over the two-year period the Standard and Poor’s 500 Index rose by 16% Is there sufficient evidence to infer that Mr Cramer’s picks have done less well? Source: YourMoneyWatch.com 12.163 Xr12-163*  Unfortunately, it is not uncommon for high school students in the United States to carry weapons (guns, knives, or clubs) To determine how prevalent this practice is, a survey of high school students was undertaken Students were asked whether they carried a weapon at least once in the previous 30 days (1 = No, = Yes) Estimate with 95% confidence the proportion of all high school students who have carried weapons in the last 30 days Source: Adapted from Statistical Abstract of the United States, 2009, Table 239 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 I n f erence A bout a P opu l ation 12.164 Xr12-164  In 2016, the average household debt ser- vice ratio for homeowners was 10.02 The household debt service ratio is the ratio of debt payments to disposable personal income Debt payments consist of mortgage payments and payments on consumer debts To determine whether this economic measure has increased a random sample of Americans was drawn Can we infer from the data that the debt service ratio has increased since 2016? States made up an average of 65.8% of total compensation To determine if this changed, a random sample of manufacturing employees was drawn Can we infer that percentage of total compensation for wages and salaries increased in 2013? Source: Adapted from Statistical Abstract of the United States, 2009, Table 970 12.169 Xr12-169  Several decades ago a large proportion of Americans smoked cigarettes However, in recent years many adults have quit To measure the extent of current smoking a random sample of American adults was asked to report whether they smoked (1 = yes, = no) There are 244,137,873 American adults Estimate with 95% confidence the number of American adults who smoke cigarettes (Source: Federal Reserve Board) 12.165 Xr12-165  Refer to Exercise 12.164 Another mea- sure of indebtedness is the financial obligations ratio, which adds automobile lease payments, rental on tenant occupied property, homeowners insurance, and property tax payments to the debt service ratio In 2016, the ratio for homeowners was 15.31 Can we infer that financial obligations ratio for homeowners has increased between 2016 and this year? 421 Source: Adapted from Statistical Abstract of the United States 2012, Table 1343 12.170 Xr12-170  Unfortunately, robbery is an all-too- frequent crime Bank robberies tend to be the most lucrative for criminals In most cases banks not report the size of the loss However, several researchers were able to gain access to bank robberies in England Here are the variables recorded: 12.166 Xr12-166  Refer to Exercise 12.165 In 2006 the financial obligations ratio for renters was 23.65 Can we infer that financial obligations ratio for renters has increased between 2016 and this year? 12.167 Xr12-167  In 2015, there were 124,587,000 (Source: Bank raid successful from the point of view of the robbers (2 = yes and = no) Amount stolen (for successful raids only) Number of bank staff present Number of customers present United States Census) households in the United States There were 81,716,000 family households made up of married couples, single male, and single female households To determine how many of each type a survey was undertaken The results were stored using the codes = married couple, = single male, and = single female Estimate with 95% confidence the total number of American households with ­married couples If these data can be considered a random sample of British bank robberies estimate with 95% confidence the following parameters a Proportion of all bank robberies that are successful b Mean amount stolen in successful robberies c Mean number of bank staff present d Mean number of customers present Source: Adapted from Statistical Abstract of the United States 2009, Table 58 12.168 Xr12-168  Wages and salaries make up only part of a total compensation Other parts include paid leave, health insurance, and many others In 2013, wages and salaries among manufacturers in the United Source: Adapted from Barry Reilly, Neil Rickman, and Robert Witt, “Robbing Banks,” Significance, June 2012, Volume 9, Issue G e n e r a l S o c i a l S u rv e y E x e rc is e s In 2014, the population of the United States was 318,907,401, and the number of Americans 18 and over was 244,137,873 (Source: Factfinder.census.gov) 12.171 GSS2014*  It has been said that America is a nation of immigrants Estimate with 95% confidence the number of Americans 18 and over who were born outside the United States (BORN: = Born outside the United States) 12.172 GSS2014*  How many people work for the federal, state, or local government? Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 422 CHAPTER 12 Estimate with 95% confidence the number of adults (18 and over) who work for the federal, state, or local government (WRKGOVT: = Government) 12.173 GSS2014*  Is the entrepreneurial spirit of the 12.175 GSS2014*  Among Democratic and Republicans only is there enough evidence to infer that there are more Democrats than Republicans (PARTYID3: = Democrat, = Republican)? (Caution: Tricky question) United States alive and well? Estimate with 95% confidence the number of Americans who work for themselves (WRKSLF: = Self-employed) 12.176 GSS2014*  Among Liberals and Conservatives only 12.174 GSS2014*  How much television are Americans 12.177 Is there a contradiction between the results in watching? Because of all the other forms of electronic amusement Americans may be watching less television A marketing specialist believes that Americans are watching less than hours per day (TVHOURS) a Conduct a test to determine whether there is enough evidence to support the claim b Is the required condition for the test satisfied? Explain S u rv e y of is there enough evidence to infer that there are more Conservatives than Liberals (POLVIEWS3: = Liberal, = Conservative)? Exercises 12.175 and 12.176? Explain 12.178 GSS2014*  The birth rate in many countries is fall- ing This will create problems in the future because there will be less people contributing taxes and more retired people receiving government pensions The birth rate needed to maintain current population levels is 2.08 children per woman The General Social Survey asked “How many children have you ever had?” Conduct a test to determine whether the mean number of children is less than 2.08 (CHILDS) C o n s u m e r F i n a n c e s E x e rc is e s In 2013, the population of the United States was 316,427,395, the number of Americans 18 and over was 242,823,652, and the number of households was 123,460,000 (Source: Factfinder.census.gov) Use a 95% confidence level unless otherwise specified 12.179 SCF2013:\All*  If there was gender equality in the head of household designation the number of households with males head of households would equal the number of households with females as heads of households Conduct a test to determine that there is no gender equality (HHSEX: = Male, = female) 12.180 SCF2013:\All*  How many American adults (18 and over) are working in some way? Estimate the number (LF: = Working in some way) 12.181 SCF2013:\All*  Government debt and personal debt are a growing concern Estimate the number of households that have debts (HDEBT: = Yes) 12.182 SCF2013:\All  Another sign of financial problems is when a household is late with at least one payment Estimate with 90% confidence the number of households that had a least one late payment in the preceding 12 months (LATE: = Yes) 12.183 SCF2013:\All*  Another sign of financial difficulties is when a household finds that overall expenses are unusually high Estimate with 99% confidence the number of households whose expenses are unusually high (EXPENSHILO: = Unusually high) Exercises 12.184–12.190 deal with the wealthy category defined in terms of the respondents’ net worth, which lies between $9, 498, 400 and $32,790,000 12.184 SCF2013:\W*  Is a graduate degree a pathway to a wealthy household? Estimate the proportion of wealthy households whose heads have graduate degrees (EDUC: 17 = Graduate school) 12.185 SCF2013:\W*  How long does it take to become wealthy? One way to answer the question is to examine the age of the head of an average wealthy household a Conduct a test to determine whether there is enough evidence to conclude that the mean age is greater than 60 (AGE) b What is the required condition for the test in part (a)? Is it satisfied? Explain 12.186 SCF2013:\W*  How does one get to be in this class whose minimum household net worth is about $9.5 million Could this be achieved through high income alone? Examine this issue by estimating the mean annual income of wealthy households (INCOME) Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 I n f erence A bout a P opu l ation 12.187 SCF2013:\W*  Do wealthy households have late payments? Estimate the proportion of wealthy households that had at least one late payment in the previous year (LATE: 1) 12.188 SCF2013:\W*  Net worth is defined as the difference between total assets and total liabilities including debt Does high net worth mean that these households have little or no debt? a Answer the question by estimating the mean debt of all wealthy households (DEBT) b Is the required condition satisfied? Explain 12.189 SCF2013:\W*  Checking accounts are often used 423 interest, most households including wealthy ones keep a minimum amount in these accounts a Estimate the mean total value of checking accounts held by wealthy households (CHECKING) b Is the required condition satisfied? If not, why not? 12.190 SCF2013:\W*  According to the Bureau of Labor Statistics, the average American family spent $2625 on food at restaurants Is there enough evidence that wealthy households spend more than twice that figure (FOODAWAY)? for household expenditures Because they pay no DATA C12-01 Pepsi’s Exclusivity Agreement with a University I n the last few years, colleges and The management at Pepsi quickly universities have signed exclusiv- reviews what it knows