Statistics for Business & Economics, 13th ed 85317 FM ptg01 indd 3 07/01/16 3 50 PM Australia Brazil Mexico Singapore United Kingdom United States David R Anderson University of Cincinnati Dennis J Sw[.]
iStockphoto.com/alienforce; iStockphoto.com/TommL Statistics for Business & Economics 13e David R Anderson University of Cincinnati Dennis J Sweeney University of Cincinnati Thomas A Williams Rochester Institute of Technology Jeffrey D Camm Wake Forest University James J Cochran University of Alabama Australia Brazil Mexico Singapore United Kingdom United States Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest Important Notice: Media content referenced within the product description or the product text may not be available in the eBook version Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Statistics for Business and Economics, Thirteenth Edition David R Anderson, Dennis J Sweeney, Thomas A Williams, Jeffrey D Camm, James J Cochran Vice President, General Manager: Science, Math & Quantitative Business: Balraj Kalsi Product Director: Mike Schenk Product Team Manager: Joe Sabatino Product Manager: Aaron Arnsparger Content Developer: Anne Merrill Senior Marketing Manager: Nate Anderson â 2017, 2015 Cengage Learningđ WCN: 02-200-203 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 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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 Canada Print Number: 01 Print Year: 2015 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Dedicated to Marcia, Cherri, Robbie, Karen, and Teresa Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Brief Contents Preface xxiii About the Authors xxix Chapter Data and Statistics Chapter Descriptive Statistics: Tabular and Graphical Displays 32 Chapter Descriptive Statistics: Numerical Measures 102 Chapter Introduction to Probability 171 Chapter Discrete Probability Distributions 217 Chapter Continuous Probability Distributions 269 Chapter Sampling and Sampling Distributions 302 Chapter Interval Estimation 346 Chapter Hypothesis Tests 385 Chapter 10 Inference About Means and Proportions with Two Populations 443 Chapter 11 Inferences About Population Variances 483 Chapter 12 Comparing Multiple Proportions, Test of Independence and Goodness of Fit 507 Chapter 13 Experimental Design and Analysis of Variance 544 Chapter 14 Simple Linear Regression 598 Chapter 15 Multiple Regression 681 Chapter 16 Regression Analysis: Model Building 754 Chapter 17 Time Series Analysis and Forecasting 805 Chapter 18 Nonparametric Methods 871 Chapter 19 Statistical Methods for Quality Control 916 Chapter 20 Index Numbers 950 Chapter 21 Decision Analysis (On Website) Chapter 22 Sample Survey (On Website) Appendix A References and Bibliography 972 Appendix B Tables 974 Appendix C Summation Notation 1001 Appendix D Self-Test Solutions and Answers to Even-Numbered Exercises 1003 Appendix E Microsoft Excel 2013 and Tools for Statistical Analysis 1070 Appendix F Computing p-Values Using Minitab and Excel 1078 Index 1082 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Contents Preface xxiii About the Authors xxix Chapter Data and Statistics Statistics in Practice: Bloomberg Businessweek 1.1 Applications in Business and Economics Accounting Finance Marketing Production Economics Information Systems 1.2 Data Elements, Variables, and Observations Scales of Measurement Categorical and Quantitative Data Cross-Sectional and Time Series Data 1.3 Data Sources 11 Existing Sources 11 Observational Study 12 Experiment 13 Time and Cost Issues 13 Data Acquisition Errors 13 1.4 Descriptive Statistics 14 1.5 Statistical Inference 16 1.6 Analytics 17 1.7 Big Data and Data Mining 18 1.8 Computers and Statistical Analysis 20 1.9 Ethical Guidelines for Statistical Practice 20 Summary 22 Glossary 23 Supplementary Exercises 24 Chapter Descriptive Statistics: Tabular and Graphical Displays 32 Statistics in Practice: Colgate-Palmolive Company 33 2.1 Summarizing Data for a Categorical Variable 34 Frequency Distribution 34 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it viii Contents Relative Frequency and Percent Frequency Distributions 35 Bar Charts and Pie Charts 35 2.2 Summarizing Data for a Quantitative Variable 41 Frequency Distribution 41 Relative Frequency and Percent Frequency Distributions 43 Dot Plot 43 Histogram 44 Cumulative Distributions 45 Stem-and-Leaf Display 46 2.3 Summarizing Data for Two Variables Using Tables 55 Crosstabulation 55 Simpson’s Paradox 58 2.4 Summarizing Data for Two Variables Using Graphical Displays 64 Scatter Diagram and Trendline 64 Side-by-Side and Stacked Bar Charts 65 2.5 Data Visualization: Best Practices in Creating Effective Graphical Displays 71 Creating Effective Graphical Displays 71 Choosing the Type of Graphical Display 72 Data Dashboards 72 Data Visualization in Practice: Cincinnati Zoo and Botanical Garden 74 Summary 77 Glossary 78 Key Formulas 79 Supplementary Exercises 79 Case Problem Pelican Stores 84 Case Problem Motion Picture Industry 85 Case Problem Queen City 86 Appendix 2.1 Using Minitab for Tabular and Graphical Presentations 87 Appendix 2.2 Using Excel for Tabular and Graphical Presentations 90 Chapter Descriptive Statistics: Numerical Measures 102 Statistics in Practice: Small Fry Design 103 3.1 Measures of Location 104 Mean 104 Weighted Mean 106 Median 107 Geometric Mean 109 Mode 110 Percentiles 111 Quartiles 112 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1076 Appendix E FIGURE E.6 Microsoft Excel 2013 and Tools for Statistical Analysis INSERT FUNCTION DIALOG BOx It contains a drop-down list of several categories of functions provided by Excel Figure E.6 shows that we selected the Statistical category As a result, Excel’s statistical functions appear in alphabetic order in the Select a function box We see the AVEDEV function listed first, followed by the AVERAGE function, and so on The AVEDEV function is highlighted in Figure E.6, indicating it is the function currently selected The proper syntax for the function and a brief description of the function appear below the Select a function box We can scroll through the list in the Select a function box to display the syntax and a brief description for each of the statistical functions that are available For instance, scrolling down farther, we select the COUNTIF function as shown in Figure E.7 Note that COUNTIF is now highlighted, and that immediately below the Select a function box we see COUNTIF(range,criteria), which indicates that the COUNTIF function contains two inputs, range and criteria In addition, we see that the description of the COUNTIF function is “Counts the number of cells within a range that meet the given condition.” If the function selected (highlighted) is the one we want to use, we click OK; the Function Arguments dialog box then appears The Function Arguments dialog box for the COUNTIF function is shown in Figure E.8 This dialog box assists in creating the appropriate arguments (inputs) for the function selected When finished entering the arguments, we click Ok; Excel then inserts the function into a worksheet cell Using Excel Add-Ins Excel’s Data Analysis Add-In Excel’s Data Analysis add-in, included with the basic Excel package, is a valuable tool for conducting statistical analysis Before you can use the Data Analysis add-in it must be installed To see if the Data Analysis add-in has already been installed, click the DATA tab on the Ribbon In the Analysis group you should see the Data Analysis command If you Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Appendix E Microsoft Excel 2013 and Tools for Statistical Analysis FIGURE E.7 1077 DESCRIPTION OF THE COUNTIF FUNCTION IN THE INSERT FUNCTION DIALOG BOx not have an Analysis group and/or the Data Analysis command does not appear in the Analysis group, you will need to install the Data Analysis add-in The steps needed to install the Data Analysis add-in are as follows: Step Click the FILE tab Step Click Options Step When the Excel Options dialog box appears: Select Add-Ins from the list of options (on the pane on the left) In the Manage box, select Excel Add-Ins Click Go Step When the Add-Ins dialog box appears: Select Analysis ToolPak Click OK FIGURE E.8 FUNCTION ARGUMENTS DIALOG BOx FOR THE COUNTIF FUNCTION Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Appendix F: Computing p-Values Using Minitab and Excel Here we describe how Minitab and Excel can be used to compute p-values for the z, t, x2, and F statistics that are used in hypothesis tests As discussed in the text, only approximate p-values for the t, x2, and F statistics can be obtained by using tables This appendix is helpful to a person who has computed the test statistic by hand, or by other means, and wishes to use computer software to compute the exact p-value Using Minitab Minitab can be used to provide the cumulative probability associated with the z, t, x2, and F test statistics So the lower tail p-value is obtained directly The upper tail p-value is computed by subtracting the lower tail p-value from The two-tailed p-value is obtained by doubling the smaller of the lower and upper tail p-values The z test statistic We use the Hilltop Coffee lower tail hypothesis test in Section 9.3 as an illustration; the value of the test statistic is z = −2.67 The Minitab steps used to compute the cumulative probability corresponding to z = −2.67 follow Step Step Step Step Select the Calc menu Choose Probability Distributions Choose Normal When the Normal Distribution dialog box appears: Select Cumulative probability Enter in the Mean box Enter in the Standard deviation box Select Input Constant Enter −2.67 in the Input Constant box Click OK Minitab provides the cumulative probability of 0037926 This cumulative probability is the lower tail p-value used for the Hilltop Coffee