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David r anderson dennis j sweeney thomas a williams james j cochran David r anderson dennis j sweeney thomas a williams james j cochran David r anderson dennis j sweeney thomas a williams james j cochran David r anderson dennis j sweeney thomas a williams james j cochran statistics for business economics, revised south western educational publishing (2017) statistics for business economics, revised south western educational publishing (2017) v CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Cumulative probability Entries in the table give the area under the curve to the left of the z value For example, for z = 1.25, the cumulative probability is 8944 z z 00 01 02 03 04 05 06 07 08 09 5000 5398 5793 6179 6554 5040 5438 5832 6217 6591 5080 5478 5871 6255 6628 5120 5517 5910 6293 6664 5160 5557 5948 6331 6700 5199 5596 5987 6368 6736 5239 5636 6026 6406 6772 5279 5675 6064 6443 6808 5319 5714 6103 6480 6844 5359 5753 6141 6517 6879 6915 7257 7580 7881 8159 6950 7291 7611 7910 8186 6985 7324 7642 7939 8212 7019 7357 7673 7967 8238 7054 7389 7704 7995 8264 7088 7422 7734 8023 8289 7123 7454 7764 8051 8315 7157 7486 7794 8078 8340 7190 7517 7823 8106 8365 7224 7549 7852 8133 8389 1.0 1.1 1.2 1.3 1.4 8413 8643 8849 9032 9192 8438 8665 8869 9049 9207 8461 8686 8888 9066 9222 8485 8708 8907 9082 9236 8508 8729 8925 9099 9251 8531 8749 8944 9115 9265 8554 8770 8962 9131 9279 8577 8790 8980 9147 9292 8599 8810 8997 9162 9306 8621 8830 9015 9177 9319 1.5 1.6 1.7 1.8 1.9 9332 9452 9554 9641 9713 9345 9463 9564 9649 9719 9357 9474 9573 9656 9726 9370 9484 9582 9664 9732 9382 9495 9591 9671 9738 9394 9505 9599 9678 9744 9406 9515 9608 9686 9750 9418 9525 9616 9693 9756 9429 9535 9625 9699 9761 9441 9545 9633 9706 9767 2.0 2.1 2.2 2.3 2.4 9772 9821 9861 9893 9918 9778 9826 9864 9896 9920 9783 9830 9868 9898 9922 9788 9834 9871 9901 9925 9793 9838 9875 9904 9927 9798 9842 9878 9906 9929 9803 9846 9881 9909 9931 9808 9850 9884 9911 9932 9812 9854 9887 9913 9934 9817 9857 9890 9916 9936 2.5 2.6 2.7 2.8 2.9 9938 9953 9965 9974 9981 9940 9955 9966 9975 9982 9941 9956 9967 9976 9982 9943 9957 9968 9977 9983 9945 9959 9969 9977 9984 9946 9960 9970 9978 9984 9948 9961 9971 9979 9985 9949 9962 9972 9979 9985 9951 9963 9973 9980 9986 9952 9964 9974 9981 9986 3.0 9987 9987 9987 9988 9988 9989 9989 9989 9990 9990 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 CUMULATIVE PROBABILITIES FOR THE STANDARD NORMAL DISTRIBUTION Entries in this table give the area under the curve to the left of the z value For example, for z = –.85, the cumulative probability is 1977 Cumulative probability z z 00 01 02 03 04 05 06 07 08 09 Ϫ3.0 0013 0013 0013 0012 0012 0011 0011 0011 0010 0010 Ϫ2.9 Ϫ2.8 Ϫ2.7 Ϫ2.6 Ϫ2.5 0019 0026 0035 0047 0062 0018 0025 0034 0045 0060 0018 0024 0033 0044 0059 0017 0023 0032 0043 0057 0016 0023 0031 0041 0055 0016 0022 0030 0040 0054 0015 0021 0029 0039 0052 0015 0021 0028 0038 0051 0014 0020 0027 0037 0049 0014 0019 0026 0036 0048 Ϫ2.4 Ϫ2.3 Ϫ2.2 Ϫ2.1 Ϫ2.0 0082 0107 0139 0179 0228 0080 0104 0136 0174 0222 0078 0102 0132 0170 0217 0075 0099 0129 0166 0212 0073 0096 0125 0162 0207 0071 0094 0122 0158 0202 0069 0091 0119 0154 0197 0068 0089 0116 0150 0192 0066 0087 0113 0146 0188 0064 0084 0110 0143 0183 Ϫ1.9 Ϫ1.8 Ϫ1.7 Ϫ1.6 Ϫ1.5 0287 0359 0446 0548 0668 0281 0351 0436 0537 0655 0274 0344 0427 0526 0643 0268 0336 0418 0516 0630 0262 0329 0409 0505 0618 0256 0322 0401 0495 0606 0250 0314 0392 0485 0594 0244 0307 0384 0475 0582 0239 0301 0375 0465 0571 0233 0294 0367 0455 0559 Ϫ1.4 Ϫ1.3 Ϫ1.2 Ϫ1.1 Ϫ1.0 0808 0968 1151 1357 1587 0793 0951 1131 1335 1562 0778 0934 1112 1314 1539 0764 0918 1093 1292 1515 0749 0901 1075 1271 1492 0735 0885 1056 1251 1469 0721 0869 1038 1230 1446 0708 0853 1020 1210 1423 0694 0838 1003 1190 1401 0681 0823 0985 1170 1379 Ϫ.9 Ϫ.8 Ϫ.7 Ϫ.6 Ϫ.5 1841 2119 2420 2743 3085 1814 2090 2389 2709 3050 1788 2061 2358 2676 3015 1762 2033 2327 2643 2981 1736 2005 2296 2611 2946 1711 1977 2266 2578 2912 1685 1949 2236 2546 2877 1660 1922 2206 2514 2843 1635 1894 2177 2483 2810 1611 1867 2148 2451 2776 Ϫ.4 Ϫ.3 Ϫ.2 Ϫ.1 Ϫ.0 3446 3821 4207 4602 5000 3409 3783 4168 4562 4960 3372 3745 4129 4522 4920 3336 3707 4090 4483 4880 3300 3669 4052 4443 4840 3264 3632 4013 4404 4801 3228 3594 3974 4364 4761 3192 3557 3936 4325 4721 3156 3520 3897 4286 4681 3121 3483 3859 4247 4641 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 ISBN: 978-1-337-09419-1 Statistics for Business & Economics, Revised 13e Anderson/Sweeney/Williams/Camm/Cochran MindTap® Business Statistics for Statistics for Business & Economics, Revised 13e J00001 MindTap® Business Statistics, Semesters Printed Access Card for AGREEMENT URLs: CengageBrain Service Agreement: www.cengagebrain.com/shop/terms.html MindTap Service Agreement: www.cengage.com/mindtap-service-agreement Cengage Learning Privacy Statement: www.cengage.com/privacy ©2018 Cengage Learning 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 iStockphoto.com/alienforce; iStockphoto.com/TommL Statistics for Business & Economics 13e Revised 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 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Statistics for Business and Economics, Thirteenth Edition, Revised David R Anderson, Dennis J Sweeney, Thomas A Williams, Jeffrey D Camm, James J Cochran Vice President, General Manager: Social Science and Qualitative Business: Erin Joyner Product Director: Mike Schenk Product Team Manager: Joe Sabatino Senior Product Manager: Aaron Arnsparger â 2018, 2015 Cengage Learningđ 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 Content Developer: Anne Merrill Senior Marketing Manager: Nate Anderson Digital Content Designer: Brandon Foltz Product Assistant: Audrey Jacobs Senior Content Project Manager:  Colleen Farmer Unless otherwise noted, all items â Cengage Learning Microsoft Excelđ is a registered trademark of Microsoft Corporation © 2014 Microsoft Library of Congress Control Number: 2016954099 Manufacturing Planner: Ron Montgomery Package ISBN: 978-1-337-09416-0 Production Service: MPS Limited Book only ISBN: 978-1-305-88188-4 Senior Art Director: Michelle Kunkler Internal Designer: Beckmeyer Design Cover Designer: Beckmeyer Design Cover Image: iStockphoto.com/alienforce Intellectual Property   Analyst: Brittani Morgan   Project Manager: Nick Barrows 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 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 Dedicated to Marcia, Cherri, Robbie, Karen, and Teresa 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 Preface xxi About the Authors  xxvi Chapter Data and Statistics  Chapter Descriptive Statistics: Tabular and Graphical Displays 32 Chapter Descriptive Statistics: Numerical Measures  102 Chapter Introduction to Probability  173 Chapter Discrete Probability Distributions  219 Chapter Continuous Probability Distributions  271 Chapter Sampling and Sampling Distributions  304 Chapter Interval Estimation  348 Chapter Hypothesis Tests  387 Chapter 10 Inference About Means and Proportions with Two Populations  445 Chapter 11 Inferences About Population Variances  485 Chapter 12 Comparing Multiple Proportions, Test of Independence and Goodness of Fit  509 Chapter 13 Experimental Design and Analysis of Variance  546 Chapter 14 Simple Linear Regression  600 Chapter 15 Multiple Regression  683 Chapter 16 Regression Analysis: Model Building  756 Chapter 17 Time Series Analysis and Forecasting  807 Chapter 18 Nonparametric Methods  873 Chapter 19 Statistical Methods for Quality Control  918 Chapter 20 Index Numbers  952 Chapter 21 Decision Analysis  (On Website) Chapter 22 Sample Survey  (On Website) Appendix A References and Bibliography  974 Appendix B Tables 976 Appendix C Summation Notation  1003 Appendix D Self-Test Solutions and Answers to Even-Numbered Exercises 1005 Appendix E Microsoft Excel 2016 and Tools for Statistical Analysis  1072 Appendix F Computing p-Values Using Minitab and Excel  1080 Index 1084 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Contents Preface xxi About the Authors  xxvi Chapter Data and Statistics  Statistics in Practice: Bloomberg Businessweek  1.1Applications in Business and Economics  Accounting 3 Finance 4 Marketing 4 Production 4 Economics 4 Information Systems  1.2Data  Elements, Variables, and Observations  Scales of Measurement  Categorical and Quantitative Data  Cross-Sectional and Time Series Data  1.3Data 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 2.1Summarizing Data for a Categorical Variable  34 Frequency Distribution  34 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 vi Contents Relative Frequency and Percent Frequency Distributions  35 Bar Charts and Pie Charts  35 2.2Summarizing 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 2.3Summarizing Data for Two Variables Using Tables  55 Crosstabulation 55 Simpson’s Paradox  58 2.4Summarizing Data for Two Variables Using Graphical Displays  64 Scatter Diagram and Trendline  64 Side-by-Side and Stacked Bar Charts  65 2.5Data 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 3.1Measures of Location  104 Mean 104 Weighted Mean  106 Median 107 Geometric Mean  109 Mode 110 Percentiles 111 Quartiles 112 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Appendix F Computing p-Values Using Minitab and Excel 1081 Step 3. Choose t Step 4. 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 1. Select the Calc menu Step 2. Choose Probability Distributions Step 3. Choose Chi-Square Step 4. 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 1. Select the Calc menu Step 2. Choose Probability Distributions Step 3. Choose F Step 4. 