The ity agreements with a variety of market for soft drinks is measured iStockphoto.com/SKrow C a s e  1 revenue would be computed as follows*: private companies These agree- in terms of the equivalent of 12- ments bind the university to sell that ounce cans Pepsi currently sells company’s products exclusively on an average of 22,000 cans or their Gross revenue = 3,520,000 cans × $1.00 revenue/can = $3,520,000 the campus Many of the agreements equivalents per week (over the 40 This figure must be multiplied by involve food and beverage firms weeks of the year that the univer- 65% because the university would A large university with a total sity operates) The cans sell for an rake in 35% of the gross Thus, enrollment of about 50,000 average of one dollar each The students has offered Pepsi-Cola costs, including labor, amount to 65% × $3,520,000 = $2,288,000 The total cost of 30 cents per can an exclusivity agreement that $.30 per can Pepsi is unsure of (or $1,056,000) and the annual would give Pepsi exclusive rights its market share but suspects it payment to the university of to sell its products at all university is considerably less than 50% A $200,000 is subtracted to obtain facilities for the next year and an quick analysis reveals that if its the net profit: option for future years In return, current market share were 25%, the university would receive 35% then with an exclusivity agree- of the on-campus revenues and an ment Pepsi would sell 88,000 additional lump sum of $200,000 cans per week Thus, annual sales Its current annual profit is per year Pepsi has been given would be 3,520,000 cans per Current profit = 40 weeks × 22,000 cans/week × $.70/can = $616,000 weeks to respond year (calculated as 88,000 cans per week × 40 weeks) The gross Net profit = $2,288,000−$1,056,000 − $200,000 = $1,032,000 *We have created an Excel spreadsheet that does the calculations for this case To access it, click Excel Workbooks and Case 12.1 The only cell you may alter is cell C3, which contains the average number of soft drinks sold per week per student, assuming a total of 88,000 drinks sold per year Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 424 CHAPTER 12 If the current market share is 25%, A recent graduate of a business problem Use the estimate to the potential gain from the agree- program believes that a survey compute estimates of the annual ment is of the university’s students can profit Assume that Coke and supply the needed information Pepsi drinkers would be willing to $1,032,000 − $616,000 = $416,000 Accordingly, she organizes a buy either product in the absence The only problem with this analy- survey that asks 500 students to of their first choice sis is that Pepsi does not know keep track of the number of soft how many soft drinks are sold drinks they purchase on campus weekly at the university In addi- over the next days tion, Coke is not likely to supply Pepsi with information about its sales, which together with Pepsi’s line of products constitutes virtu- extract the needed information from the data Estimate with profits from sales of soft drinks at the university, should Pepsi agree to the exclusivity agreement? b Write a report to the 95% confidence the parameter company’s executives that is at the core of the decision describing your analysis 2 ally the entire market Perform a statistical analysis to a On the basis of maximizing place The executives at Pepsi Pepsi Cola are trying would like to know how likely it is to decide what to do, that Coke will want exclusive rights the university informs them that a under the conditions outlined by similar offer has gone out to the the university Coca-Cola Company Furthermore, if both companies want exclusive rights, a bidding war will take C a s e  3 want to conclude an exclusivity agreement with the university? Discuss the reasons for your one you did in Case 12.1, but conclusions irtually all countries have In Canada, hospitals are financed universal government- and administered by provincial run health-care systems governments Physicians are paid The United States is one notable by the government for each patient exception This is an issue in every service As a result, Canadians election, with some politicians pay nothing for these services The pushing for the United States revenues that support the system to adopt a program similar to are derived through income taxes, Canada’s corporate taxes, and sales taxes DATA C12-01 view Is it likely that Coke will Perform a similar analysis to the Estimating Total Medical Costs V this time from Coke’s point of Petrea Alexandru/E+/Getty Images W hile the executives of iStockphoto.com/SKrow Pepsi’s Exclusivity Agreement with a University: The Coke Side of the Equation C a s e  Despite higher taxes in Canada than those in the United States, the system is chronically underfunded, resulting in long waiting times for, sometimes, critical procedures For example, in some provinces, Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 DATA C12-03 I n f erence A bout a P opu l ation newly diagnosed cancer