hypothesis test For an upper tail test, the p-value is computed from the cumulative probability provided by Minitab as follows: p-value = − cumulative probability For instance, the upper tail p-value corresponding to a test statistic of z = −2.67 is − 0037926 = 996207 The two-tailed p-value corresponding to a test statistic of z = −2.67 is 2 times the minimum of the upper and lower tail p-values; that is, the two-tailed p-value corresponding to z = −2.67 is 2(.0037926) = 007585 The t test statistic We use the Heathrow Airport example from Section 9.4 as an illustration; the value of the test statistic is t = 1.84 with 59 degrees of freedom The Minitab steps used to compute the cumulative probability corresponding to t = 1.84 follow Step Select the Calc menu Step Choose Probability Distributions Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Appendix F Computing p-Values Using Minitab and Excel 1079 Step Choose t Step When the t Distribution dialog box appears: Select Cumulative probability Enter 59 in the Degrees of freedom box Select Input Constant Enter 1.84 in the Input Constant box Click OK Minitab provides a cumulative probability of 9646, and hence the lower tail p-value = 9646 The Heathrow Airport example is an upper tail test; the upper tail p-value is − 9646 = 0354 In the case of a two-tailed test, we would use the minimum of 9646 and 0354 to compute p-value = 2(.0354) = 0708 The x2 test statistic We use the St Louis Metro Bus example from Section 11.1 as an illustration; the value of the test statistic is x2 = 28.18 with 23 degrees of freedom The Minitab steps used to compute the cumulative probability corresponding to x2 = 28.18 follow Step Step Step Step Select the Calc menu Choose Probability Distributions Choose Chi-Square When the Chi-Square Distribution dialog box appears: Select Cumulative probability Enter 23 in the Degrees of freedom box Select Input Constant Enter 28.18 in the Input Constant box Click OK Minitab provides a cumulative probability of 790949, which is the lower tail p-value The upper tail p-value = − the cumulative probability, or − 790949 = 209051 The two-tailed p-value is times the minimum of the lower and upper tail p-values Thus, the two-tailed p-value is 2(.209051) = 418102 The St Louis Metro Bus example involved an upper tail test, so we use p-value = 209051 The F test statistic We use the Dullus County Schools example from Section 11.2 as an illustration; the test statistic is F = 2.40 with 25 numerator degrees of freedom and 15 denominator degrees of freedom The Minitab steps to compute the cumulative probability corresponding to F = 2.40 follow Step Step Step Step Select the Calc menu Choose Probability Distributions Choose F When the F Distribution dialog box appears: Select Cumulative probability Enter 25 in the Numerator degrees of freedom box Enter 15 in the Denominator degrees of freedom box Select Input Constant Enter 2.40 in the Input Constant box Click OK Minitab provides the cumulative probability and hence a lower tail p-value = 959401 The upper tail p-value is − 959401 = 040599 Because the Dullus County Schools example is a two-tailed test, the minimum of 959401 and 040599 is used to compute p-value = 2(.040599) = 0811198 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1080 Appendix F Computing p-Values Using Minitab and Excel Using Excel p-Value Excel functions and formulas can be used to compute p-values associated with the z, t, x2, and F test statistics We provide a template in the data file entitled p-Value for use in computing these p-values Using the template, it is only necessary to enter the value of the test statistic and, if necessary, the appropriate degrees of freedom Refer to Figure F.1 as we describe how the template is used For users interested in the Excel functions and formulas being used, just click on the appropriate cell in the template The z test statistic We use the Hilltop Coffee lower tail hypothesis test in Section 9.3 as an illustration; the value of the test statistic is z = −2.67 To use the p-value template for this hypothesis test, simply enter −2.67 into cell B6 (see Figure F.1) After doing so, p-values for all three types of hypothesis tests will appear For Hilltop Coffee, we would use the lower tail p-value = 0038 in cell B9 For an upper tail test, we would use the p-value in cell B10, and for a two-tailed test we would use the p-value in cell B11 The t test statistic We use the Heathrow Airport example from Section 9.4 as an illus- tration; the value of the test statistic is t = 1.84 with 59 degrees of freedom To use the p-value template for this hypothesis test, enter 1.84 into cell E6 and enter 59 into cell E7 (see Figure F.1) After doing so, p-values for all three types of hypothesis tests will appear FIGURE F.1 EXCEL WoRkSHEET FoR CoMpUTINg p-VALUES Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Appendix F Computing p-Values Using Minitab and Excel 1081 The Heathrow Airport example involves an upper tail test, so we would use the upper tail p-value = 0354 provided in cell E10 for the hypothesis test The x2 test statistic We use the St Louis Metro Bus example from Section 11.1 as an illustration; the value of the test statistic is x2 = 28.18 with 23 degrees of freedom To use the p-value template for this hypothesis test, enter 28.18 into cell B18 and enter 23 into cell B19 (see Figure F.1) After doing so, p-values for all three types of hypothesis tests will appear The St Louis Metro Bus example involves an upper tail test, so we would use the upper tail p-value = 2091 provided in cell B23 for the hypothesis test The F test statistic We use the Dullus County Schools example from Section 11.2 as an illustration; the test statistic is F = 2.40 with 25 numerator degrees of freedom and 15 denominator degrees of freedom To use the p-value template for this hypothesis test, enter 2.40 into cell E18, enter 25 into cell E19, and enter 15 into cell E20 (see Figure F.1) After doing so, p-values for all three types of hypothesis tests will appear The Dullus County Schools example involves a two-tailed test, so we would use the two-tailed p-value = 0812 provided in cell E24 for the hypothesis test Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it Index Note: Chapters 21 and 22 can be found with the Online Content for this book Index entries found in these chapters are denoted by the chapter number (bolded), hyphen, and page number Page numbers followed by f indicate figures; n indicate footnotes; and t indicate tables A Acceptable quality level (AQL), 943 Acceptance criterion, 938 Acceptance sampling, 921, 936–943 advantages of, 937 binomial probability function, 946 KALI, Inc example, 937–938 multiple sampling plans, 942 overview, 943, 944 probability of accepting a lot, 938–940 selecting a plan for, 941–942 Accounting applications, 3–4 ACNielsen, 4, 11 Addition law, 188–191, 209 Additive decomposition models, 848–849, 860 Adjusted multiple coefficient of determination, 695, 738, 740 Aggregate price indexes, 952–954 applications, 955, 957–958 computing from price relatives, 956–957 Air traffic controller stress test, 569–570, 571–572, 595 Alliance Data Systems, 599 Alpha to enter or remove, 782, 784, 786, 804 Alternative hypothesis, 386–388 developing, 387–388 American Military Standard Table (MIL-STD-105D), 942 American Society for Quality (ASQ), 917–918 American Statistical Association, 21–22 Analysis of variance (ANOVA), 548–559 applications, 561–562 assumptions for, 548 completely randomized designs and, 551–555 computer results for, 557–558 using Excel, 594–597, 680 using Minitab, 592–593 overview, 548–551 total sum of squares, 556 See also ANOVA tables Analytics, 17–18 defined, 18 types of, 18 ANOVA See Analysis of variance (ANOVA) ANOVA procedures, 546, 570–571, 577 ANOVA tables, 556, 557, 570–571 Air traffic controller stress test, 570, 572, 595 block designs, 570, 571 Chemitech experiment, 556, 557 experimental designs, 560, 577 randomized design, 556, 571 multiple regression, 701 significance testing, 627 simple linear regression, 627–628, 639 time series forecasting, 832 Applications, statistical, 5, 22, 119, 415n, 495 Approximate class width, 42 Area, as measure of probability, 272–274 Arithmetic mean, 104 Assignable causes, 922 Association, measures of, 138–145 Attributes sampling plans, 931, 943 Autocorrelation of data, 793–796 first-order, 756–758, 764, 794–794 formula, 798 Average outgoing quality limit (AOQL), 943 Average range, 927–928, 929, 945 B Backward elimination procedure, 784–785 using Minitab, 804 Baldrige, Malcolm, 919 Baldrige National Quality Program (BNQP), 919 Baldrige stock study, 919 Bar charts, 35–36 descriptive statistics, 14–15 examples, 15f, 36f, 91f, 522f, 530 selection of, 72, 77, 91, 98, 99, 100 side by side, 65–67 stacked, 67–68 using Excel, 90–92 Barnett, Bob, 919 Basic requirements, for assigning probabilities, 178, 223 Bayes, Thomas, 204 Bayes’ theorem, 202–206 applications, 206–207 branch probabilities, 175, 180, 202–203, 21–24–21–27 formula, 210 tabular approach, 205–206 Bernoulli, Jakob, 242 Bernoulli process, 242 Best-subsets regression, 785–786 using Minitab, 795, 803, 804 Between-treatments estimates, 552–553 Biased estimators, 333 Bias in selections, 308 Big data, 19 Bimodal data, 111 Binomial experiments, 242–243 Binomial probability distributions, 241–249 for acceptance sampling, 938–939, 941 applications, 250–252 defined, 242 expected values of, 248–249, 252 experiment, 242–243 Martin Clothing Store example, 243–247 using Minitab, 249f normal approximation of, 265, 287–289 and the sign test, 874–876 tables of, 247–248 variances of, 248–249 Binomial probability functions, 246–247 for acceptance sampling, 938–939, 941 formula, 261, 946 Binomial random variables, 287, 388 Bivariate probability distributions, 232–238 defined, 232 