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 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1082 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 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Appendix F Computing p-Values Using Minitab and Excel 1083 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 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 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), 945 Acceptance criterion, 940 Acceptance sampling, 923, 938–945 advantages of, 939 binomial probability function, 948 KALI, Inc example, 939–940 multiple sampling plans, 944 overview, 945, 946 probability of accepting a lot, 940–942 selecting a plan for, 943–944 Accounting applications, 3–4 ACNielsen, 4, 11 Addition law, 190–193, 211 Additive decomposition models, 850–851, 862 Adjusted multiple coefficient of determination, 697, 740, 742 Aggregate price indexes, 954–956 applications, 957, 959–960 computing from price relatives, 958–959 Air traffic controller stress test, 571–572, 573–574, 597 Alliance Data Systems, 601 Alpha to enter or remove, 784, 786, 788, 806 Alternative hypothesis, 388–390 developing, 389–390 American Military Standard Table (MIL-STD-105D), 944 American Society for Quality (ASQ), 919–920 American Statistical Association, 21–22 Analysis of variance (ANOVA), 550–561 applications, 563–564 assumptions for, 550 completely randomized designs and, 553–557 computer results for, 559–560 overview, 550–553 total sum of squares, 558 using Excel, 596–599, 682 using Minitab, 594–595 See also ANOVA tables ANOVA See Analysis of variance (ANOVA) ANOVA procedures, 548, 572–573, 579 ANOVA tables, 558, 559, 572–573 Air traffic controller stress test, 572, 574, 597 block designs, 572, 573 Chemitech experiment, 558, 559 experimental designs, 572, 573 multiple regression, 703 significance testing, 629 simple linear regression, 629–630, 641 time series forecasting, 834 Applications, statistical, 5, 22, 119, 417n, 497 Approximate class width, 42 Area, as measure of probability, 274–276 Arithmetic mean, 104 Assignable causes, 924 Association, measures of, 138–145 Attributes sampling plans, 933, 945 Autocorrelation of data, 795–798 first order, 758–760, 766, 796 formula, 800 Average outgoing quality limit (AOQL), 945 Average range, 929–930, 931, 947 B Backward elimination procedure, 786–787 using Minitab, 806 Baldrige, Malcolm, 921 Baldrige National Quality Program (BNQP), 921 Baldrige stock study, 921 Bar charts, 35–36 descriptive statistics, 14–15 examples of, 15f, 36f, 91f, 524f, 532 selection of, 72, 77, 91, 98, 99, 100 side by side, 65–67 stacked, 67–68 using Excel, 90–92 Barnett, Bob, 921 Basic requirements, for assigning probabilities, 180, 225 Bayes, Thomas, 206 Bayes’ theorem, 204–208 applications, 208–209 branch probabilities, 177, 182, 204–205, 21-24–21-27 formula, 212 tabular approach, 207–208 Bernoulli, Jakob, 244 Bernoulli process, 244 Best-subsets regression, 787–788 using Minitab, 797, 805, 806 Between-treatments estimates, 554–555 Biased estimators, 335 Bias in selections, 310 Big data, 19 Bimodal data, 111 Binomial experiments, 244–245 Binomial probability distributions, 243–251 for acceptance sampling, 940–941, 943 applications, 252–254 defined, 244 expected values of, 250–251, 254 experiment, 244–245 Martin Clothing Store example, 245–249 normal approximation of, 267, 289–291 and the sign test, 876–878 tables of, 249–250 using Minitab, 251f variances of, 250–251 Binomial probability functions, 248–249 for acceptance sampling, 940–941, 943 formula, 263, 948 Binomial random variables, 289, 390 Bivariate probability distributions, 234–240, 261 defined, 234 empirical discrete probability distribution, 234–237 financial applications, 235–238, 237–240 methods, 241–243 overview, 240 Blocking, 570, 571–572, 574, 584 Blocks, in stress test, 571 Bloomberg Businessweek, 2–3 Bonferroni adjustment, 567–568, 585 Bound on sampling errors, 22-7 Box plots, 134–135 applications, 136–138 comparison 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., 547 C Case problems African elephant populations, 164–165 Air Force training program, 504 bipartisan agenda for change, 542 Buckeye Creek Amusement Park, 676–677 business schools of Asia-Pacific, 162 calculus-based derivation of least squares formulas, 677–678 Cincinnati Zoo and Botanical Garden data visualization, 74–76 compensation for sales professionals, 593–594 Consumer Research, Inc., 750 ethical behavior of business students, 437–438 finding the best car value, 675–676, 752–753 forecasting food and beverage sales, 349, 866–867 forecasting lost sales, 867–868 Go Bananas!, 268–269 Gulf Real Estate Properties, 380 Hamilton County Judges, 216–218 Heavenly Chocolates, 162–164 lawsuit defense strategy, 21-33 Marion Dairies, 344 measuring stock market risk, 122, 672–673 Metropolitan Research, Inc., 380–382 motion picture industry, 85–86, 161–162 NASCAR drivers winnings, 751–752 Par, Inc., 479–480 Pelican Stores, 84–85, 160–161 PGA tour statistics, 803–804 point-and-shoot digital camera selection, 674–675 Quality Associates, Inc., 435–436 Queen City, 86–87 significance testing using correlation, 678–679 Specialty Toys, 301–302 U.S Department of Transportation, 673–675 Wentworth Medical Center, 592–593 wines from the Piedmont region of Italy, 804–805 Young Professional magazine, 379–380 Categorical data, 8, 34 Categorical variables, 8, 711–716 applications, 717–720 complex, multiple regression, 715–716 defined, frequency distributions, 34–35, 90–92 independent, multiple regression, 711–716 Johnson Filtration, Inc example, 711–713, 714, 715 summarizing data for, 34–37 Cause-and-effect relationships in observational studies, 548, 630 Census, 16, 851 Centered moving average, 852–853 Center for Drug Evaluation and Research (CDER), 446 Central limit theorem, 321 Chance events, 21-3 Chance nodes, 21-4–21-5 Chebyshev’s Theorem, 127–128, 131–132 Chemitech problem, example of, 548–549 Chi-square distribution, 511–518 formula, 539 goodness of fit tests, 529–536, 539 hypothesis testing, 491–494, 512–514, 520 independence of two categorical variables, 523–525 interval estimation, 487–491, 504 multiple comparison procedures, 516–518 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1085 Index population proportions, multiple, 511–516 population variances, 487–492 test of independence, 521–525, 543 test statistic, 491–494, 513, 530–536, 543 using Excel, 543–544 using Minitab, 543–544 Cincinnati Zoo and Botanical Gardens, 74–76 Citibank, 220 Classes of a frequency distribution, 41–43 lower class limit, 42 midpoints, 43 upper class limit, 42, 45–46 Classical method for assigning probabilities, 180–181 Class width, approximate, 42 Cluster sampling, 337–338, 22-21–22-23 Coefficient of determination, 616–619 applications, 621–623 correlation coefficient, 619–620 formula, 664, 742 multiple regression, 696–697 sum of squares due to error (SSE), 616–617 sum of squares due to regression (SSR), 617–618 total sum of squares (SST), 617–618 Coefficients, for multiple regression, 690–691 Coefficients of variation, 121–122, 154 Colgate-Palmolive Company, 33 Combinations, 179 Common causes, 924 Comparisonwise Type I error rate, 567 Complements, 189–190 of an event (of A), 189–190 computing probabilities using, 211 Venn diagrams and, 189–190 Complete block designs, 574–575 Completely randomized design, 553–557 analysis of variance (ANOVA), 553–557 between-treatments estimate of population variance, 554–555 Chemitech problem, example of, 548–549 experimental design, 548–550 formulas, 585–586 using Excel, 596–597 using Minitab, 594–595 within-treatments estimate of population variance, 552, 555–556 Computers, 20 computing betas, 673n observation identification and, 660 packages, 776, 21-6 ranking combined samples and, 892 regression analysis and, 641–642 use of software, 660 using Excel, 20 using Minitab, 20, 641–642 See also specific computer programs Conditional probabilities, 196–199, 211, 21-24–21-26 Confidence coefficients, 353 Confidence intervals defined, 634 formula, 490, 665 hypothesis testing, 405–406 least squares estimators, 605–609 linear regression equation, estimated, 627–628, 636f, 638f margin of error, 635 for mean value of y, 635–636 multiple regression equation, estimated, 708–709 as 95% term, 353 for normal probability distribution, 651–652 for proportions, 369 regression results and, 634 simple linear regression, 635–636 using Excel, 383 using F’s least significant difference, 564–567 See also Interval estimation Confidence levels, 353–354 Consequences, 21-3 Consistency of estimators, 336 Consumer Price Index (CPI), 960–961 Consumer’s risk, 939 Continuity correction factor, 290–291 Continuous improvement, 920, 924 Continuous probability distributions, 302–303 binomial, normal approximation of, 290–291 exponential distribution, 293, 296, 297 normal distribution, 289–291, 533 uniform distribution, 275 using Excel, 303 using Minitab, 302 Continuous random variables, 222, 281 Control charts, 925–936 applications, 936–938 formulas, 947–948 interpretation of, 935 np chart, 935 overview, 925–926 p chart, 933–934 R chart, 926, 931–932, 948 structure, 925f–926 using Minitab, 950–951 x charts, 926–931 Control limits, 350n formula, 947 np chart, 935 p charts, 933–934 x charts, 926–931 Convenience sampling, 338–339 in sample surveys, 22-4 Cook’s distance measure, 723–725, 742 Correlation coefficient, 141–145 applications, 146–147 of bivariate probability distributions, 235–237, 240 coefficient of determination, 619–620 interpretation of the, 143–145 sample, 141–145 using Excel, 915, 916 Counting rules for experiments, 176–180, 211 Covariance, 138–140 of bivariate probability distributions, 235–237 interpretation of the, 140–141 population, 140 of random variables formula, 236, 263 using Minitab, 167 Cravens, David W., 780 