victims and 1966), and because medical random samples of four groups of must wait several weeks before costs are generally higher for older Canadians were drawn They are treatments can begin Virtually people everyone agrees that more money is needed No one can agree however, on how much is needed Unfortunately, the problem is going to worsen Canada, like the United States, has an aging population because of the large numbers of so-called baby boomers (those born between 1946  Ages 45–64 65–74 75–84 85+ One of the first steps in addressing the problem is to forecast medical costs, particularly for the 20-year period starting when the first baby boomers reached age 60 (in 2006) A statistics practitioner has been given the task of making these predictions Accordingly, Age Category The medical expenses for the previous 12 months were recorded and stored in columns A to D, respectively, in C12-03 2023 2028 2033 2038 45–64 10,045 9,970 10,172 10,671 65–74 4,264 4,804 4,873 4,621 75–84 2,413 2,987 3,536 4,042 924 1,095 1,429 1,793 85+ Source: Statistics Canada Projections for 2023, 2028, 2033, a Determine the 95% confidence b For each year listed, determine and 2038 of the numbers of interval estimates of the mean 95% confidence interval esti- Canadians (in thousands) in each medical costs for each of the mates of the total medical costs for age category are listed here four age categories Canadians 45 years old and older C a s e  4 DATA C12-04 Group 425 Estimating the Number of Alzheimer’s Cases A s the U.S population ages, To estimate the total number of (Adapted from the Alzheimer’s the number of people need- Alzheimer’s cases in the future, a Association, www.alz.org.) ing medical care increases survey was undertaken The survey Here are the projections for the Unless a cure is found in the next determined the age bracket where = 65–74, = 75–84, = 85 and number of Americans (thou- decade, one of the most expensive diseases requiring such care is over and whether the individual had Alzheimer’s, a form of dementia Alzheimer’s (1 = no and = yes) sands) in each of the three age categories Age Category 2020 2025 2030 2035 2040 65–74 33,076 37,093 39,227 38,162 36,644 75–84 16,639 21,345 25,750 29,162 31,067 6,726 7,482 9,131 11,908 14,634 85+ Source: United States Census Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 426 CHAPTER 12 a Determine the 95% confidence interval estimates of the proportion of Alzheimer’s patients in each of the three interval estimates of the total age categories number of Americans with b For each year listed, deter- Alzheimer’s disease mine 95% confidence C a s e  5 T Bias in Roulette Betting he game of roulette consists Two statisticians recorded the bets of a wheel with 38 colored on 904 spins There were 21,731 and numbered slots The bets numbers are to 36, and 00 Half of the slots numbered to 36 are red and the other half are black The two “zeros” are green The wheel is spun and an iron ball is rolled, which eventually comes to rest in one of the slots Gamblers can make several different kinds of bets Most players Researchers wanted to use these data to examine middle bias, which is the tendency for guessers in multiplechoice exams to select the middle answers For example, if there are five choices a, b, c, d, and e, guessers will tend to select answer c will be on of the 12 middle numbers? b Conduct a test at the 5% significance level to determine whether middle bias exists c The middle of the middle are the numbers 17 and 20 If there is no middle bias, what proportion of the bets will be either 17 or 20? d Test with a 5% significance bet on one or more numbers or on Most players stand on both sides level to determine whether a color (black or red) Here is the of the betting table so that the middle of the middle bias layout of the roulette betting table: middle numbers are 2, 5, 8, 11, exists 14, 17, 20, 23, 26, 29, 32, and 35 12 15 18 21 24 27 30 33 36 00 11 14 17 20 23 26 29 32 35 10 13 16 19 22 25 28 31 34 a If there is no middle bias, what proportion of the bets Source: Maya Bar-Hillel and Ro’I Zultan, “We Sing the Praise of Good Displays: How Gamblers Bet in Casino Roulette,” Chance, Volume 25, No 2, 2012 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 DATA C12-05 ... 14 .98? ?14 .99 A14 .19 –A14. 31 15. 21? ? ?15 .23 15 .53? ?15 .62 A15 .17 –A15.32 16 .50? ?16 .65 16 .10 1? ?16 .11 2 16 .14 2? ?16 .15 0 A16 .17 –A16. 31 17 .18 ? ?17 . 21 17.43? ?17 .46 A17 .17 –A17.35 18 .24? ?18 .33 18 .40? ?18 .42 19 .17 ? ?19 .30 19 .58? ?19 .59... 4 .19 –4.22 4.49–4.52 4.77–4.79 4 .14 5–4 .15 0 12 .54? ?12 .58 12 .11 7? ?12 .12 3 12 .17 1? ?12 .17 8 13 .54? ?13 .68 13 .10 6? ?13 .10 9 13 .12 1? ?13 .12 2 13 .16 7? ?13 .18 4 13 .235? ?13 .257 A13 .18 –A13.28 14 .23? ?14 .46 14 .67? ?14 .80 14 .98? ?14 .99... 3.28–3. 31 3.79–3. 81 4.23–4.26 4.53–4.56 4.80–4.82 4 .15 1–4 .15 4 12 .59? ?12 .69 12 .12 4? ?12 .12 9 12 .17 9? ?12 .19 0 13 .69? ?13 .80 13 .11 0? ?13 .11 1 13 .12 3? ?13 .12 6 13 .18 5? ?13 .19 3 13 .258? ?13 .260 A13.29–A13.38 14 .47? ?14 .56 14 . 81? ? ?14 .82