empirical discrete probability distribution, 232–235 financial applications, 235–238 methods, 239–241 overview, 238 Blocking, 568, 569–570, 572, 582 Blocks, in stress test, 569 Bloomberg Businessweek, 2–3 Bonferroni adjustment, 565–566, 583 Bound on sampling errors, 22–7 Box plots, 134–135 applications, 136–138 comparative analysis using, 135–136 using Minitab, 135, 167 Branches, 21–4, 21–20, 21–24–21–27 See also Bayes’ theorem Bubble charts, 76, 96 Burke Marketing Services, Inc., 545 C Case problems African elephant populations, 165–166 Air Force training program, 504 bipartisan agenda for change, 540 Buckeye Creek Amusement Park, 674–675 business schools of Asia-Pacific, 162–164 calculus-based derivation of least squares formulas, 675–676 Cincinnati Zoo and Botanical Garden data visualization, 74–76 compensation for sales professionals, 591–592 Consumer Research, Inc., 748 ethical behavior of business students, 435–436 finding the best car value, 673–674, 750–751 forecasting food and beverage sales, 347, 864–865 forecasting lost sales, 865–866 Go Bananas!, 266–267 Gulf Real Estate Properties, 378 Hamilton County Judges, 214–216 Heavenly Chocolates, 164–165 lawsuit defense strategy, 21–33 Marion Dairies, 342 measuring stock market risk, 122, 670–671 Metropolitan Research, Inc., 378–380 motion picture industry, 85–86, 161–162 NASCAR drivers winnings, 749–750 Par, Inc., 477–478 Pelican Stores, 84–85, 160–161 PGA tour statistics, 801–802 point-and-shoot digital camera selection, 672–673 Quality Associates, Inc., 433–434 Queen City, 86–87 Significance test using correlation, 676–677 Specialty Toys, 299–300 U.S Department of Transportation, 671–673 Wentworth Medical Center, 590–591 wines from the Piedmont region of Italy, 802–803 Young Professional magazine, 377–378 Categorical data, 8, 34 Categorical variables, 8, 709–714 applications, 715–718 complex, multiple regression, 713–714 defined, frequency distributions, 34–35, 90–92 independent, multiple regression, 709–714 Johnson Filtration, Inc example, 709–711, 712, 713 summarizing data for, 34–37 Cause-and-effect relationships in observational studies, 546, 628 Census, 16, 849 Centered moving average, 850–851 Center for Drug Evaluation and Research (CDER), 444 Central limit theorem, 319 Chance events, 21–3 Chance nodes, 21–4–21–5 Chebyshev’s Theorem, 127–128, 131–132 Chemitech problem, example of, 546–547 Chi-square distribution, 509–516 formula, 537 goodness of fit tests, 527–534, 537 hypothesis testing, 489–492, 510–512, 518 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1083 Index independence of two categorical variables, 521–523 interval estimation, 485–489, 502 multiple comparison procedures, 514–516 population proportions, multiple, 509–514 population variances, 485–490 test of independence, 519–523, 541 test statistic, 489–492, 511, 541, 528–534 using Excel, 542–543 using Minitab, 541–542 Cincinnati Zoo and Botanical Gardens, 74–76 Citibank, 218 Classes of a frequency distribution, 41–43 lower class limit, 42 midpoints, 43 upper class limit, 42, 45–46 Classical method for assigning probabilities, 178–179 Class width, approximate, 42 Cluster sampling, 335–336, 22–21–22–23 Coefficient of determination, 614–617 applications, 619–621 correlation coefficient, 617–618 formula, 662, 740 multiple regression, 694–695 sum of squares due to error (SSE), 614–615 sum of squares due to regression (SSR), 615–616 total sum of squares (SST), 615–616 Coefficients, for multiple regression, 688–689 Coefficients of variation, 121–122, 154 Colgate-Palmolive Company, 33 Combinations, 177 Common causes, 922 Comparisonwise Type I error rate, 565 Complements, 187–188 computing probabilities using, 209 of an event (of A), 187–188 Venn diagrams and, 187–188 Complete block designs, 572–573 Completely randomized design, 551–555 analysis of variance (ANOVA), 551–555 between-treatments estimate of population variance, 552–553 Chemitech problem, example of, 546–547 experimental design, 546–548 using Excel, 594–595 formulas, 583–584 using Minitab, 592–593 within-treatments estimate of population variance, 550, 553–554 Computers, 20 computing betas, 671n using Excel, 20 using Minitab, 20, 639–640 observation identification and, 658 packages, 774, 21–6 ranking combined samples and, 890 regression analysis and, 639–640 use of software 658 See also specific computer programs Conditional probabilities, 194–197, 209, 21–24–21–26 Confidence coefficients, 351 Confidence intervals defined, 632 formula, 488, 663 hypothesis testing, 403–404 least squares estimators, 603–607 linear regression equation, estimated, 625–626, 634f, 636f margin of error, 633 for mean value of y, 633–634 multiple regression equation, estimated, 706–707 as 95% term, 351 for normal probability distribution, 649–650 population means: s known, 351–352 for proportions, 367 regression results and, 632 simple linear regression, 633–634 using Excel, 381 using F’s least significant difference, 562–565 See also Interval estimation Confidence levels, 351–352 Consequences, 21–3 Consistency of estimators, 334 Consumer Price Index (CPI), 958–959 Consumer’s risk, 937 Continuity correction factor, 288–289 Continuous improvement, 918, 922 Continuous probability distributions, 300–301 binomial, normal approximation of, 288–289 exponential distribution, 291, 294, 295 normal distribution, 287–289, 531 uniform distribution, 273 using Excel, 301 using Minitab, 300 Continuous random variables, 220, 279 Control charts, 923–934 applications, 934–936 formulas, 945–946 interpretation of, 933 np chart, 933 p chart, 931–932 R chart, 924, 929–930, 946 using Minitab, 948–949 overview, 923–924 structure, 923f–924 x– chart, 924–929 Control limits, 348n formula, 945 np chart, 933 p charts, 931–932 x– chart, 924–929 Convenience sampling, 336–337 in sample surveys, 22–4 Cook’s distance measure, 721–723, 740 Correlation coefficient, 141–144 applications, 146–148 of bivariate probability distributions, 233–235, 238 coefficient of determination, 617–618 using Excel, 913, 914 interpretation of the, 144–145 sample, 141–144 Counting rules for experiments, 174–178, 209 Covariance, 138–140 of bivariate probability distributions, 233–235 interpretation of the, 140–141 using Minitab, 167–168 population, 140 of random variables formula, 234, 261 Cravens, David W., 778 Cravens data, 778, 779, 782–783, 785–786, 803–804 Critical value approach Marscuilo pairwise comparison procedure, 515, 537 one-tailed test, 397–399 rejection rule, 396–398 two-tailed test, 401 Crosby, Philip B., 918 Cross-sectional data, 8–9 Cross-sectional regression, 807 Crosstabulations, 55–58 using Excel, 93–96 using Minitab, 89 Cumulative frequency distributions, 45–46 Cumulative percent frequency distribution, 46 Cumulative r frequency distribution, 46 Curvilinear relationships models, 756–763 Cyclical patterns, 810–812 D Dashboards, data, 72–74, 148–151 effectiveness, improvement of, 148–151 Data, 1–31 analytics and, 17–18 categorical and quantitative, 8, 34 collection of, 7, 19, 20, 547–548 company internal records of, 11–12 computers and statistical analysis, 20 cross-sectional and time series, 8–10 defined, descriptive statistics, 14–16 elements, variables, and observations, 5–7 errors in acquisition, 13–14 existing sources, 11–12 experiments, 13, 547–548 government agencies providing, 12, 16 mining of, 18–20 observational study, 12–13, 558–559 overview, 22 scales of measurement, 7–8 sources of, 11–14 statistical inference, 16–17, 312 statistical studies, 24–31 summarizing See Summarizing data terms for, 23 time and cost issues, 13, 305 variety of, 19 velocity of, 19 volume of, 19 See also Statistics analysis Data dashboards, 72–74 effectiveness, improvement of, 148–151 DATAfiles, 90, 87 in Excel, 90 using minitab, 87 Data mining, 18–20 Data set, 5, 6–7, 31t, 344t, 653f, 654f, 655t, 656t, 657t, 722t, 794t Data visualization, 34, 71–78 data dashboards, 72–74 effective graphical displays, 71–72 practice case, 74–77 Data warehousing, 19 Decision analysis, 21–2–21–35 applications, 21–10–21–13, 21–21–21–24, 21–27–21–29 with Bayes’ theorem, 206, 21–24–21–27 formulas, 21–30 with probabilities, 21–5–21–9 problem formulation, 21–3–21–5 with sample information, 21–13–21–20 Decision making, 419–420, 923, 21–5–21–9 Decision nodes, 21–4–21–5 Decision strategies, 21–15–21–18 Decision trees, 21–4–21–5, 21–14–21–15 Decomposition, 848–856 Deflating a series, 960–962 Degree of belief, 179 Degrees of freedom of the t distribution, 354–355, 453–454, 473, 533 Deming, W Edwards, 918 De Moivre, Abraham, 275 Dependent events, 197 Dependent variables, 600, 603–605, 645–647, 698 Descriptive analytics, 18 Descriptive statistics, 14–16 association, measures of, 20, 138–148 distribution shape, measures of, 125 graphical displays See Graphical displays of data location, measures of, 104–113 numerical measures, 15, 148–151 tabular displays See Tables for summarizing data using Excel, 168–170 using Minitab, 166–167 variability, measures of, 118–122 See also Summarizing data Deseasonalized time series, 853–855 Deviation about the mean, 119–120 Difference of population means hypothesis testing, 447–449, 454–456 interval estimates, 445–449, 452–454 Difference of population proportions hypothesis testing, 468–469 inference about two populations, 445–449 interval estimates, 466–468 standard error, 318, 446, 448, 466, 468, 473 Digital dashboards, 72 Discrete probability distributions, 222–227 applications, 225–227 binomial distributions, 248–249, 261–262 bivariate distributions, 232–235 developing, 222–225 hypergeometric distribution, 256–257 overview, 222–224 Poisson distribution, 252–254 random variables, 219–220 using Excel, 267–268 using Minitab, 267 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1084 Index Discrete probability function formula, 223, 224, 261 Discrete random variables, 