Cravens data, 780, 781, 784–785, 787–788, 805–806 Critical value approach Marscuilo pairwise comparison procedure, 517, 539 one-tailed test, 399–401 rejection rule, 398–400 two-tailed test, 403 Crosby, Philip B., 920 Cross-sectional data, 8–9 Cross-sectional regression, 809 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, 758–765 Cyclical patterns, 812–814 D Dashboards, data, 72–74, 147–151 effectiveness, improvement of, 147–151 Data, 1–31 analytics and, 17–18 categorical and quantitative, 8, 34 collection of, 7, 19, 20, 549–550 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, 549–550 government agencies providing, 12, 16 mining of, 18–20 observational study, 12–13, 560–561 overview, 22 scales of measurement, 7–8 sources of, 11–14 statistical inference, 16–17, 314 statistical studies, 24–31 summarizing See Summarizing data terms for, 23 time and cost issues, 13, 307 variety of, 19 velocity of, 19 volume of, 19 See also Statistics analysis Data dashboards, 72–74 effectiveness, improvement of, 147–151 DATAfiles, 87, 90 in Excel, 90 using Minitab, 87 Data mining, 18–20 Data set, 5, 6–7, 31t, 346t, 655f, 657f, 657t, 658t, 659t, 724t, 796t 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, 208, 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, 421–422, 925, 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, 850–858 Deflating a series, 962–964 Degree of belief, 181 Degrees of freedom of the t distribution, 356–357, 455–456, 475, 535 Deming, W Edwards, 920 De Moivre, Abraham, 277 Dependent events, 199 Dependent variables, 602, 605–607, 647–649, 700 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, 147–151 tabular displays See Tables for summarizing data using Excel, 167–172 using Minitab, 166–167 using StatTools, 166 variability, measures of, 118–122 See also Summarizing data Deseasonalized time series, 855–857 Deviation about the mean, 119–120 Difference of population means hypothesis testing, 449–451, 456–458 interval estimates, 447–451, 454–456 Difference of population proportions hypothesis testing, 470–471 inference about two populations, 447–451 interval estimates, 468–470 standard error, 320, 448, 450, 468, 470, 475 Digital dashboards, 72 Discrete probability distributions, 224–229 applications, 227–229 binomial distributions, 250–251, 263–264 bivariate distributions, 234–237 developing, 224–227 hypergeometric distribution, 257–259 overview, 224–226 Poisson distribution, 254–256 random variables, 221–222 using Excel, 269–270 using Minitab, 269 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1086 Index Discrete probability function formula, 225, 226, 263 Discrete random variables, 221–222, 263 Discrete uniform probability function, 263 Dispersion, measures of, 118, 151, 229 Distance or length intervals, 256 Distribution-free statistical methods, 875 See also Nonparametric statistical methods Distributions, sampling, 316–318 of p, 328–332 of x, 318–327 Distribution shapes, measures of, 125 Dot plot graphs, 43, 72 using Minitab, 88 Double-blind experimental design, 553 Dow, Charles Henry, 961 Dow Chemical Company, 919 Dow Jones averages, 961–962 Dow Jones Industrial Average (DJIA), 961 Drilling down, 151 Duke Energy, 22-2 Dummy variables, 712, 713, 715–716 categorical variable and, 715, 846 Johnson Filtration example, 712–713 seasonal pattern forecasts, 842–846 Dunnhumby, 684 Durbin-Watson Test, 795–798, 800 E EAI problem, 321–322 Economics applications, statistical, Efficiency of estimators, 335–336 Electronics Associates, Inc (EAI), 306–307 sampling distribution, 321–322 Elements of data, 5–7, 13, 16 in sample surveys, 304, 307, 309–310, 22-2–22-23 Empirical discrete distributions, 224, 234–237 Empirical rule, 128–130, 279 Error term « assumptions about, 567n, 623, 699–700 assumptions about, multiple regression, 699–700 and autocorrelation, 795–798 simple linear regression, 646 Estimated logistic regression equations, 729–732, 742 Estimated logit, 735, 742 Estimated multiple regression equations, 686 using, 687, 714 Estimated regression equations, 603–605, 708–709 formula, 664 least squares method, 605–609, 605–616 linear regression, 602–603 multiple regression, 708–709 simple linear regression, 603–605 slope, 603, 604 using Excel, 681 y-intercept, 603, 604, 606, 664 Estimated regression line, 604, 606, 617–618 Estimated simple linear regression equation, 603–605, 608 Ethical guidelines for statistical practice, 20–22 Events, 185–193, 199 complement of A, 189–190 defined, 185–186 independent, 199–200, 212 intersection of, 191–192 mutually exclusive, 193 and probabilities, 174–175, 186–187, 190 union of, 190–191 Excel analysis of variance (ANOVA), 596–599, 682 bar charts, 90–92, 98–101 chi-square distribution, 544–545 completely randomized design, 596–597 continuous probability distributions, 101, 303 crosstabulations, 93–96 DATAfiles, 90 for data presentations, 90–101 descriptive statistics, 167–172 discrete probability distributions, 269–270 exponential smoothing, 871 factorial experiments, 598–599 forecasting, 871–872 frequency distributions, 90–93 graphical displays of data, 90–101 histograms, 92–93 hypothesis testing, 440–444 inference about two populations, 482–484 interval estimates, 482–484 moving averages, 871 multiple regression, 753–755 nonparametric statistical methods, 915–916 PERCENTILE.EXC, 111 PivotChart, 92–93 population means: s known, 440 population means: s unknown, 440–442 population proportions, 443–444 population variance, 508 POWER function, 110 randomized block design, 597–598 random sampling, 347 regression analysis, 680–682 sampling, 347 scatter diagrams and trendlines, 96–98 sign test, 915–916 Spearman rank-correlation coefficient, 916–917 tables for summarizing data, 90–101 time series forecasting, 871–872 trend projection, 871–872 Expected frequencies, 512–513, 539 Expected value, 319, 21-6, 21-30 Expected value approach, 229, 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, 319 Expected values (EVs), 229, 260 for the binomial distribution, 248–249, 250–251, 263 decision analysis, 21-5–21-7 of discrete random variables, 229–230, 263 formula, 341 of the hypergeometric probability distribution, 259, 264 of a linear combination of variables, 237–239, 263 of sample means, 319, 341, 344–345 sample proportion, 341 standard deviation, 344–345 Experimental designs, 548–550 applications, 794–795 multiple regression approach to, 790–794 sampling distributions, 552 Experimental outcomes, 176 Experimental statistical studies, 13, 547, 548, 561 Experimental units, 548, 550, 570, 571 Experiments binomial, 244–245 Poisson, 254–256 See also Random experiments Experimentwise Type I error rate, 567–568 Exponential probability density function, 293, 297 See also Exponential probability distribution Exponential probability distribution, 293–295 computing probabilities for, 293–294 cumulative probabilities, 294, 297 formula, 297 mean, 293, 294, 295 and the Poisson distribution, 294–295 standard deviation, 294 Exponential smoothing, 823–827 formula, 862 using Excel, 871 using Minitab, 869 Exponential trend equation, 837, 862 sample mean, standard deviation of, 313–314 sample proportion, standard deviation of, 306, 313–314 sample random sample, 306, 307–309 sampling from, 307–310 sampling without replacement, 309 sampling with replacement, 309 Fisher, Ronald Aylmer, 548 Fisher’s least significant difference (LSD), 564–567 Fitch Group, Fitness for use, 920 Five-number summaries, 133–134, 136–138 Food Lion, 349 Forecast accuracy, 825–826 exponential smoothing, 823–827 managers and, 809 moving averages, 820–823 Forecast error, 815–816 Forecasting See Time series forecasting Forward selection procedure, 786 using Minitab, 806 Frames, 306 in sample surveys, 22-3 Frequency distributions, 34–35, 41–43 for categorical variables, 34–35, 90–92 cumulative, 45–46 descriptive statistics, 14t for quantitative variables, 41–43, 90–93 sampling distributions and, 317f, 497f using Excel, 90–93 F Test, 556–558 formula, 665, 742, 800 independent variables, adding to model, 628, 631, 777–778 least squares estimators, 628–630 multiple regression, 701–703 simple linear regression, 701–703 variance estimates, 556–558 F G Factorial experiments, 577–582 ANOVA procedure, 579 applications, 582–584 computations, 579–582 defined, 577 formulas, 587–588 overview, 577–578, 584–585 using Excel, 598–599 using Minitab, 595 Factorial notation, 179 Factor of interest, 571 Factors, 548 Failure in trials, 244–245, 258–259 F distribution, 497–502 Federal Reserve Board, 12, 261, 839, 967 Feigenbaum, A.V., 920 Fermat, Pierre de, 174 Financial applications, with bivariate probability distributions, 237–240 statistical, Finite population correction factor, 320 Finite populations, 307–309 combinations and, 179 probability sampling methods, 307–310 Galton, Francis, 602 Gauss, Carl Freidrich, 607 General linear model, 758–770 applications, 771–773 curvilinear relationships, 758–765 dependent variable transformations, 765–769 formula, 800 nonlinear models and, 769–770 See also Linear trend regression Geographic Information System (GIS), 76 Geometric means, 109–110, 153 Goodness of fit tests, 529–536 applications, 537–538 formula, 539 multinomial probability distribution, 529–532 normal probability distribution, 532–536 overview, 538 test statistic for, 530–536, 543 using Excel, 544–545 using Minitab, 543–544 Google revenue, 27f Gosset, William Sealy, 356 Graphical displays of data, 64–70 applications of, 69–72 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1087 Index bar charts, 36–37, 65–69, 72 data dashboards, 72–74, 147–151 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 types of, 72, 77f using Excel, 90–101 using Minitab, 87–90 Gross domestic product (GDP), 5, 6, 14–15, 661, 963 H