219–220, 261 Discrete uniform probability function, 261 Dispersion, measures of, 118, 152, 227 Distance or length intervals, 254 Distribution-free statistical methods, 873 See also Nonparametric statistical methods Distributions, sampling, 314–316 of p–, 326–330 of x–, 316–325 Distribution shapes, measures of, 125 Dot plot graphs, 43, 72 using Minitab, 88 Double-blind experimental design, 551 Dow, Charles Henry, 959 Dow Chemical Company, 917 Dow Jones averages, 959–960 Dow Jones Industrial Average (DJIA), 959 Drilling down, 151 Duke Energy, 22–2 Dummy variables, 710, 711, 713–714 categorical variable and, 713, 844 seasonal pattern forecasts, 840–844 Johnson Filtration example, 710–711 Dunnhumby, 682 Durbin-Watson Test, 793–796, 798 E EAI problem, 319–320 Economics applications, statistical, Efficiency of estimators, 333–334 Electronics Associates, Inc (EAI), 304–305 sampling distribution, 319–320 Elements of data, 5–7, 13, 16 in sample surveys, 302, 305, 307–308, 22–2–22–23 Empirical discrete distributions, 222, 232–235 Empirical rule, 128–130, 277 Error term € assumptions about, 565n, 621, 697–698 assumptions about, multiple regression, 697–698 and autocorrelation, 793–796 simple linear regression, 644 Estimated logistic regression equations, 727–730, 740 Estimated logit, 734, 740 Estimated multiple regression equations, 684 using, 685, 712 Estimated regression equations, 601–603, 706–707 formula, 662 least squares method, 603–607 linear regression, 600–601 multiple regression, 706–707 simple linear regression, 601–603 slope, 601, 602 using Excel, 679 y-intercept, 601, 602, 604, 662 Estimated regression line, 602, 604, 615–616 Estimated simple linear regression equation, 601–603, 606 Ethical guidelines for statistical practice, 20–22 Events, 183–191, 197 complement of A, 187–188 defined, 183–184 independent, 197–198, 210 intersection of, 189–190 mutually exclusive, 191 and probabilities, 172–173, 184–185, 188 union of, 188–189 Excel analysis of variance (ANOVA), 594–597, 680 bar charts, 90–92, 98–101 chi-square distribution, 542–543 completely randomized design, 594–595 continuous probability distributions, 101, 301 crosstabulations, 93–96 DATAfiles, 90 for data presentations, 90–101 descriptive statistics, 168–170 discrete probability distributions, 267–268 exponential smoothing, 869 factorial experiments, 596–597 forecasting, 869–870 frequency distributions, 90–93 graphical displays of data, 90–101 histograms, 92–93 hypothesis testing, 438–442 inference about two populations, 480–482 interval estimates, 480–482 moving averages, 869 multiple regression, 751–753 nonparametric statistical methods, 913–915 PERCENTILE.EXC, 111 PivotChart, 92–93 population means: s known, 438 population means: s unknown, 438–440 population proportions, 441–442 population variance, 506 POWER function, 110 randomized block design, 595–596 random sampling, 345 regression analysis, 678–680 sampling, 345 scatter diagrams and trendlines, 96–98 sign test, 913–914 Spearman rank-correlation coefficient, 914–915 tables for summarizing data, 90–101 time series forecasting, 869–870 trend projection, 869–870 Expected frequencies, 510–511, 537 Expected value, 317, 21–6, 21–30 Expected value approach, 227, 21–5–21–7 Expected Value of Perfect Information (EVPI), 21–7–21–9, 21–30 Expected Value of Sample Information (EVSI), 21–18–21–20, 21–30 Expected value of x–, 317 Expected values (EVs), 227 for the binomial distribution, 248–249, 261 decision analysis, 21–5–21–7 of discrete random variables, 227–228, 261 formula, 339 of the hypergeometric probability distribution, 257, 262 of a linear combination of variables, 235–237 261 of sample means, 317, 339, 343–343 sample proportion, 339 standard deviation, 342–344 Expected value without perfect information (EVwoPI), Expected value with perfect information (EVwPI), Experimental designs, 546–548 applications, 792–793 multiple regression approach to, 788–792 sampling distributions, 550 Experimental outcomes, 174 Experimental statistical studies, 13, 545, 546, 559 Experimental units, 546, 548, 568, 569 Experiments binomial, 242–243 Poisson, 252–254 See also Random experiments Experimentwise Type I error rate, 565–566 Exponential probability density function, 291, 295 See also Exponential probability distribution Exponential probability distribution, 291–293 computing probabilities for, 291–292 cumulative probabilities, 292, 295 formula, 295 mean, 291, 292, 293 and the Poisson distribution, 292–293 standard deviation, 292 Exponential smoothing, 821–825 using Excel, 869 formula, 860 using Minitab, 867 Exponential trend equation, 835, 860 F Factorial experiments, 575–580 applications, 580–582 ANOVA procedure, 577 computations, 577–580 defined, 575 using Excel, 596–597 formulas, 585–586 using Minitab, 593 overview, 575–576, 582–583 Factorial notation, 177 Factorial experiment, 575–580 with Excel, 596–597 Factor of interest, 569 Factors, 546 Failure in trials, 242–243, 256–257 F distribution, 495–500 Federal Reserve Board, 12, 259, 837, 965 Feigenbaum, A.V., 918 Fermat, Pierre de, 172 Finance applications, statistical, Financial applications, with bivariate probability distributions, 235–238 statistical, Finite population correction factor, 318 Finite populations, 305–307 combinations and, 177 probability sampling methods, 305–308 sample mean, standard deviation of, 311–312 sample proportion, standard deviation of, 304, 311–312 sample random sample, 304, 305–307 sampling from, 305–308 sampling with replacement, 307 sampling without replacement, 307 Fisher, Ronald Aylmer, 546 Fisher’s least significant difference (LSD), 562–565 Fitch Group, Fitness for use, 918 Five-number summaries, 133–134, 136–138 Food Lion, 347 Forecast accuracy, 823–824 exponential smoothing, 821–825 managers and, 807 moving averages, 818–821 Forecast error, 813–814 Forecasting See Time series forecasting Forward selection procedure, 784 using Minitab, 804 Frames, 304 in sample surveys, 22–3 Frequency distributions, 34–35, 41–43 for categorical variables, 34–35, 90–92 cumulative, 45–46 descriptive statistics, 14t sampling distributions and, 315f, 495f for quantitative variables, 41–43, 90–93 using Excel, 90–93 F Test, 554–556 formula, 663, 740, 798 independent variables, adding to model, 626, 629, 775–776, 798 least squares estimators, 626–628 multiple regression, 699–702 simple linear regression, 626–628 variance estimates, 554–556 G Galton, Francis, 600 Gauss, Carl Freidrich, 605 General linear model, 756–768 applications, 769–771 curvilinear relationships, 756–763 dependent variable transformations, 763–767 formula, 798 nonlinear models and, 767–768 See also Linear trend regression Geographic Information System (GIS), 76 Geometric means, 109–110, 153 Goodness of fit tests, 527–534 applications, 535–536 formula, 537 multinomial probability distribution, 527–530 normal probability distribution, 530–534 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1085 Index overview, 536 test statistic for, 541, 528–534 using Excel, 542–543 using Minitab, 541–542 Google revenue, 27f Gosset, William Sealy, 354 Graphical displays of data, 64–70 applications of, 69–72 bar charts, 36–37, 65–69, 72 data dashboards, 72–74, 148–151 dot plots, 72 effective use of, 71–72 histograms, 44–46, 72, 92–93 pie charts, 36–37, 72 scatter diagrams and trendlines, 64–65, 96–98 stem-and-leaf displays, 46–49, 72 summarizing data for two variables, 64–68, 77f using Excel, 90–101 using Minitab, 87–90 types of, 72, 77f Gross domestic product (GDP), 5, 6, 14–15, 659, 961 H High leverage points, 656–657 Histograms, 44–46, 72 descriptive statistics, 14, 15 examples, 15f, 44f, 45f, 126f, 315f, 316f, 359f and stem-and-leaf displays, 46–49, 72 using Excel, 92–93 using Minitab, 88 Horizontal patterns, 807–809 Hypergeometric probability distribution, 256–257 Hypergeometric probability function, 256–257, 262 Hypothesis testing, 385–442 alternative hypotheses, 387–388 applications, 417–419, 423–424 chi-square distribution, 489–492, 510–512, 518, 523 confidence intervals, 403–404 and decision making, 419–420 of difference of population means, 445–449, 454–456 of difference of population proportions, 468–469 Durbin-Watson, 796f forms of, 389 interval estimates, 403–404 lower tail test, 396, 398–399, 402, 411, 414, 416, 420, 425 matched samples, 460–462, 878–879 null and alternative hypotheses, 387–390, 395f one-tailed test, 393–399, 408–409, 430, 498 population mean: s known, 393–404, 430 population mean: s unknown, 408–411, 430 population means, 430, 447–449, 454–456 population median, 873–877 and population proportions, 414–416 of population variance, 489–492 sample sizes, 425–427 standard error of the mean, 318, 448, 468 steps for, 402, 423 test statistic formula, 430, 473, 474 two-tailed test, 400f, 403–404, 409–411 Type I and Type II errors, 390–393, 420–423 upper tail test, 393, 398–399, 402, 408–409, 411, 414–415, 416 using Excel, 438–442 using Minitab, 436–427, 456 I Incomplete block designs, 572 Independence, test of, 519–523 using Minitab, 541 Independent events, 197 multiplication law for, 197–198, 210 and mutually exclusive events, 191 Independent sample design, 460–461 Independent simple random samples, 445–447, 448, 466, 467, 472 Independent variables adding or deleting from model, 600, 621, 775–776, 798 correlation of, 703 defined, 600, 703 experimental design, 546 F test and, 626 using Minitab, 687, 688, 701, 710, 712, 780f multiple regression, 683–688 regression analysis, 600, 605, 606, 655, 656 against residual plots, 644–645, 647–649 selection procedures, 782–786 types of, 709 Index numbers, 950–969 Consumer Price Index (CPI), 958–959 price indexes See Price indexes price relatives, 951 Producer Price Index (PPI), 958–959 quality indexes, 943 Index of Industrial Production, 965 Indicator variables, 710, 711, 713–714 Indifference quality level (IQL), 943 Individual significance, 699 Inference about two populations, 445–449, 466–469, 495–50 applications, 450–452, 457–460, 457–460, 463–466, 500–502 degrees of freedom, 496, 498 difference between population means: matched samples, 460–462 difference between population means: s1 and s1 known, 445–449 difference between population means: s and s unknown, 452–456 of difference of population proportions, 466–469 hypothesis tests, 447–449, 447–449, 454–456, 468–469 interval estimation, 445–447, 452–454, 466–468 overview, 449, 502 sampling distribution, 495–497 test statistics, 497–499 upper-tail testing, 496, 498 using Excel, 481–482, 506 using Minitab, 478–480, 505–506 See also Population variance Infinite populations, 307–308 sampling from, 307–308 Influential observations in linear regression models, 654–657 in multiple regression models, 721–723 Information Resources, Inc., 4, 11 Information systems applications, statistical, Interactions, 576–577, 759–763 effect, experimental design, 576–577 general linear model, 759–763 second order models, 758–760 International Organization of Standardization (ISO), 919 Interquartile ranges (IQRs), 119 formula, 154 outlier identification, 130–131 Intersection of events, 189–190 Interval estimation, 403–404, 445–447 applications, 406–407 with chi-square distribution, 485–492 of difference of population means, 445–447, 452–454, 473 of difference of population proportions, 466–468, 474 and hypothesis testing, 403–404, 447–449 limits, 636 margin of error, 348–352, 633, 635 methods, 405–406 of population means, 347–348, 373 and population proportion, 322, 373 of population variance, 347–348, 485–489, 502 procedures for, 403 regression equation, estimated, 632 and sample size, 363–365, 373 using Excel, 382–384 using Minitab, 380–381 Interval scale of measurement, Ishikawa, Karou, 918 ISO 9000, 919 ith observation, 603, 605, 614, 656 ith residual, 614, 643, 647, 648 standard deviation of, 919 standardized residual of, 647–649 J John Morrell & Company, 386 Joint probabilities, 195, 21–26–21–27 Judgment sampling, 337, 22–4 Juran, Joseph, 918 K Key performance indicators (KPIs), 73, 75, 148 Kruskal-Wallis test, 897–899 applications, 899–901 formula, 908 medians of two populations and, 899 using Minitab, 912–913 Kruskal-Wallis test statistic, 897–899 L Laspeyres index, 954 Leaf unit, 49 Least squares criterion, 604, 605, 607, 662 formula, 740 multiple regression, 684–685 Least squares estimators, 601–603 confidence intervals, 625–626 F Test, 626–628 sampling distributions, 618, 624 standard deviations, 604, 607 t Test, 623–625 Least squares formulas, 662 Least squares method, 603–607, 684–689 applications, 689–694 coefficients interpretation and, 688–689 estimated regression equation, 601–603, 683–684 formula, 740 using Minitab, 687f multiple regression, 684–689 Butler Trucking Company example, 685–688 Length or distance intervals, 254 Levels of significance, 391–392, 429 Leverage of an observation, 648n, 656–657, 664, 718–719 Limits of box plots, 134–135 Linear exponential smoothing, 821–825 Linear regression, simple See Simple linear regression Linear trend equation, 830–831, 854, 860 Linear trend regression, 828–833 trend projection, 828–833 Location, measures of See Measures of location; individual measurements Location of the pth percentile, 111–112, 153 Logarithmic transformations, 764, 766–767 Logistic regression, 725–726 using Minitab, 753 Logistic regression equation, 726–734 applications, 735–738 estimating, 727–730 formula, 740 interpreting, 731–733 logit transformation, 734 managerial use, 730–731 with Minitab, 753 overview, 726–727 significance testing, 730 Logit, 734, 740 Logit transformation, 734 Lots, 936, 938–940 Lot tolerance percent defective (LTPD), 943 Lower tail test critical value approach, 397–398 hypothesis testing, 396, 398–399, 402, 411, 414, 416, 420, 425 for population variance, 492, 497, 498 p-value approach, 395–397 M MAE (mean absolute error), 122 time series forecasting, 814–816, 820, 825, 858 Magazines, use of statistics in, 2–3, 14 Malcolm Baldrige National Quality Award, 919 Mann-Whitney-Wilcoxon (MWW) test, 886–893, 912 applications, 894–896 formula, 907 medians of two populations and, 893 using Minitab, 912 ordinal (rank-ordered) data and, 888 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1086 Index MAPE (mean absolute percentage error), 815–816, 820, 825, 833, 835, 858 Marascuilo procedures, 515, 537 Marginal probabilities, 195–196 Margins of error, 347–348 difference between population means, 445–447 and interval estimates, 347–348 for population proportions, 366–369 regression equation, estimated, 625, 632, 633, 635 and sample size, 358–360 Market basket, 958 Marketing applications, statistical, Matched sample design, 460–461 Matched samples, 460–462 applications, 463–466 hypothesis testing, 460–462 sign test, 878–879, 911 using Excel, 482 using Minitab, 479, 911–912 MeadWestvaco Corporation, 303–304 Mean, 104–107 arithmetic, 104 defined, 104 expected value, 339, 342–343 of the exponential distribution, 291, 292, 293 for the Mann-Whitney-Wilcoxon test distribution, 886–893, 912 of the normal distribution, 276– 277, 278, 280, 282–283, 284 regression equation, estimated, 601–603 for the sign test distribution, 873, 876, 877 standard deviation, 343–344, 924–929 weighted, 106–107 for the Wilcoxon signed-rank test distribution, 881–884 Mean absolute error (MAE), 814 time series forecasting, 814 Mean absolute percentage error (MAPE), 815–816 Means, 104–107 deviation about the, 119–120 sample, 104–106 Mean squared error (MSE), 553–554 defined, 553 estimate of s2, 623 formula, 553, 662, 740 multiple regression, 699–701, 740 simple linear regression, 623, 626– 628 time series forecasting, 815 Mean square due to regression (MSR) formula, 663, 740 multiple, 699–701, 740 simple linear, 626–628 Mean square due to treatments (MSTR), 552–554 Measures of association, 138–145 Measures of distribution shapes, 125 Measures of location, 104–113 applications for, 114–117 geometric mean, 109–110, 153 means, 104–106 median, 107–108 mode, 110–111 percentiles, 111–112 quartiles, 112–113 weighted mean, 106–107 See also individual measurements Measures of variability, 118–122 applications, 122–125 coefficient of variation, 121–122 interquartile range, 119 range, 118–119 standard deviation, 120–121 variance, 119–120 Medians, 107–108, 893 Minitab analysis of variance (ANOVA), 592–593 backward elimination procedure, 804 best-subsets regression, 804 box plots, 167 chi-square distribution, 541–542 completely randomized design, 592–593 continuous probability distributions, 300 control charts, 948–949 correlation coefficient, 167–168 covariance, 167 crosstabulations, 89 DATAfiles, 87 for data presentations, 87–89 descriptive statistics, 166–167 difference between population means, 478–479 difference between population proportions, 480 discrete probability distributions, 267 dot plot graphs, 88 Exact option, 437 exponential smoothing, 867 factorial experiment, 593 forecasting, 866–867 forward selection procedure, 804 goodness of fit tests, 541–542 graphical displays of data, 87–89 histograms, 88 hypothesis testing, 436–437 independence, test of, 541 inference about two populations, 478–480 interval estimates, 380–381, 436n Kruskal-Wallis test, 912–913 logistic regression, 753 Mann-Whitney-Wilcoxon (MWW) test, 912 matched samples, 479, 911 moving averages, 867 multiple regression, 751 nonparametric statistical methods, 911–913 population means: s known, 380, 436 population means: s unknown, 381, 437 population median, 911 population proportions, 381, 437 population variances, 505–506 randomized block design, 593 random sampling, 344–345 regression analysis, 639–640, 677–678, 757, 759, 763, 765, 780, 781, 783, 785 sampling, 344–345 scatter diagrams and trendlines, 89 sign test, 911 simple linear regression, 677–678 Spearman rank-correlation coefficient, 913 stem-and-leaf displays, 88 stepwise regression procedure, 782–784, 804 tables for summarizing data, 87–89 test of independence, 541 time series decomposition, 868 time series forecasting, 866–868 trend projection, 868 using computers and, 639–640 variable selection procedures, 803–804 Wilcoxon signed-rank test, 911–912 Modes, 110–111 Monsanto Company, 755 Monthly data, 844, 855 Moody’s investor service, 5n Moving averages, 818–825 using Excel, 869 exponential smoothing and, 821–825 formula, 860 using Minitab, 867 weighted, 821 See also Forecast accuracy MSE See Mean squared error (MSE) MSR See Mean square due to regression (MSR) MSTR (mean square due to treatments), 552–553, 554–556, 559 Multicollinearity, 703 Multimodal data, 111 Multinomial probability distribution, 527–530 Multiple coefficient of determination, 694–695 Multiple comparison procedures, 514–516, 562–566 applications, 567–568 for equality of population proportions, 509–516, 541 Fisher’s least significant difference (LSD), 562–565 formulas, 585 using Minitab, 541 Type I error rates and, 565–566 Multiple regression, 683–684 categorical independent variables, 709–714 coefficient of determination, 614–617 coefficients, 688–689 experimental design for, 788–792 formulas, 739, 740 least squares method, 603–607 logistic regression, 725–726 model, 683–684 multiple coefficient of determination, 694–695 residual analysis, 600, 639, 647, 718–723 using Excel, 751–753 using Minitab, 751 Multiple regression analysis, defined, 683 Multiple regression equation, 683–684 Multiple regression models, 683–684 Multiple sampling plans, 942 Multiple-step experiments, 174 Multiplication law, 197–198, 210 Multiplicative decomposition model, 849, 860 Mutually exclusive events, 191 N Naive forecasting method, 813–816, 817 National Aeronautics and Space Administration (NASA), 172 Nevada Occupational Health Clinic, 806 Newspapers, statistics