High leverage points, 658–659 Histograms, 44–46, 72 descriptive statistics, 14, 15 examples, 15f, 44f, 45f, 126f, 317f, 318f, 361f and stem-and-leaf displays, 46–49, 72 using Excel, 92–93 using Minitab, 88 Horizontal patterns, 809–811 Hypergeometric probability distribution, 258–259 Hypergeometric probability function, 258–259, 264 Hypothesis testing, 387–444 alternative hypotheses, 389–390 applications, 419–421, 425–426 chi-square distribution, 491–494, 512–514, 520, 525 confidence intervals, 405–406 and decision making, 421–422 of difference of population means, 447–451, 456–458 of difference of population proportions, 470–471 Durbin-Watson, 798f forms of, 391 interval estimates, 405–406 lower tail test, 398, 400–401, 404, 413, 416, 418, 422, 427 matched samples, 462–464, 880–881 null and alternative hypotheses, 389–392, 397f one-tailed test, 395–401, 410–411, 432, 500 population mean: s known, 395–406, 432 population mean: s unknown, 410–413, 432 population means, 432, 449–451, 456–458 population median, 875–879 and population proportions, 416–418 of population variance, 491–494 sample sizes, 427–429 standard error of the mean, 320, 450, 470 steps for, 404, 425 test statistic formula, 432, 475, 476 two-tailed test, 402f, 405–406, 411–413 Type I and Type II errors, 392–395, 422–425 upper tail test, 395, 400–401, 404, 410–411, 413, 416–417, 418 using Excel, 440–444 using Minitab, 438–439, 458 I Incomplete block designs, 574 Independence, test of, 521–525 using Minitab, 543 Independent events, 199 multiplication law for, 199–200, 212 and mutually exclusive events, 193 Independent sample design, 462–463 Independent simple random samples, 447–449, 450, 468, 469, 474 Independent variables adding or deleting from model, 602, 623, 777–778, 800 correlation of, 705 defined, 602, 705 experimental design, 548 F test and, 628 multiple regression, 685–690 regression analysis, 602, 607, 608, 657, 658 against residual plots, 646–647, 649–651 selection procedures, 784–788 types of, 711 using Minitab, 689, 690, 703, 712, 714, 782f Index numbers, 952–971 Consumer Price Index (CPI), 960–961 price indexes See Price indexes price relatives, 953 Producer Price Index (PPI), 960–961 quality indexes, 945 Index of Industrial Production, 967 Indicator variables, 712, 713, 715–716 Indifference quality level (IQL), 945 Individual significance, 701 Inference about two populations, 447–451, 468–471, 497–502 applications, 452–454, 459–462, 465–468, 502–504 degrees of freedom, 498, 500 difference between population means: matched samples, 462–464 difference between population means: s1 and s2 known, 447–451 difference between population means: s1 and s2 unknown, 454–458 of difference of population proportions, 468–471 hypothesis tests, 449–451, 456–458, 470–471 interval estimation, 447–449, 454–456, 468–470 overview, 451, 504 sampling distribution, 497–499 test statistics, 499–501 upper-tail testing, 498, 500 using Excel, 483–484, 508 using Minitab, 480–482, 507–508 See also Population variances Infinite populations, 309–310 sampling from, 309–310 Influential observations in linear regression models, 656–659 in multiple regression models, 723–725 Information Resources, Inc., 4, 11 Information systems applications, statistical, Interactions, 578–579, 761–765 effect, experimental design, 578–579 general linear model, 761–765 second order models, 760–762 International Organization of Standardization (ISO), 921 Interquartile ranges (IQRs), 119 formula, 153 outlier identification, 130–131 Intersection of events, 191–192 Interval estimation, 405–406, 447–449 applications, 408–409 with chi-square distribution, 487–494 of difference of population means, 447–449, 454–456, 475 of difference of population proportions, 468–470, 476 and hypothesis testing, 405–406, 449–451 limits, 638 margin of error, 350–354, 635, 637 methods, 407–408 of population means, 349–350, 375 and population proportion, 324, 375 of population variance, 349–350, 487–491, 504 procedures for, 405 regression equation, estimated, 634 and sample size, 365–367, 375 using Excel, 384–386 using Minitab, 382–383 Interval scale of measurement, Ishikawa, Karou, 920 ISO 9000, 921 ith observation, 605, 607, 616, 658 ith residual, 616, 645, 649, 650 standard deviation of, 921 standardized residual of, 649–651 J John Morrell & Company, 388 Joint probabilities, 197, 21-26–21-27 Judgment sampling, 339, 22-4 Juran, Joseph, 920 K Key performance indicators (KPIs), 73, 75, 148 Kruskal-Wallis test, 899–901 applications, 901–903 formula, 910 medians of two populations and, 901 using Minitab, 914–915 Kruskal-Wallis test statistic, 899–901 L Laspeyres index, 956 Leaf unit, 49 Least squares criterion, 606, 607, 609, 664 formula, 742 multiple regression, 686–687 Least squares estimators, 603–605 confidence intervals, 627–628 F Test, 628–630 sampling distributions, 620, 626 standard deviations, 606, 609 t Test, 625–627 Least squares formulas, 664 Least squares method, 605–609, 686–691 applications, 691–696 Butler Trucking Company example, 687–690 coefficients interpretation and, 690–691 estimated regression equation, 603–605, 685–686 formula, 742 multiple regression, 686–691 using Minitab, 689f Length or distance intervals, 256 Levels of significance, 393–394, 431 Leverage of an observation, 650n, 658–659, 666, 720–721 Limits of box plots, 134–135 Linear exponential smoothing, 823–827 Linear regression, simple See Simple linear regression Linear trend equation, 832–833, 856, 862 Linear trend regression, 830–835 trend projection, 830–835 Location, measures of See Measures of location; individual measurements Location of the pth percentile, 111–112, 153 Logarithmic transformations, 766, 768–769 Logistic regression, 727–728 using Minitab, 755 Logistic regression equation, 728–736 applications, 737–740 estimating, 729–732 formula, 742 interpreting, 733–735 logit transformation, 736 managerial use, 732–733 overview, 728–729 significance testing, 732 using Minitab, 755 Logit, 736, 742 Logit transformation, 736 Lots, 938, 940–942 Lot tolerance percent defective (LTPD), 945 Lower tail test critical value approach, 399–400 hypothesis testing, 398, 400–401, 404, 413, 416, 418, 422, 427 for population variance, 494, 499, 500 p-value approach, 397–399 M MAE (mean absolute error), 122 time series forecasting, 816–818, 822, 827, 860 Magazines, use of statistics in, 2–3, 14 Malcolm Baldrige National Quality Award, 921 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1088 Index Mann-Whitney-Wilcoxon (MWW) test, 888–895, 914 applications, 896–898 formula, 909 medians of two populations and, 895 ordinal (rank-ordered) data and, 890 using Minitab, 914 MAPE (mean absolute percentage error), 817–818, 822, 827, 835, 837, 860 Marascuilo procedures, 517, 539 Marginal probabilities, 197–198 Margins of error, 349–350 difference between population means, 447–449 and interval estimates, 349–350 for population proportions, 368–371 regression equation, estimated, 627, 634, 635, 637 and sample size, 360–362 Market basket, 960 Marketing applications, statistical, Matched sample design, 462–464 Matched samples, 462–464 applications, 465–468 hypothesis testing, 462–464 sign test, 880–881, 913 using Excel, 484 using Minitab, 481, 913–914 MeadWestvaco Corporation, 305–306 Mean, 104–107 arithmetic, 104 defined, 104 expected value, 341, 344–345 of the exponential distribution, 293, 294, 295 for the Mann-Whitney-Wilcoxon test distribution, 888–895, 914 of the normal distribution, 278– 279, 280, 282, 284–285, 286 regression equation, estimated, 603–605 for the sign test distribution, 875, 878, 879 standard deviation, 345–346, 926–931 weighted, 106–107 for the Wilcoxon signed-rank test distribution, 883–886 Mean absolute error (MAE), 816 time series forecasting, 816 Mean absolute percentage error (MAPE), 817–818 Means, 104–107 deviation about the, 119–120 sample, 104–106 Mean squared error (MSE), 555–556 defined, 555 estimate of s2, 625 formula, 555, 664, 742 multiple regression, 701–703, 742 simple linear regression, 625, 628–630 time series forecasting, 817 Mean square due to regression (MSR) formula, 665, 742 multiple, 701–703, 742 simple linear, 628–630 Mean square due to treatments (MSTR), 554–556 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, 895 Minitab analysis of variance (ANOVA), 594–595 backward elimination procedure, 806 best-subsets regression, 806 box plots, 167 chi-square distribution, 543–544 completely randomized design, 594–595 continuous probability distributions, 302 control charts, 950–951 correlation coefficient, 167 covariance, 167 crosstabulations, 89 DATAfiles, 87 for data presentations, 87–89 descriptive statistics, 166–167 difference between population means, 480–481 difference between population proportions, 482 discrete probability distributions, 269 dot plot graphs, 88 Exact option, 439 exponential smoothing, 869 factorial experiment, 595 forecasting, 868–869 forward selection procedure, 806 goodness of fit tests, 543–544 graphical displays of data, 87–89 histograms, 88 hypothesis testing, 438–439 independence, test of, 543 inference about two populations, 480–482 interval estimates, 382–383, 438n Kruskal-Wallis test, 914–915 logistic regression, 755 Mann-Whitney-Wilcoxon (MWW) test, 914 matched samples, 481, 913 moving averages, 869 multiple regression, 753 nonparametric statistical methods, 913–915 population means: s known, 382, 438 population means: s unknown, 383, 439 population median, 913 population proportions, 383, 439 population variances, 507–508 randomized block design, 595 regression analysis, 641–642, 679–680, 759, 761, 765, 767, 782, 783, 785, 787 sampling, 346–347 scatter diagrams and trendlines, 89 sign test, 913 simple linear regression, 679–680 Spearman rank-correlation