use in, 2–3, 14 Neyman allocation, 22–17–22–19, 22–32 Nodes, 21–4–21–5 Nominal scale of measurement, Nonlinear models, 767–768 curvilinear relationships models, 756–763 intrinsically linear, 767–768 Nonlinear trend regression, 833–835 Nonparametric statistical methods, 873 Kruskal-Wallis test, 897–899, 912–913 Mann-Whitney-Wilcoxon test, 886–893, 912 rank correlation, 901–903, 913, 914–915 sign test, 873–877, 911, 913–914 using Excel, 913–915 using Minitab, 911–913 overview, 906 Wilcoxon signed-rank test, 881–884 Nonprobabilistic sampling, 336–337, 22–4 Nonsampling errors, 22–5 Normal curve, 275–277 Normal probability density function, 275, 276, 278, 295 Normal probability distribution, 275–285, 530–534 applications, 286–287 approximations for nonparametric methods, 876–877, 883, 890, 892, 898, 903, 906 binomial probability estimation with, 287–289 central limit theorem, 319, 320f computing probabilities for, 282–283 confidence intervals for, 649–650 empirical rule, 128–130, 277 Great Tire Company example, 283–285 goodness of fit test, 530–534 mean, 276–277, 278, 280, 282–283, 284 median, 276 mode, 276 normal curve, 275–277 sampling distribution approximation, 315–316, 318, 319, 328, 329–330, 334 sign test, 875f–876 standard deviation, 277–282, 531, 533–534 Normal probability plots, 649–650 Normal scores, 649–650 Np chart, 933, 946 Null hypothesis, 387–390 challenging, 388–389 developing, 387–388 forms for, 389–390 O Observational statistical studies, 12–13, 546 Observations of data, 5–7 Observed frequencies, 536 goodness of fit, 527–528, 530, 532, 534 in multiple population proportions, 509, 510, 511, 512, 514 test of independence, 520–521, 523 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1087 Index Observed level of significance, 397, 398 Odd ratios, 731–733 Odds in favor of an event occurring, 731–732, 740 Ohio Edison Company, 21–2 One-tailed test, 393–399, 498, 523 critical value approach, 397–398 overview, 398–399 population means: s known, 393–399 population means: s unknown, 408–409 p-value approach, 395–397 sample size for, 426, 430 test statistic, 394–395 Open-end classes, 49 Operating characteristic (OC) curves, 939–940 Ordinal scale of measurement, Outcomes, formula for, 261 Outliers, 130–131 of box plots, 134–135 data acquisition errors, 13–14 detecting in regression models, 652–654 interquartile ranges (IQRs), 130–131 using Minitab, 654f, 655f, 657f Overall sample means, 945 formula, 927, 945 quality control, 36, 448–449, 466 Overall significance, 699 P Paasche index, 954 Parameters multiple regression and, 711–713 of a sampling population, 305 Parametric statistical methods, 872–873 Pareto, Vilfredo, 36 Pareto diagram, 36 Partitioning total sum of squares, 556 Pascal, Blaise, 172 Payoffs, 21–4 Payoff tables, 21–4 p chart, 931–932, 946 Pearson, Karl, 600 Pearson product moment correlation coefficient, 141–143, 154 Percent frequency distributions, 35 Percentiles, 111–112 quartiles, 112–113 Perfect information, 21–7–21–9 Permutations, 177–178 counting rules for, 178, 209 Pie charts, 36–37, 72 Point estimates, 311–312 Point estimation, 310–312 Point estimators, 310–312, 332–334 applications, 312–313 consistency of, 334 difference between population means, 311, 446, 448, 466, 468, 473 difference between population proportions, 466–468, 474 efficiency of, 333–334 population parameters, 332–334, 335, 337 of population variance, 456, 481, 485 properties of, 332–334 regression equation, estimated, 602, 625, 632 and sample means, 445–456, 448 and sample standard deviations, 121 and sample variances, 119–120, 481 simple random samples,305, 307–308, 312 unbiased, 332–333 Poisson, Siméon, 252 Poisson experiments, 252–254 Poisson probability distribution, 252–254 assumptions for, 260 applications, 255 Bell Labs, 253 Citibank ATM wait times, 218 distance or length intervals, 254 and the exponential distribution, 292–293 function, 252 mean and variance, 254 time intervals, 253–254 Poisson probability function, 252, 262 Pooled estimators of population proportions, 468–469, 473, 474 Pooled sample variances, 456 Population correlation coefficient, 143, 629, 676 Population covariance, 140, 154 Population means, 106, 444–482 applications, 406–407 cluster sampling, 335–336, 22–23–22–25 difference between, estimating, 445–449 formula, 153 hypothesis testing, 393–404, 430 inference about difference between: matched samples, 460–462 inference about difference between: s and s known, 445–449 inference about difference between: s and s unknown, 452–456 interval estimates, 347–352, 355– 358, 360, 373, 445–449, 473 observational study, 558–559 sample sizes, 363–365, 373, 425–427, 430 simple random sampling, 307–308, 312, 22–6–22–7 standard deviation, 445–447, 448, 452–453, 545–455, 456, 461, 472 stratified simple random sampling, 335, 22–12–22–14 testing for equality of, 468, 558–559 using Excel, 481 using Minitab, 478–479 Population means: s known, 348–352, 445–452 applications, 353–354, 450–452, 457–460 critical value approach, 397–398, 401 hypothesis testing, 403–404, 430, 447–449 interval estimate, 348–352, 373, 382, 445–447 margin of error, 348–352, 447 one-tailed test, 393–399 overview, 398–399, 401–403, 449 p-value approach, 395–397, 398–399, 400–401 standard deviation, 924–926, 945 test statistic, 394–395, 473 two-tailed test, 399–401 using Excel, 383, 438, 481 using Minitab, 380, 436, 480–481 Population means: s unknown, 354–361, 452–456 applications, 358, 362–363, 412–414, 457–460 hypothesis testing, 408–411, 430, 454–456 interval estimate, 355–358, 360, 382–383, 452–454 matched samples, 482 margin of error, 355–358 one-tailed test, 408–409 overview, 354–355, 411, 456 using small samples, 358–360 standard deviation, 926–929, 946 test statistic, 410–411, 473 two-tailed test, 409–411 using Excel, 382–383, 438–440, 481 using Minitab, 381, 437 summarization of, 360 Population median, 873–877, 911 Population in surveys, 22–2 Population of a study defined, 16 finite, sampling from, 305–307 infinite, sampling from, 307–308 Population parameters, 601–602 defined, 305 and hypothesis testing, 386, 387, 388, 389, 404, 428 and point estimators, 332–334 regression equation, 601–602 Population proportions, 326–330, 414–416, 509–516 applications, 370–372, 417–419, 470–472 and chi-square distribution, 509–510, 511–515, 516 cluster sampling, 335–336, 22–25–22–27 equality of, 509–516, 541, 554–555 expected value, 327, 339 formula, 326–327 and hypothesis testing, 414–416, 468–469 inference about difference between, 466–469 and interval estimation, 322, 366–367, 373, 383–384, 466–468, 474 Marascuilo pairwise comparisons, 515, 537 and margin of error, 347–352, 366–369 multiple comparison procedures, 514–516 multiple population testing, 509–516, 519 overview, 416, 472 pooled estimators, 468–469, 473, 474 sample, 509–516 sample sizes estimates, 368–369 simple random sampling, 305, 307–308, 312, 22–8–22–9 sampling distribution, 328–330 standard deviation, 327–328 stratified simple random sampling, 335, 22–15–22–16 testing for equality of, 509–516, 541, 555 test statistic, 474 using Excel, 383–384, 441–442 using Minitab, 381, 437, 480, 541 Populations, 16 Population totals cluster sampling, 335–336, 22–25 simple random sampling, 305, 22–7–22–8 stratified simple random sampling, 335, 22–14–22–15 Population variances, 119, 154, 485–492 applications, 492–489, 500–502 between-treatments estimates of, 552–553 formula, 154, 502 inferences about, 485–500 interval estimates, 347–348, 485–489, 502 lower tail test, 492, 497, 498 overview, 502 point estimators, 456, 481, 485 single population, 445, 462, 485 stratified random sampling, 335, 22–17, 22–19 test statistic, 489–492, 497–499, 502 two populations, 495–500 two-tailed test, 489, 491, 492, 498–499 upper tail test, 487, 490–492, 496–499 using Excel, 506 using Minitab, 505–506 within-treatments estimates of, 550, 553–554 Posterior probabilities, 202, 21–13, 21–26–21–27 Power curves, 422 Power of the test, 422 Power value, 422 Prediction intervals, 632, 634–636 Butler Trucking Company example, 707 formula, 663 linear regression equation, estimated, 634–636 margin of error, 635 multiple regression equation, estimated, 706–707 new observations and, 636 Predictive analytics, 18 Predictors, 632, 779, 804 Prescriptive analytics, 18 Price indexes, 955–964 aggregate, 952–954, 956–957 considerations, 963–964 Consumer Price Index (CPI), 958 deflating a series by, 960–962 Dow Jones averages, 959–960 formulas, 967 and price relatives, 952, 967 Producer Price Index (PPI), 958–959 quality changes in, 964 selection of, 963 weighted aggregated, 953–954, 967 Price relatives, 952 and aggregate price indexes, 952–954, 956–957 formulas, 967 Prior probabilities, 202, 21–13 Probabilistic sampling, 22–4 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1088 Index Probabilities, 173–216 applications, 182–183, 186–187, 192–194, 199–201 assigning, 178–180, 223 conditional, 194–197, 209, 21–24–21–26 counting rules, 174–178, 209 decision analysis, 21–5–21–9 See also Bayes’ theorem defined, 172–173 events and, 172–173, 183–185, 188 experiments, 173–174 KP&L project, 176, 180–181 measuring by area, 272–274 relationships of, 187–191 of single points, 273 standard normal table and, 281 Probability density functions, 277–282 normal, 275, 276, 278, 295 standard normal, 277–282, 295 Probability distributions, 222, 224, 247f See also Continuous probability distributions; Discrete probability distributions Probability functions, 222, 252, 262 Probability samples, 181, 305, 308, 337 Probability sampling techniques, 335–336 Probability tree, 175–176, 202–204 Procter & Gamble, 270 Producer Price Index (PPI), 958–959 Producer’s risk, 937 Production applications, statistical, Proportional allocation, 22–19, 22–33 Protected LSD test, 565 Purchasing power vs real wages, 961 p-value approach independent variables, adding to model, 775–776, 798 interpreting, 395–397 lower tail test, 395–397 one-tailed test, 395–397 rejection rule, 402 two-tailed test, 400–401 Q Quadratic trend equation, 833–835, 860 Quality assurance, 921 Quality control, 918–934 acceptance sampling, 936–943 bar charts and, 36 history of, 918–922 ISO 9000, 919 Malcolm Baldrige National Quality Award, 919 in population means, 448–449 in population proportions, 466 in the service sector, 922 Six Sigma, 919–921 statistical process control, 922–934 Quality engineering, 921 Quality indexes, 964 Quantitative data, 8, 34, 92–93 Quantitative variables, 8, 41–49 crosstabulation and, 55 defined, frequency distributions, 41–43, 90–93 summarizing data for, 41–49 Quantity indexes, 964–965 Quartiles, 112–113 R Radar charts, 76 Random experiments, 173–174 Randomization, 546, 551 Randomized block design, 568–573 air traffic controller stress test, 569–570 ANOVA procedure, 570–571, 577 applications, 573–575 computations, 571–573 formulas, 585 overview, 568–569 using Excel, 595–596 using Minitab, 593, 580f Random numbers, 303, 305–307, 345, 22–6 Random samples, 344–345 infinite population, 307 using excel, 345 using minitab, 344–345 Random variables, 219–221, 261, 278, 282, 295 Ranges, 41, 795, 903, 928, 930 Rank correlation, 901–903, 913, 914–915 Ratio scale of measurement, 7–8 R chart, 924, 929–930, 946 Reciprocal transformation, 767 Regression analysis computers, need for, 639–640 departure from normality and, 648 estimated, 606–607 independent variables, 600, 618, 626, 656, 663 larger problems, 778–781 mean square error (MSE), 815 model building, 621–622 residuals, 814 results, precision of, 632 simple linear regression, 600–603 time series See Time series analysis using Excel, 678–680 using Minitab, 677–678 variables and, 628 See also Multiple regression; Simple linear regression Regression equation, 631–636 confidence interval, 633–634 estimated, interval, 632 estimated, linear, 631–636 estimated, multiple, 683–684 multiple regression, 683–684, 706–707 prediction interval, 631–636 Regression models, 600–603 assumptions about, 622f multiple, 683–684 simple linear, 600–603 variance of error, 553–554, 621, 622–625, 640, 644, 645 Rejectable quality level (RQL), 943 Relative efficiency of an estimator, 333–334 Relative frequency distributions for categorical variables, 35, 37 cumulative, 46, 49, 78 for quantitative variables, 43 for summarizing data, 77 Relative frequency formula, 79 Relative frequency method, 179 Replications, 578 Research hypothesis, 387–388 Residual analysis of regression model, 643–650, 718–723 applications, 651–652, 725–725, 724–725 Butler Trucking example, 720–721 Cook’s distance measure, 721–723 influential observations, 654–657, 721–723 multiple regression, 718–723 outliers, 652–654, 721 studentized deleted, 720–721 validating, 643–650 Residual for observation i, 643, 648, 653, 663, 664 Residual plots, 644–647 defined, 644 of dependent variable, 645–647 against independent variable, 644–645 Response surface, 698 Response variables, 516, 546, 548, 698 Restricted LSD test, 565 S Sample arithmetic means, 104, 109, 110 Sample correlation coefficients, 141–144, 662 Sample covariance, 138–140, 142f, 154 Sampled populations, 304, 22–3 Sample information, 21–13–21–20 Sample in surveys, 22–2 Sample means, 316–314 expected value of, 317 formulas, 104, 153 measures of location and, 104–105 as sample statistic, 104, 106 sampling distribution of, 318–322 standard deviation of, 317–318 for treatments, 335, 549–550, 551–554 Sample points, 174, 176 Sample proportions for the EAI Problem, 319–320 expected value of, 317 sampling distributions, 316–314 standard deviation of, 317–318 Sample ranges, 928, 930 Samples in auditing accounts, 484 defined, 16 in sample surveys, 22–2, 22–3 statistical inference, 16–17, 312 Sample sizes, 363–365 applications, 365–366, 428 cluster sampling, 335–336, 22–27 determining, 368–369, 425–427 formula, 430 hypothesis testing, 68–369, 425–427 and interval estimates, 363–365, 368f, 373 large, 358 margin of error and, 364, 365 one-tailed test, 426, 430 overview, 428–429 planning value, 364 population mean, 425–427 population proportion estimates, 368–369 recommendation, 364, 456 and sampling distributions, 324, 326–328 simple random sampling, 305–307, 22–9–22–11 small, 318 stratified simple random sampling, 335, 22–16–22–19 Sample space, 174 Sample standard deviation, 121 Sample statistics, 151, 311–312 Sample surveys, 22–2–22–36 applications, 22–12, 22–20–22–21, 22–28–22–29 classification, 22–4 cluster sampling, 335–336, 22–21–22–27, 22–33–22–34 defined, 16 formulas, 22–30–22–34 market research, 16 sampling methods, 22–3–22–4 simple random sampling, 22–6–22–11, 22–30–22–31 stratified simple random sampling, 335, 22–12–22–19, 22–32– 22–33 survey errors, 22–5–22–6 systematic sampling, 336, 22–29 terminology used in, 22–2–22–3 types of, 22–3–22–4 Sample variances, 119–121 formula, 154 for treatments, 554, 559, 566 Sampling, 305–310 applications, 309–310 cluster, 335–336, 22–21–22–27 convenience, 336–337, 22–4 distributions, 314–324 estimates, 304 estimation errors, 304 infinite populations, 307–308 judgment, 337, 22–4 point estimation, 310–312 selecting a sample, 305–307, 22–6 stratified random sampling, 335, 22–12–22–19 systematic, 336, 22–29 using Excel, 345 using Minitab, 344–345 Sampling distributions, 314–324 applications, 325–326, 330–332 binomial, for the sign test, 873, 874–877 chi-square distribution, 485–486, 488–491, 502 defined, 314 F distribution, 495–499 least squares estimators, 603–607 for the Mann-Whitney-Wilcoxon test, 886–893, 912 normal approximation of, 287–289, 328, 366, 367, 369 overview, 314–316 of the point estimator, 326–330, 334f population variance, 485, 495 probability information, 322 for the rank correlation test, 901–903, 913, 914–915 of the sample mean, 316–322, 349f of the sample proportion, 368–369 and sample size, 322–324 for the sign test, 873–877 for the Wilcoxon signed-rank test, 881–884 of x–, 316–324 Sampling errors, 333, 22–5–22–6 bound on, 22–7 Sampling methods, 335–337, 22–3–22–4 Sampling population parameters, 22–4, 22–5, 22–7, 22–12, 22–17, 22–19, 22–29 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1089 Index Sampling units, 22–3 Sampling without replacement, 307 Sampling with replacement, 307 San José copper and gold mine, 172 Scatter diagrams, 64–65 examples, 66f, 144f, 604f, 653f, 656f, 686f, 713f, 722f, 764f influential observations, 655–656 least squares method and, 603, 604, 606 and outliers, 652–653 using Excel, 97f, 98f Scatter diagrams and trendlines, 64–65 examples, 65f, 141f time series plots, 43, 64, 68 using Excel, 96–98 using Minitab, 89 Seasonal adjustments, 855 Seasonal indexes, 849–852 Seasonality, 839–844 irregular values and, 851 monthly data, models based on, 844 with trend, 841–844 without trend, 839–841 Seasonal patterns, 809–810 Second order models, 758–760 interactions, 759–763 Serial correlation of data, 793–796 Shewhart, Walter A., 918 Side-by-side bar charts, 65–67 examples, 67f, 71f using Excel, 98–100 Significance, level of, 391–392 Significance testing, 622–629, 699–703 applications, 630–631, 704–706 F test, 680, 699–702 Butler Trucking Company example, 701 interpreting, 628–629 logistic regression, 730 multicollinearity, 703 multiple regression, 699–703 simple linear regression, 623 t test, 623–625, 702 using correlation, 676–677 Significance tests, 622–629 Sign test, 873–879 about a population median, 873–877 applications, 879–881 formula, 907 with matched samples, 878–879 using Excel, 913–914 using Minitab, 911 skewed differences and, 881 Simple first-order model, 756–759, 764, 794–794 Simple linear regression, 600–603 ANOVA table, 627–628 applications, 608–613 assumptions for the model, 621–622 assumptions for the model, validating, 643–650 coefficient of determination, 614–618 computer solution, 639–640 equation for, 601–603 formulas, 662 F test, 626–628 influential observations, 654–657 least squares method, 603–607 model of, 600–601 outliers, 652–654 regression analysis, 600–603 residual analysis, 643–657 significance testing, 622–629 t Test, 623–625 using estimated regression equation, 623–625 using Minitab, 625, 626, 639–640, 650, 653–654, 655–657, 677–678 values for, 603 Simple random samples, 305–307, 308–309, 312, 22–6–22–11 finite populations, 305–307 point estimators, 332–334 sample surveys, 22–6–22–11 See also Random samples Simple variance formula, 154 Simpson’s paradox, 58–59 Single-factor experiments, 546, 582 Single-stage cluster sampling, 22–21 Six Sigma, 919–921 limits and defects, 920–921 Skewed histograms, 44–45, 126 Skewness of distributions, 45, 125, 126, 152 Slope, 605, 607, 617–618, 662 Small Fry Design, 103 Smoothing constant, 822 Spearman rank-correlation coefficient, 901–903, 913, 914–915 applications, 904–906 using Excel, 914 formula, 908 using Minitab, 913 SSAB (sum of squares for interaction), 577, 578, 586 SSA (sum of squares for Factor A), 577–578, 585, 586 SSBL (sum of squares due to blocks), 570–571, 585 SSB (sum of squares for Factor B), 577, 578, 585, 586 SSE See Sum of squares due to error (SSE) SSR See Sum of squares due to regression (SSR) SST See Total sum of squares (SST) SSTR (sum of squares due to treatments), 553, 556, 570, 571, 584, 585 Stacked bar charts, 67–68, 100–101 Standard deviations, 120–121 of coefficient of variation, 121, 151, 154 of discrete random variables, 227–228 expected value, 342–344 of the exponential distribution, 292 formula, 154, 339, 663, 664, 740 of the ith residual, 614, 643, 647, 648 least squares estimators, 603–607 for the Mann-Whitney-Wilcoxon test distribution, 886–893, 881–884 means, 343–344, 924–929 measure of risk and, 236 of normal approximation of the sign test, 911 of the normal distribution, 275, 277, 282–283, 319 population, 121 