coefficient, 915 stem-and-leaf displays, 88 stepwise regression procedure, 784–786, 806 tables for summarizing data, 87–89 test of independence, 543 time series decomposition, 870 time series forecasting, 868–870 trend projection, 870 using computers and, 641–642 variable selection procedures, 805–806 Wilcoxon signed-rank test, 913–914 Modes, 110–111 Monsanto Company, 757 Monthly data, 846, 857 Moody’s investor service, 5n Moving averages, 820–827 exponential smoothing and, 823–827 formula, 862 using Excel, 871 using Minitab, 869 weighted, 823 See also Forecast accuracy MSE See Mean squared error (MSE) MSR See Mean square due to regression (MSR) MSTR (mean square due to treatments), 554–555, 556–558, 561 Multicollinearity, 705 Multimodal data, 111 Multinomial probability distribution, 529–532 Multiple coefficient of determination, 696–697 Multiple comparison procedures, 516–518, 564–568 applications, 569–570 for equality of population proportions, 511–518, 543 Fisher’s least significant difference (LSD), 563–567 formulas, 587 type I error rates and, 567–568 using Minitab, 543 Multiple regression, 685–686 categorical independent variables, 711–716 coefficient of determination, 616–619 coefficients, 690–691 experimental design for, 790–794 formulas, 741, 742 least squares method, 605–609 logistic regression, 727–728 model, 685–686 multiple coefficient of determination, 696–697 residual analysis, 602, 641, 649, 720–725 using Excel, 753–755 using Minitab, 753 Multiple regression analysis, defined, 685 Multiple regression equation, 685–686 Multiple regression models, 685–686 Multiple sampling plans, 944 Multiple-step experiments, 176 Multiplication law, 199–200, 212 Multiplicative decomposition model, 851, 862 Mutually exclusive events, 193 N Naive forecasting method, 815–818, 819 National Aeronautics and Space Administration (NASA), 174 Nevada Occupational Health Clinic, 808 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, 769–770 curvilinear relationships models, 758–765 intrinsically linear, 769–770 Nonlinear trend regression, 835–837 Nonparametric statistical methods, 875 Kruskal-Wallis test, 899–901, 914–915 Mann-Whitney-Wilcoxon test, 888–895, 914 overview, 908 rank correlation, 903–905, 915, 916–917 sign test, 875–879, 913, 915–916 using Excel, 915–917 using Minitab, 913–915 Wilcoxon signed-rank test, 883–886 Nonprobabilistic sampling, 338–339, 22-4 Nonsampling errors, 22-5 Normal curve, 277–279 Normal probability density function, 277, 278, 280, 297 Normal probability distribution, 277–287, 532–536 applications, 288–289 approximations for nonparametric methods, 877, 878–879, 886, 892, 894, 900, 905, 908 binomial probability estimation with, 289–291 central limit theorem, 321, 322f computing probabilities for, 284–285 confidence intervals for, 651–652 empirical rule, 128–130, 279 goodness of fit test, 532–536 Great Tire Company example, 285–287 mean, 278–279, 280, 282, 284–285, 286 median, 278 mode, 278 normal curve, 277–279 sampling distribution approximation, 317–318, 320, 321, 330, 331–332, 336 sign test, 877f–878 standard deviation, 279–284, 533, 535–536 Normal probability plots, 651–652 Normal scores, 651–652 Np chart, 935, 948 Null hypothesis, 389–392 challenging, 390–391 developing, 389–390 forms for, 391–392 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1089 Index O Observational statistical studies, 12–13, 548 Observations of data, 5–7 Observed frequencies, 538 goodness of fit, 529–530, 532, 534, 536 in multiple population proportions, 511, 512, 513, 514, 516 test of independence, 522–523, 525 Observed level of significance, 399, 400 Odd ratios, 733–735 Odds in favor of an event occurring, 733–734, 742 Ohio Edison Company, 21-2 One-tailed test, 395–401, 491, 525 critical value approach, 399–400 overview, 400–401 population means: s known, 395–401 population means: s unknown, 410–411 p-value approach, 397–399 sample size for, 428, 432 test statistic, 396–397 Open-end classes, 49 Operating characteristic (OC) curves, 941–942 Ordinal scale of measurement, Outcomes, formula for, 263 Outliers, 130–131 of box plots, 134–135 data acquisition errors, 13–14 detecting in regression models, 654–656 interquartile ranges (IQRs), 130–131 using Minitab, 656f, 657f, 659f Overall sample means, 947 formula, 929, 947 quality control, 36, 450–451, 468 Overall significance, 701 P Paasche index, 956 Parameters multiple regression and, 713–715 of a sampling population, 307 Parametric statistical methods, 874–875 Pareto, Vilfredo, 36 Pareto diagram, 36 Partitioning total sum of squares, 558 Pascal, Blaise, 174 Payoffs, 21-4 Payoff tables, 21-4 P chart, 933–934, 948 Pearson, Karl, 602 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, 179–180 counting rules for, 180, 211 Pie charts, 36–37, 72 Point estimates, 313–314 Point estimation, 312–314 Point estimators, 312–314, 334–336 applications, 314–315 consistency of, 336 difference between population means, 313, 448, 450, 468, 470, 475 difference between population proportions, 468–470, 476 efficiency of, 335–336 population parameters, 334–336, 337, 339 of population variance, 458, 483, 487 properties of, 334–336 regression equation, estimated, 604, 627, 634 and sample means, 447–458, 450 and sample standard deviations, 121 and sample variances, 119–120, 483 simple random samples, 307, 309–310, 314 unbiased, 334–335 Poisson, Siméon, 254 Poisson experiments, 254–256 Poisson probability distribution, 254–256 applications, 257 assumptions for, 262 Bell Labs, 255 Citibank ATM wait times, 220 distance or length intervals, 256 and the exponential distribution, 294–295 function, 254 mean and variance, 256 time intervals, 255–256 Poisson probability function, 254, 264 Pooled estimators of population proportions, 470–471, 475, 476 Pooled sample variances, 458 Population correlation coefficient, 143, 631, 678 Population covariance, 140, 154 Population in surveys, 22-2 Population means, 106, 446–484 applications, 408–409 cluster sampling, 337–338, 2223–22-25 difference between, estimating, 447–451 formula, 153 hypothesis testing, 395–406, 432 inference about difference between: matched samples, 462–464 inference about difference between: s1 and s2 known, 447–451 inference about difference between: s1 and s2 unknown, 454–458 interval estimates, 349–354, 357–360, 362, 375, 447–451, 475 sample sizes, 365–367, 375, 427–429, 432 simple random sampling, 309–310, 314, 22-6–22-7 standard deviation, 447–449, 450, 454–455, 456–457, 458, 463, 474 stratified simple random sampling, 337, 22-12–22-14 testing for equality of, 470, 560–561 using Excel, 483 using Minitab, 480–481 Population means: s known, 350–354, 447–454 applications, 355–356, 452–454, 459–462 critical value approach, 399–400, 403 hypothesis testing, 405–406, 432, 449–451 interval estimate, 350–354, 375, 384, 447–449 margin of error, 350–354, 449 one-tailed test, 395–401 overview, 400–401, 403–405, 451 p-value approach, 397–399, 400–401, 402–403 standard deviation, 926–928, 947 test statistic, 396–397, 475 two-tailed test, 400–403 using Excel, 385, 440, 483 using Minitab, 382, 438, 482–483 Population means: s unknown, 356–363, 454–458 applications, 360, 364–365, 414–416, 459–462 hypothesis testing, 410–413, 432, 456–458 interval estimate, 357–360, 362, 384–385, 454–456 margin of error, 357–360 matched samples, 484 one-tailed test, 410–411 overview, 356–357, 413, 458 standard deviation, 928–931, 948 summarization of, 362 test statistic, 412–413, 475 two-tailed test, 411–413 using Excel, 384–385, 440–442, 483 using Minitab, 383, 439 using small samples, 360–362 Population median, 875–879, 913 Population of a study defined, 16 finite, sampling from, 307–309 infinite, sampling from, 309–310 Population parameters, 603–604 defined, 307 and hypothesis testing, 388, 389, 390, 391, 406, 430 and point estimators, 334–336 regression equation, 603–604 Population proportions, 328–332, 416–418, 511–518 applications, 372–374, 419–421, 472–474 and chi-square distribution, 511–512, 513–517, 518 cluster sampling, 337–338, 22-25–22-27 equality of, 511–518, 543, 556–557 expected value, 329, 341 formula, 328–329 and hypothesis testing, 416–418, 470–471 inference about difference between, 468–471 and interval estimation, 324, 368–369, 375, 385–386, 468–470, 476 Marascuilo pairwise comparisons, 517, 539 and margin of error, 349–354, 368–371 multiple comparison procedures, 516–518 multiple population testing, 511–518, 521 overview, 418, 474 pooled estimators, 470–471, 475, 476 sample, 511–518 sample sizes estimates, 370–371 sampling distribution, 330–332 simple random sampling, 307, 309–310, 314, 22-8–22-9 standard deviation, 329–330 stratified simple random sampling, 337, 22-15–22-16 testing for equality of, 511–518, 543, 557 test statistic, 476 using Excel, 385–386, 443–444 using Minitab, 383, 439, 482, 543 Populations, 16 Population totals cluster sampling, 337–338, 22-25 simple random sampling, 307, 22-7–22-8 stratified simple random sampling, 337, 22-14–22-15 Population variances, 119, 154, 487–494 applications, 494–497, 502–504 between-treatments estimates of, 554–555 formula, 154, 504 inferences about, 487–502 interval estimates, 349–350, 487–491, 504 lower tail test, 494, 499, 500 overview, 504 point estimators, 458, 483, 487 single population, 447, 464, 487 stratified random sampling, 337, 22-17, 22-19 test statistic, 491–494, 499–501, 504 two populations, 497–502 two-tailed test, 491, 493, 494, 500–501 upper tail test, 489, 492–494, 498–501 using Excel, 508 using Minitab, 507–508 within-treatments estimates of, 552, 555–556 Posterior probabilities, 204, 21-13, 21-26–21-27 Power curves, 424 Power value, 424 Prediction intervals, 634, 636–638 Butler Trucking Company example, 709 formula, 665 linear regression