and population means, 445–449, 452–456 sample, 121 of sample means, 445–456, 448 of sample proportion, 466–470 for the Wilcoxon signed-rank test distribution, 881–884 variance and, 228 of x–, 317–318 Standard error, 167, 473 difference between population means, 318, 333, 446–447 difference between population proportions, 446, 448, 474 of difference of population proportions, 466, 468, 473 formula, 473 mean vs median and, 333 Standard error of the estimate, 623, 647–648, 662, 663, 680, 700, 718, 723 Standard error of the mean, 167, 318, 333, 446–447 formula, 446, 945 hypothesis testing, 394, 448, 468 quality control, 448–449, 466 Standard error of the proportion, 446, 448, 466, 468, 473, 946 Standardized residuals, 647–649 formula, 664, 740 of the ith observation, 603, 605, 614, 656 Standardized values, 127, 130 Standard normal probability distribution, 277–282, 532 random variable formula, 295 and the t distribution, 355 Standard and Poor’s, 5n States of nature, 21–3, 21–6, 21–9, 21–30 Stationarity assumption, 243 Stationary time series, 808 Statistical analysis, 20 ethical guidelines for, 20–22 Statistical inference, 16–17, 152, 312 Statistical process control, 921–934 applications, 934–936 control charts, 923–933 overview, 922–923, 934 Statistical studies, 13, 20–21, 58, 393, 444, 545 Statistics, defined, Stem-and-leaf displays, 46–49, 72 using Minitab, 88 Stepwise regression procedure, 782–784 using Minitab, 782–784, 786, 804 Strata, defined, 335 Stratified random sampling, 335, 22–12–22–19 population means, 335, 22–12–22–14 population proportions, 22–15–22–16 population totals, 22–14–22–15 sample sizes, 335, 22–16–22–19 sample surveys, 22–3–22–4 Studentized deleted residuals, 720–721 Subjective method for assigning probabilities, 179–180, 223 Successful trials, 242–246 Summarizing data, 34–70 applications for, 38–41, 50–55, 60–64 bar charts and pie charts, 35–37 for categorical variables, 8, 34–38 crosstabulation, 55–58 cumulative distributions, 45–46 dot plot graphs, 43 using Excel, 34, 93–96 frequency distributions, 34–35, 41–43 histograms, 44–45 using Minitab, 34, 89 for quantitative variables, 8, 41–49 stem-and-leaf displays, 46–49 Simpson’s paradox, 58–59 using graphical displays See Graphical displays of data using tables, 55–59 Summation sign (∑), 104 Sum of squares due to blocks (SSBL), 570–571, 585 Sum of squares due to error (SSE), 553–554, 616 coefficient of determination, 614–617 formula, 662 relationship among SST, SSR and, 616, 694 and sum of squares due to regression or total sum of squares, 553–554 within-treatments estimate of population variance, 553–554 Sum of squares due to regression (SSR), 616 coefficient of determination, 614–617 formula, 662 multiple regression, 694–695 relationship among SST, SSE and, 616, 694 and sum of squares due to error or total sum of squares, 553–554, 662 Sum of squares due to treatments (SSTR), 553, 556, 570, 571, 584, 585 Sum of squares for Factor A (SSA), 577–578, 585, 586 Sum of squares for Factor B (SSB), 577, 578, 585, 586 Sum of squares for interaction (SSAB), 577, 578, 586 Sum of squares of the deviations, 119–121, 122 Survey errors, 22–5–22–6 Surveys, 13, 16, 308, 22–3–22–4 See also Sample surveys Symmetric histograms, 44–45 Systematic sampling, 336, 22–29 T Tables for summarizing data crosstabulation, 55–58 two variables, 55–59 Tabular approach, Bayes’ theorem, 205–206 Taguchi, Genichi, 918 Target populations, 312, 22–3 t distribution, 354–355, 456, 623–625 degrees of freedom, calculating, 354–355 Test of independence, 519–523 applications, 524–526 using Minitab, 541 Test statistics, 394–395, 509–516 applications, 517–519 chi-square distribution, 489–492, 489–492, 519–523, 528–534, 537, 541 difference in population means, 22–4 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it 1090 Index Test statistics (continued ) difference in population proportions, 509–516 Durbin-Watson, 793–796 for equality of population means, 468, 558–559 for equality of population proportions, 509–516, 541 Fisher’s least significant difference (LSD) procedure, 562–565 for goodness of fit, 541, 528–534, 537 for hypothesis tests, 394–395, 419, 473, 474 one-tailed test, 394–395 population mean: s known, 394–395, 430, 473 population mean: s unknown, 408–411, 430, 473 and population proportions, 414–415, 416, 430 and population variances, 489–492, 497–499, 502 and sampling distributions, 394–395 Thearling, Kurt, 19 Time series, 10f, 807 Time series analysis, 807, 858 See also Time series forecasting Time series data, 8–10, 807 Time series decomposition, 848–856 applications, 856–858 cyclical component, 855 deseasonalizing the time series, 853–855 monthly data, models based on, 855 overview, 848–849, 858 seasonal adjustments, 853, 855 seasonal indexes, 849–852 using Minitab, 868 Time series forecasting, 812–813, 864–868 accuracy of, 813–817 comparisons, 820 decomposition, 848–856 moving average, 821 patterns, 809–813 seasonality and trend, 839–844 trend projection, 809, 810 using Excel, 869–870 using Minitab, 866–868 Time series method, 807 Time series patterns, 807–813 cyclical patterns, 810–812 exponential smoothing, 821–825 forecasting method, selecting, 812–813 horizontal patterns, 807–809 moving averages, 818–825 seasonal patterns, 809–810 trend patterns, 809, 810 Time series plots, 807 Time series regression, 807, 832–834, 858 Total quality (TQ), 917–988 management movement, 922 See also; Quality control; Statistical process control Total sum of squares (SST), 615 coefficient of determination, 614–617 formula, 662 relationship among SSE, SSR and, 616, 694 and sums of squares due to regression or error, 556, 570, 577, 584, 615, 6166–17 Transformations of dependent variables, 763–767 Treatments, 546 Tree diagrams, 175–176, 203f, 244f Trendlines and scatter diagrams, 64–65, 96–98 Trend patterns, 809–810 seasonality, 839–844 Trend projection, 828–855 applications, 836–839 control conditions and, 933 linear trend regression, 828–833 nonlinear trend regression, 833–835 time series forecasting, 809, 810 using Excel, 866–868 using Minitab, 868, 869–870 Trials, experimental, 173, 308 Trimmed means, 108, 113 t Tests formula, 663, 740 individual significance, 702 least squares estimators, 603–607 multiple regression, 623–625, 702 simple linear regression, 623–624 Two-stage cluster sampling, 22–21 Two-tailed tests, 399–404 applications, 406–407 critical value approach, 401 hypothesis testing, 403–404 interval estimate, 403–404 of the null hypothesis, 399–404 overview, 401–403 population means: s known, 399–401 population means: s unknown, 409–411 for population variance, 489, 491, 492, 498–499 p-value approach, 400–401 Type I errors, 390–393 applications, 423–424 comparison procedures, 565–566 probability of, 391–392 Fisher’s least significant difference (LSD) and, 562–565 sample size, determining, 425–426 and Type II errors, 390–393 Type II errors, 390–393 probability of, 392, 394, 420–423 sample size, determining, 425–426 and Type I errors, 390–393 U Unbiased estimators, 332–333 Uniform probability density function, 271, 295 Uniform probability distributions, 271–272 applications, 274–275 area as a measure of probability, 272–274 Uniform probability functions, 224 continuous, 271 discrete, 224, 260, 261 Union of events, 188–189 United Way, 508, Unweighted aggregated price index, 952–954, 967 Upper tail tests hypothesis testing, 393, 396, 398– 399, 400, 401, 402, 408–409, 410–11, 414–416, 425–429 for population variance, 487, 490–492, 496–499 U.S Commerce Department’s National Institute of Standards and Technology (NIST), 919 U.S Department of Labor, Bureau of Labor Statistics, 12, 951 U.S Food and Drug Administration (FDA), 444 U.S Government Accountability Office (GAO), 484 V Variability, measures of, 118–122 applications, 122–125 coefficient of variation, 121–122 interquartile range, 119 range, 118–119 standard deviation, 120–121, 227–228 variance, 119–120 Variable selection procedures, 782–786 applications, 787–788 using Minitab, 803–804 Variable selection procedures, 782–786 chose of final model, 786 backward elimination, 784–785 best-subsets regression, 785–786, 804 forward selection, 784 stepwise regression procedure, 782–784 Variables, 771–778 applications, 776–778 in data, adding or deleting from model, 771–775, 798 general case, 773–774 prediction errors and, 695 selection procedures, 782–786 use of p- values and, 774–775 Variables sampling plans, 943 Variances, 119–120 for the binomial distribution, 248–249, 262 of discrete random variables, 219–220, 227–228, 261 of the hypergeometric probability distribution, 257, 262 of a linear combination of variables, 236–237, 238, 239, 261 in manufacturing applications, 485 using Minitab, 557f regression model error, 627 Variety, of data, 19 Velocity, of data, 19 Venn diagrams, 187–188 Volume, of data, 19 W Warehousing, data, 19 Weighted aggregated price indexes, 953–954, 967 Weighted aggregated quantity index, 964, 967 Weighted average of price relatives, 967 Weighted means, 106–107, 153 Weighted moving averages, 821 West Shell Realtors, 872 Whiskers of box plots, 134, 151 Wilcoxon signed-rank test, 881–884 applications, 884–886 formula, 907 hypotheses, 884 using Minitab, 911–912 using StatTools, 913 Williams, Walter, 392 Within-treatments estimates, 550, 553–554 World Trade Organization (WTO), 5–6, 7, 8, 14 X x-bars, x– chart, 924–929 Y y-intercept estimated regression equation, 623–625 formula, 662 linear trend equation, 830–831, 854, 860 Z z-scores, 125–127 formula, 154 outlier identification, 130–131 z transformation, 127 z value and table interpolation, 282 Copyright 2017 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) Editorial review has deemed that any suppressed content does not materially affect the overall learning experience Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it