equation, estimated, 636–638 margin of error, 637 multiple regression equation, estimated, 708–709 new observations and, 638 Predictive analytics, 18 Predictors, 634, 781, 806 Prescriptive analytics, 18 Price indexes, 957–966 aggregate, 954–956, 955–958, 958–959 considerations, 965–966 Consumer Price Index (CPI), 960 deflating a series by, 962–964 Dow Jones averages, 961–962 formulas, 969 and price relatives, 954, 969 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1090 Index Price indexes (continued) Producer Price Index (PPI), 960–961 quality changes in, 966 selection of, 965 weighted aggregated, 955–956, 969 Price relatives, 954 and aggregate price indexes, 954–956, 958–959 formulas, 969 Prior probabilities, 204, 21-13 Probabilistic sampling, 22-4 Probabilities, 175–218 applications, 184–185, 188–189, 194–196, 201–203 assigning, 180–181, 225 conditional, 196–199, 211, 2124–21-26 counting rules, 176–180, 211 decision analysis, 21-5–21-9 (See also Bayes’ theorem) defined, 174–175 events and, 174–175, 185–187, 190 experiments, 175–176 KP&L project, 178, 182–183 measuring by area, 274–276 relationships of, 189–193 of single points, 275 standard normal table and, 283 Probability density functions, 279–284 normal, 277, 278, 280, 297 standard normal, 279–284, 297 Probability distributions, 224, 226, 249f See also Continuous probability distributions; Discrete probability distributions Probability functions, 224, 254, 264 Probability samples, 183, 307, 310, 339 Probability sampling techniques, 337–338 Probability tree, 177–178, 204–206 Procter & Gamble, 272 Producer Price Index (PPI), 960–961 Producer’s risk, 939 Production applications, statistical, Proportional allocation, 22-19, 22-33 Protected LSD test, 567 Purchasing power vs real wages, 963 p-value approach independent variables, adding to model, 777–778, 800 interpreting, 397–399 lower tail test, 397–399 one-tailed test, 397–399 rejection rule, 404 two-tailed test, 402–403 Q Quadratic trend equation, 835–837, 862 Quality assurance, 923 Quality control, 920–936 acceptance sampling, 938–945 bar charts and, 36 history of, 920–924 ISO 9000, 921 Malcolm Baldrige National Quality Award, 921 in population means, 450–451 in population proportions, 468 in the service sector, 924 Six Sigma, 921–923 statistical process control, 924–936 Quality engineering, 923 Quality indexes, 966 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, 966–967 Quartiles, 112–113 R Radar charts, 76 Random experiments, 175–176 Randomization, 548, 553 Randomized block design, 570–575 air traffic controller stress test, 571–572 ANOVA procedure, 572–573, 579 applications, 575–577 computations, 573–575 formulas, 587 overview, 570–571 using Excel, 597–598 using Minitab, 582f, 595 Random numbers, 305, 307–309, 347, 22-6 Random samples, 346–347 infinite population, 309 using Excel, 347 using Minitab, 346–347 Random variables, 221–223, 263, 280, 284, 297 Ranges, 41, 797, 905, 930, 932 Rank correlation, 903–905, 915, 916–917 Ratio scale of measurement, 7–8 R chart, 926, 931–932, 948 Reciprocal transformation, 769 Regression analysis computers, need for, 641–642 departure from normality and, 650 estimated, 608–609 independent variables, 602, 620, 628, 658, 665 larger problems, 780–783 mean square error (MSE), 817 model building, 623–624 residuals, 816 results, precision of, 634 simple linear regression, 602–605 time series See Time series analysis using Excel, 680–682 using Minitab, 679–680 variables and, 630 See also Multiple regression; Simple linear regression Regression equation, 633–638 confidence interval, 635–636 estimated, interval, 634 estimated, linear, 633–638 estimated, multiple, 685–686 multiple regression, 685–686, 708–709 prediction interval, 633–638 Regression models, 602–605 assumptions about, 624f multiple, 685–686 simple linear, 602–605 variance of error, 555–556, 623, 624–627, 642, 646, 647 Rejectable quality level (RQL), 945 Relative efficiency of an estimator, 335–336 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, 181 Replications, 580 Research hypothesis, 389–390 Residual analysis of regression model, 645–652, 720–725 applications, 653–654, 726–727 Butler Trucking example, 722–723 Cook’s distance measure, 723–725 influential observations, 656–659, 723–725 multiple regression, 720–725 outliers, 654–656, 723 studentized deleted, 722–723 validating, 645–652 Residual for observation i, 645, 650, 655, 665, 666 Residual plots, 646–649 defined, 646 of dependent variable, 647–649 against independent variable, 646–647 Response surface, 700 Response variables, 518, 548, 550, 700 Restricted LSD test, 567 S Sample arithmetic means, 104, 109, 110 Sample correlation coefficients, 141–145, 664 Sample covariance, 138–140, 142f, 154 Sampled populations, 306, 22-3 Sample information, 21-13–21-20 Sample in surveys, 22-2 Sample means, 318–326 expected value of, 319 formulas, 104, 153 measures of location and, 104–105 as sample statistic, 104, 106 sampling distribution of, 32––324 standard deviation of, 319–320 for treatments, 337, 551–552, 553–556 Sample points, 176, 178 Sample proportions for the EAI Problem, 321–322 expected value of, 319 sampling distributions, 318–326 standard deviation of, 319–320 Sample ranges, 930, 932 Samples in auditing accounts, 486 defined, 16 in sample surveys, 22-2, 22-3 statistical inference, 16–17, 314 Sample sizes, 365–367 applications, 367–368, 430 cluster sampling, 337–338, 22-27 determining, 370–371, 427–429 formula, 432 hypothesis testing, 370–371, 427–429 and interval estimates, 365–367, 370f, 375 large, 360 margin of error and, 366, 367 one-tailed test, 428, 432 overview, 430–431 planning value, 366 population mean, 427–429 population proportion estimates, 370–371 recommendation, 366, 458 and sampling distributions, 326, 328–330 simple random sampling, 307–309, 22-9–22-11 small, 320 stratified simple random sampling, 337, 22-16–22-19 Sample space, 176 Sample standard deviation, 121 Sample statistics, 151, 313–314 Sample surveys, 22-2–22-36 applications, 22-12, 22-20–22-21, 22-28–22-29 classification, 22-4 cluster sampling, 337–338, 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, 337, 22-12–22-19, 22-32–22-33 survey errors, 22-5–22-6 systematic sampling, 338, 22-29 terminology used in, 22-2–22-3 types of, 22-3–22-4 Sample variances, 119–121 formula, 154 for treatments, 556, 561, 568 Sampling, 307–312 applications, 311–312 cluster, 337–338, 22-21–22-27 convenience, 338–339, 22-4 distributions, 316–326 estimates, 306 estimation errors, 306 infinite populations, 309–310 judgment, 339, 22-4 point estimation, 312–314 selecting a sample, 307–309, 22-6 stratified random sampling, 337, 22-12–22-19 systematic, 338, 22-29 using Excel, 347 using Minitab, 346–347 Sampling distributions, 316–326 applications, 327–328, 332–334 binomial, for the sign test, 875, 876–879 chi-square distribution, 487–488, 490–493, 504 defined, 316 F distribution, 497–501 least squares estimators, 605–609 for the Mann-Whitney-Wilcoxon test, 888–895, 914 normal approximation of, 289–291, 330, 368, 369, 371 overview, 316–318 of the point estimator, 328–332, 336f population variance, 487, 497 probability information, 324 for the rank correlation test, 903–905, 915, 916–917 of the sample mean, 318–324, 351f of the sample proportion, 370–371 and sample size, 324–326 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1091 Index for the sign test, 875–879 for the Wilcoxon signed-rank test, 883–886 of x, 318–326 Sampling errors, 335, 22-5–22-6 bound on, 22-7 Sampling methods, 337–339, 223–22-4 Sampling population parameters, 22-4, 22-5, 22-7, 22-12, 22-17, 22-19, 22-29 Sampling units, 22-3 Sampling without replacement, 309 Sampling with replacement, 309 San José copper and gold mine, 174 Scatter diagrams, 64–65 examples, 66f, 144f, 606f, 655f, 658f, 688f, 715f, 724f, 766f influential observations, 657–658 least squares method and, 605, 606, 608 and outliers, 654–655 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, 857 Seasonal indexes, 851–854 Seasonality, 841–846 irregular values and, 853 monthly data, models based on, 846 with trend, 843–846 without trend, 841–843 Seasonal patterns, 811–812 Second order models, 760–762 interactions, 761–765 Serial correlation of data, 795–798 Shewhart, Walter A., 920 Side-by-side bar charts, 65–67 examples, 67f, 71f using Excel, 98–100 Significance, level of, 393–394 Significance testing, 624–631, 701–705 applications, 632–633, 706–708 Butler Trucking Company example, 703 F test, 682, 701–704 interpreting, 630–631 logistic regression, 732 multicollinearity, 705 multiple regression, 701–705 simple linear regression, 625 t test, 625–627, 704 using correlation, 678–679 Significance tests, 624–631 Sign test, 875–879 about a population median, 875–879 applications, 881–883 formula, 909 with matched samples, 880–881 skewed differences and, 883 using Excel, 915–916 using Minitab, 913 Simple first-order model, 758–761, 766, 795–796 Simple linear regression, 602–605 ANOVA table, 629–630 applications, 610–615 assumptions for the model, 623–624 assumptions for the model, validating, 645–652 coefficient of determination, 616–620 computer solution, 641–642 equation for, 603–605 formulas, 664 F Test, 628–630 influential observations, 656–659 least squares method, 605–609 model of, 602–603 outliers, 654–656 regression analysis, 602–605 residual analysis, 645–659 significance testing, 624–631 t Test, 625–627 using estimated regression equation, 625–627 using Minitab, 627, 628, 641–642, 652, 655–656, 657–659, 679–680 values for, 605 Simple random samples, 307–309, 310–311, 314, 22-6–22-11 finite populations, 307–309 point estimators, 334–336 sample surveys, 22-6–22-11 See also Random samples Simple variance formula, 154 Simpson’s paradox, 58–59 Single-factor experiments, 548, 584 Single-stage cluster sampling, 22-21 Six Sigma, 921–923 limits and defects, 922–923 Skewed histograms, 44–45, 126 Skewness of distributions, 45, 125, 126, 151 Slope, 607, 609, 619–620, 664 Small Fry Design, 103 Smoothing constant, 824 Spearman rank-correlation coefficient, 903–905, 915, 916–917 applications, 906–908 formula, 910 using Excel, 916 using Minitab, 915 SSA (sum of squares for Factor A), 579–580, 587, 588 SSAB (sum of squares for interaction), 579, 580, 588 SSB (sum of squares for Factor B), 579, 580, 587, 588 SSBL (sum of squares due to blocks), 572–573, 587 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), 555, 558, 572, 573, 586, 587 Stacked bar charts, 67–68, 100–101 Standard and Poor’s, 5n Standard deviations, 120–121 of coefficient of variation, 121, 151, 153 of discrete random variables, 229–230 expected value, 344–346 of the exponential distribution, 294 formula, 153, 341, 665, 666, 742 of the ith residual, 616, 645, 649, 650 least squares estimators, 605–609 for the Mann-Whitney-Wilcoxon test distribution, 883–886, 888–895 means, 345–346, 926–931 measure of risk and, 238 of normal approximation of the sign test, 913 of the normal distribution, 277, 279, 284–285, 321 population, 121 and population means, 447–451, 454–458 sample, 121 of sample means, 447–458, 450 of sample proportion, 468–472 variance and, 230 for the Wilcoxon signed-rank test distribution, 883–886 of x, 319–320 Standard error, 166, 475 difference between population means, 320, 335, 448–449 difference between population proportions, 448, 450, 476 of difference of population proportions, 468, 470, 475 formula, 475 mean vs median and, 335 Standard error of the estimate, 625, 649–650, 664, 665, 682, 702, 720, 725 Standard error of the mean, 166, 320, 335, 448–449 formula, 448, 947 hypothesis testing, 396, 450, 470 quality control, 450–451, 468 Standard error of the proportion, 448, 450, 468, 470, 475, 948 Standardized residuals, 649–651 formula, 666, 742 of the ith observation, 605, 607, 616, 658 Standardized values, 127, 130 Standard normal probability distribution, 279–284, 534 random variable formula, 297 and the t distribution, 357 States of nature, 21-3, 21-6, 21-9, 21-30 Stationarity assumption, 245 Stationary time series, 810 Statistical analysis, 20 ethical guidelines for, 20–22 Statistical inference, 16–17, 151, 314 Statistical process control, 923–936 applications, 936–938 control charts, 925–935 overview, 924–925, 936 Statistical studies, 13, 20–21, 58, 395, 446, 547 Statistics, defined, Stem-and-leaf displays, 46–49, 72 using Minitab, 88 Stepwise regression procedure, 784–786 using Minitab, 784–786, 788, 806 Strata, defined, 337 Stratified random sampling, 337, 22-12–22-19 population means, 337, 22-12–22-14 population proportions, 22-15–22-16 population totals, 22-14–22-15 sample sizes, 337, 22-16–22-19 sample surveys, 22-3–22-4 Studentized deleted residuals, 722–723 Subjective method for assigning probabilities, 181–182, 225 Successful trials, 244–248 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 frequency distributions, 34–35, 41–43 histograms, 44–45 for quantitative variables, 8, 41–49 Simpson’s paradox, 58–59 stem-and-leaf displays, 46–49 using Excel, 34, 93–96 using graphical displays See Graphical displays of data using Minitab, 34, 89 using tables, 55–59 Summation sign (S), 104 Sum of squares due to blocks (SSBL), 572–573, 587 Sum of squares due to error (SSE), 555–556, 618 coefficient of determination, 616–619 formula, 664 relationship among SST, SSR and, 618, 696 and sum of squares due to regression or total sum of squares, 555–556, 740 within-treatments estimate of population variance, 555–556 Sum of squares due to regression (SSR), 618 coefficient of determination, 616–619 formula, 664 multiple regression, 696–697 relationship among SST, SSE and, 618, 696 and sum of squares due to error or total sum of squares, 555–556, 664 Sum of squares due to treatments (SSTR), 555, 558, 572, 573, 586, 587 Sum of squares for Factor A (SSA), 579–580, 587, 588 Sum of squares for Factor B (SSB), 579, 580, 587, 588 Sum of squares for interaction (SSAB), 579, 580, 588 Sum of squares of the deviations, 119–121, 122 Survey errors, 22-5–22-6 Surveys, 13, 16, 310, 22-3–22-4 See also Sample surveys Symmetric histograms, 44–45 Systematic sampling, 338, 22-29 T Tables for summarizing data crosstabulation, 55–58 two variables, 55–59 Tabular approach, Bayes’ theorem, 207–208 Taguchi, Genichi, 920 Target populations, 314, 22-3 t distribution, 356–357, 458, 625–627 degrees of freedom, calculating, 356–357 Test of independence, 521–525 applications, 526–528 using Minitab, 543 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 1092 Index Test statistics, 396–397, 511–518 applications, 519–521 chi-square distribution, 491–494, 521–525, 530–536, 539, 543 difference in population means, 22-4 difference in population proportions, 511–518 Durbin-Watson, 795–798 for equality of population means, 470, 560–561 for equality of population proportions, 511–518, 543 Fisher’s least significant difference (LSD) procedure, 564–567 for goodness of fit, 530–536, 539, 543 for hypothesis tests, 396–397, 421, 475, 476 one-tailed test, 396–397 population mean: s known, 396–397, 432, 475 population mean: s unknown, 410–413, 432, 475 and population proportions, 416–417, 418, 432 and population variances, 491–494, 499–501, 504 and sampling distributions, 396–397 Thearling, Kurt, 19 Time series, 10f, 809 Time series analysis, 809, 860 See also Time series forecasting Time series data, 8–10, 809 Time series decomposition, 850–858 applications, 858–860 cyclical component, 857 deseasonalizing the time series, 855–857 monthly data, models based on, 857 overview, 850–851, 860 seasonal adjustments, 855, 857 seasonal indexes, 851–854 using Minitab, 870 Time series forecasting, 814–815, 866–870 accuracy of, 815–819 comparisons, 822 decomposition, 850–858 moving average, 823 patterns, 811–815 seasonality and trend, 841–846 trend projection, 811, 812 using Excel, 871–872 using Minitab, 868–870 Time series method, 809 Time series patterns, 809–815 cyclical patterns, 812–814 exponential smoothing, 823–827 forecasting method, selecting, 814–815 horizontal patterns, 809–811 moving averages, 820–827 seasonal patterns, 811–812 trend patterns, 811, 812 Time series plots, 809 Time series regression, 809, 834–836, 860 Total quality (TQ), 919–920 management movement, 924 See also Quality control; Statistical process control Total sum of squares (SST), 617 coefficient of determination, 616–619 formula, 664 relationship among SSE, SSR and, 618, 696 and sums of squares due to regression or error, 558, 572, 579, 586, 617, 618–619 Transformations of dependent variables, 765–769 Treatments, 548 Tree diagrams, 177–178, 205f, 246f Trendlines and scatter diagrams, 64–65, 96–98 Trend patterns, 811–812 seasonality, 841–846 Trend projection, 830–857 applications, 838–841 control conditions and, 935 linear trend regression, 825–830 nonlinear trend regression, 835–837 time series forecasting, 811, 812 using Excel, 868–870 using Minitab, 870, 871–872 Trials, experimental, 175, 310 Trimmed means, 108, 113 tTests formulas, 665, 742 individual significance, 704 least squares estimators, 605–609 multiple regression, 625–627, 704 simple linear regression, 625–626 Two-stage cluster sampling, 22-21 Two-tailed tests, 401–406 applications, 408–409 critical value approach, 403 hypothesis testing, 405–406 interval estimate, 405–406 of the null hypothesis, 401–406 overview, 403–405 population means: s known, 401–403 population means: s unknown, 411–413 for population variance, 491, 493, 494, 500–501 p-value approach, 402–403 Type I errors, 392–395 applications, 425–426 comparison procedures, 567–568 Fisher’s least significant difference (LSD) and, 564–567 probability of, 393–394 sample size, determining, 427–428 and Type II errors, 392–395 Type II errors, 392–395 probability of, 394, 396, 422–425 sample size, determining, 427–428 and Type I errors, 392–395 U Unbiased estimators, 334–335 Uniform probability density function, 273, 297 Uniform probability distributions, 273–274 applications, 276–277 area as a measure of probability, 274–276 Uniform probability functions, 226 continuous, 273 discrete, 226, 262, 263 Union of events, 190–191 United Way, 510 Unweighted aggregated price index, 954–956, 969 Upper tail tests hypothesis testing, 395, 398, 400–401, 402, 403, 404, 410–411, 412–413, 416–418, 427–431 for population variance, 489, 492–494, 498–501 U.S Commerce Department’s National Institute of Standards and Technology (NIST), 921 U.S Department of Labor, Bureau of Labor Statistics, 12, 953 U.S Food and Drug Administration (FDA), 446 U.S Government Accountability Office (GAO), 486 V Variability, measures of, 118–122 applications, 122–125 coefficient of variation, 121–122 interquartile range, 201 range, 118–119 standard deviation, 120–121, 229–230 variance, 119–120 Variables, 773–780 adding or deleting from model, 773–777, 800 applications, 778–780 in data, general case, 775–776 prediction errors and, 697 selection procedures, 784–788 use of p-values and, 776–777 Variable selection procedures, 784–788 backward elimination, 786–787 best-subsets regression, 787–788, 806 chose of final model, 788 forward selection, 786 stepwise regression procedure, 784–786 Variables sampling plans, 945 Variances, 119–120 for the binomial distribution, 250–251, 264 of discrete random variables, 221–222, 229–230, 263 of the hypergeometric probability distribution, 259, 264 of a linear combination of variables, 238–239, 240, 241, 263 in manufacturing applications, 487 regression model error, 629 using Minitab, 559f Variety, of data, 19 Velocity, of data, 19 Venn diagrams, 189–190 Volume, of data, 19 W Warehousing, data, 19 Weighted aggregated price indexes, 955–956, 969 Weighted aggregated quantity index, 966, 969 Weighted average of price relatives, 969 Weighted means, 106–107, 153 Weighted moving averages, 823 West Shell Realtors, 874 Whiskers of box plots, 134, 149 Wilcoxon signed-rank test, 883–886 applications, 886–888 formula, 909 hypotheses, 886 using Minitab, 913–914 using StatTools, 915 Williams, Walter, 394 Within-treatments estimates, 552, 555–556 World Trade Organization (WTO), 5–6, 7, 8, 14 X X-bars, x charts, 926–931 Y y-intercept estimated regression equation, 625–627 formula, 664 linear trend equation, 832–833, 856, 862 Z z-scores, 125–127 formula, 154 outlier identification, 130–131 z transformation, 127 z value and table interpolation, 284 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 Business and Economics 13e Revised DATAfiles Chapter Nations Norris Shadow02 Table 1.1 Table 1.5 Exercise 25 Chapter 2011Movies 2012Names 2012Networks 2012Population AirSurvey ApTest Audit BaseballHall BBB BestPayingDegrees BrandValue CEOTime Colleges Crosstab Crosstab2 DJIIABets EngineeringSalary FortuneBest100 Franchise Frequency FuelData2012 HotelRatings Hypertension LargeCorp Majors ManagerTime Marathon MarketIndexes MedianHousehold MPG NBAPlayerPts NewSAT PelicanStores Ports Queen City Restaurant Scatter SmartPhones Snow SoftDrink StartUps Syndicated Stereo Zoo Case Problem Exercise Exercise Exercise 46 Exercise Table 2.8 Table 2.4 Exercise Exercise 48 Exercise 25 Exercise 33 Exercise 20 Exercises 56 Exercise 27 Exercise 28 Exercise 49 Exercise 24 Exercise 52 Exercise 22 Exercise 11 Exercise 35 Exercise 10 Exercise 41 Exercise 21 Exercise Exercise 43 Exercise 26 Exercise 23 Exercises 45 Exercise 39 Exercise 18 Exercise 44 Case Problem Exercise 19 Case Problem Table 2.9 Exercise 36 Exercise 42 Exercise 40 Table 2.1 Exercise 47 Exercise Table 2.14 Exercise 58 Chapter 2011Movies 2012AfricanElephants 2012 Major Salary 2012StartSalary AdmiredCompanies Advertising AdvertisingSpend Asian AustralianOpen BestPrivateColleges BigBangTheory BorderCrossings BowlGames Case Problem Case Problem Figure 3.8 Table 3.1 Exercise 53 Exercise 32 Exercise Case Problem Exercise 28 Exercise 61 Exercise 12 Exercise 54 Exercise 57 CellService Coaches Coffee CommuteTime Flights FoodIndustry JacketRatings Mutual Fund NCAA NFLTeamValue PanamaRailroad PelicanStores PharmacySales Runners Russell SFGasPrices Shoppers Sleep Smartphone SmokeDetectors SpringTraining StateUnemp Stereo Transportation Travel WaitTracking Exercise 52 Exercise 63 Exercise 31 Exercise Exercise 27 Exercise 69 Exercise 10 Table 3.2 Exercise 44 Exercise 71 Exercise 75 Case Problem Exercise 51 Exercise 50 Exercise 60 Exercise 26 Case Problem Exercise 65 Exercise 66 Exercise 59 Exercise 72 Exercise 14 Table 3.6 Exercise 67 Exercise 70 Exercise 64 Chapter Judge Case Problem Chapter Coldstream12 Exercise 17 Chapter EAI Section 7.1 MetAreasAppendix 7.2   & 7.3 Morningstar Exercise 14 ShadowStocks Exercise 42 Chapter Auto AutoInsurance CasualDining ChildOutlook CorporateBonds DrugCost Guardians GulfProp HongKongMeals Houston Interval p JobSearch Lloyd’s Miami NewBalance Professional Russia Scheer Sellers Standing TeeTimes TeleHealth TobaccoFires TravelTax Case Problem Exercise 20 Exercise 38 Exercise 37 Exercise 16 Exercise 48 Exercise 22 Case Problem Exercise 19 Exercise Appendix 8.2 Exercise 18 Section 8.1 Exercise 17 Table 8.3 Case Problem Exercise 47 Table 8.4 Exercise Exercise 49 Section 8.4 Exercise 21 Exercise Exercise Chapter Administrator Exercise 29 AirRating Section 9.4 Bayview Case Problem BritainMarriages Exercise 64 ChildCare Exercise 30 Coffee Section 9.3 Eagle Exercise 43 Fowle Exercise 21 GolfTest Section 9.3 HomeState Exercise 39 Hyp Sigma KnownAppendix 9.2 Hyp Sigma UnknownAppendix 9.2 Hypothesis p Appendix 9.2 LawSuit Exercise 44 Orders Section 9.4 Quality Case Problem UsedCars Exercise 32 WeeklyPay Exercise 65 WomenGolf Section 9.5 Chapter 10 AirDelay BusinessTravel CheckAcct CollegeCosts ExamScores Golf GolfScores HomePrices Hotel Matched Mutual Occupancy SATMath SoftwareTest StockPrices TaxPrep TestScores Twins Exercise 18 Exercise 24 Section 10.2 Exercise 13 Section 10.1 Case Problem Exercise 26 Exercise 39 Exercise Table 10.2 Exercise 40 Exercise 46 Exercise 16 Table 10.1 Exercise 22 Section 10.4 Exercise 25 Exercise 42 Chapter 11 Bags BatteryTime BusTimes Costco Halloween PriceChange SchoolBus Training Travel Yields Exercise 19 Exercise 21 Section 11.1 Exercise 10 Exercise Exercise Section 11.2 Case Problem Exercise 25 Exercise 11 Chapter 12 Ambulance AutoLoyalty AutoQuality BeerPreference Chemline ChiSquare Demand Grades M&M NYReform WorkforcePlan Exercise 32 Table 12.1 Exercise 14 Table 12.6 Table 12.10 Figure 12.5 Exercise 26 Exercise 34 Exercise 22 Case Problem Exercise 12 Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Chapter 13 AirTraffic Assembly AudJudg Browsing Chemitech ClubHead CollegeRates CompactCars Exer6 GMATStudy GrandStrand HybridTest Medical1 Medical2 MidwestGas NCP OzoneLevels Paint SalesSalary SatisJob SATScores SnowShoveling Triple-A Table 13.5 Exercise 38 Exercise 10 Exercise 39 Table 13.1 Exercise 42 Exercise 37 Exercise 41 Exercise Table 13.10 Exercise 12 Exercise 32 Case Problem Case Problem Exercise 25 Table 13.4 Exercise 36 Exercise 11 Case Problem Exercise 35 Exercise 26 Exercise 27 Exercise 20 Chapter 14 Absent Exercise 63 AgeCost Exercise 64 AirlineSeats Exercise 43 Armand’s Table 14.1 Beta Case Problem BrokerRatings Exercises & 28 BuckeyeCreek Case Problem BusinessTravelExercises 12 & 39 Cameras Case Problem Camry Exercise 68 CEOGrants Exercise 10 Charities Exercise 52 Computer Exercise 11 DJIAS&P500 Exercise 58 FamilySedans Case Problem GoldHoldings Exercise 53 HoursPts Exercise 65 IRSAudit Exercise 67 Jensen Exercise 61 MktBeta Exercise 66 MLBValues Exercise 54 NFLPassing Exercise OnlineEdu Exercise 60 RaceHelmets Exercise 44 RacingBicyclesExercises 20 & 31 RentMortgage Exercise 49 Safety Case Problem SalaryStress Exercise 27 SalesExercises 7, 19, & 36 WSHouses Exercise 59 Chapter 15 2012FuelEcon 2014LPGAStats Auto2 Bank Exercise 55 Exercise 43 Exercise 42 Exercise 46 Broker Exercise 31 ButlerTables 15.1 & 15.2 CarValues Case Problem Consumer Case Problem CruiseShips Exercise 25 Exer2 Exercise FortuneBest Exercise 57 Johnson Table 15.6 Lakeland Exercise 47 MLBPitchingExercises 10, 18, & 26 MonitorRatings Exercise MutualFunds Exercise 56 NASCAR Case Problem NFL Exercise 24 NFLPassing Exercises & 16 NFL2011 Exercise 30 PGADrivingDist Exercises & 17 Repair Exercise 35 RestaurantRatings Exercise 37 Ships Exercise ShowtimeExercises 5, 15, & 41 SimmonsTable 15.11 &   Exercise 44 Stroke Exercise 38 TireRack Exercise 54 TireRatings Exercise 48 Chapter 16 2014LPGAStats3Exercises 12,   13, & 17 Audit Exercise 31 Bikes Exercise 30 Browsing Exercise 34 CarMileage Exercise 35 Chemitech2 Table 16.10 ClassicCars Exercise ClosingPrice Exercise 27 CorporateBonds Exercise 29 Cravens Table 16.5 Layoffs Exercise 16 MetroAreas Exercise MLBPitching Exercise 15 MPG Table 16.4 PGATour Case Problem RentMortgage Exercise Reynolds Table 16.1 StrokeExercises 14 & 19 Tyler Table 16.2 WineRatings Case Problem Yankees Exercise 18 Chapter 17 AppleRetail Exercise 45 AptExpExercises 34 & 38 BicycleTable 17.3 & 17.12 CarlsonSales Case Problem CholesterolTable 17.4 & 17.15 CountySales Case Problem CrudeCost Exercise 44 Dishwasher Exercise 41 Exchange Rate Exercise 24 Facebook Exercise 27 GasolineTable 17.1 &  Exercises 7, & GasolineRevised Table 17.2 GoogleRevenue Exercise 23 HomePrices Exercise 16 HudsonMarine Exercise 53 KYBudget Exercise 21 Pasta Exercise 26 PianoSales Exercise 49 PollutionExercises 31 & 39 Portfolio Exercise 42 PowerExercises 33 & 40 ProductSales Exercise 14 SouthShore Exercise 32 Textbooks Exercise 30 TextSales Exercise 37 TVSalesTable 17.6 & 17.18 TwitterRevenue Exercise 25 UDFMilk Exercise 43 UmbrellaTable17.5 & 17.16 Vintage Table 17.25 Chapter 18 AcctPlanners Additive ChicagoIncome DelayedFlights Evaluations Exams HomeSales JapanUS Lightning LPGAANA MatchedSamples Methods Microwave MockDraft NielsenResearch OnTime Overnight PoliceRecords PotentialActual ProductWeights Professors ProGolfers Programs Refrigerators Relaxant Student SunCoast Techs TestPrepare ThirdNational Williams WritingScore Exercise 19 Exercise 12 Exercise Exercise 25 Exercise 45 Exercise 46 Section 18.1 Exercise 22 Exercise 21 Exercise 16 Appendix 18.1 Exercise 43 Exercise 24 Exercise 29 Exercise 47 Exercise 14 Exercise 15 Exercise 23 Table 18.16 Exercise 42 Exercise 37 Exercise 36 Exercise 44 Exercise 40 Exercise 13 Exercise 34 Appendix 18.1 Exercise 35 Exercise 27 Appendix 18.1 Appendix 18.1 Exercise 17 Chapter 19 Jensen Tires Coffee Table 19.2 Exercise Exercise 20 Appendix F p-Value Appendix F Copyright 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 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 2018 Cengage Learning All Rights Reserved May not be copied, scanned, or duplicated, in whole or in part WCN 02-200-203 ... 978-1-337-09419-1 Statistics for Business & Economics, Revised 13e Anderson/Sweeney/Williams/Camm/Cochran MindTap® Business Statistics for Statistics for Business & Economics, Revised 13e J00001 MindTap® Business. .. Preface This text is the revised 13th edition of STATISTICS FOR BUSINESS AND ECONOMICS The revised edition updates the material in STATISTICS FOR BUSINESS ECONOMICS 13e for use with Microsoft Excel... copied, scanned, or duplicated, in whole or in part WCN 02-200-203 Statistics for Business and Economics, Thirteenth Edition, Revised David R Anderson, Dennis J Sweeney, Thomas A Williams, Jeffrey
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