Quinton J. Nottingham | James S. Hawkes Discovering BUSINESS STATISTICS SECOND EDITION Annotated Instructor’s Edition - Not for SaleEditor: Robin Hendrix Assistant Editors: Vicente Muñoz, Lauren Tubbs Editorial Assistants: Danielle Bess, Adam O’Flaherty, Marvin Glover Manager of Math Content Development: Blair Dunivan Creative Services Manager: Trudy Tronco Designers: Lizbeth Mendoza, Patrick Thompson, Joel Travis Cover Design: Joel Travis Composition and Answer Key Assistance: Quant Systems India Pvt. Ltd. A division of Quant Systems, Inc. 546 Long Point Road Mount Pleasant, SC 29464 Copyright © 2023, 2020, 2013 by Hawkes Learning / Quant Systems, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written consent of the publisher. Library of Congress Control Number 2022901162 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 ISBN: 978-1-64277-511-2 AIE ISBN: 978-1-64277-518-1Table of Contents Preface .............................................................................................................................................................ix Chapter 1: Decision Making Using Statistics 1.1 Statistics and Global Issues ......................................................................................................................5 1.2 Statistics and Quality .............................................................................................................................. 10 1.3 Descriptive Statistics versus Inferential Statistics ............................................................................... 10 1.4 The Value of Statistical Literacy ............................................................................................................ 13 Chapter 1 Review .................................................................................................................................... 15 Additional Exercises ............................................................................................................................... 16 Discovery Project .................................................................................................................................... 19 Chapter 2: Data, Big Data, and Analytics 2.1 Data and Decision Making ..................................................................................................................... 24 2.2 Big Data and Business Analytics ........................................................................................................... 41 2.3 Data Classifications ................................................................................................................................ 46 2.4 Time Series Data and Cross-Sectional Data ........................................................................................ 52 Discovering Technology ......................................................................................................................... 62 Chapter 2 Review .................................................................................................................................... 66 Additional Exercises ............................................................................................................................... 67 Discovery Project .................................................................................................................................... 72 Chapter 3: Organizing, Displaying, and Interpreting Data 3.1 Frequency Distributions ........................................................................................................................ 79 3.2 Displaying Qualitative Data ................................................................................................................... 84 3.3 Constructing Frequency Distributions for Quantitative Data ........................................................... 96 3.4 Graphical Displays of Quantitative Data ............................................................................................ 101 3.5 Analyzing Graphs .................................................................................................................................. 119 Discovering Technology ....................................................................................................................... 127 Chapter 3 Review .................................................................................................................................. 135 Additional Exercises ............................................................................................................................. 136 Discovery Project .................................................................................................................................. 143 Chapter 4: Numerical Descriptive Statistics 4.1 Measures of Location ........................................................................................................................... 152 4.2 Measures of Dispersion ....................................................................................................................... 167 4.3 Measures of Relative Position ............................................................................................................. 178iv 4.4 Data Subsetting..................................................................................................................................... 187 4.5 Analyzing Grouped Data ...................................................................................................................... 197 4.6 Proportions ........................................................................................................................................... 200 4.7 Measures of Association Between Two Variables ............................................................................ 204 Discovering Technology ....................................................................................................................... 221 Chapter 4 Review .................................................................................................................................. 229 Additional Exercises ............................................................................................................................. 234 Discovery Project .................................................................................................................................. 238 Chapter 5: Probability, Randomness, and Uncertainty 5.1 Introduction to Probability .................................................................................................................. 244 5.2 Laws of Probability ............................................................................................................................... 255 5.3 Conditional Probability ........................................................................................................................ 263 5.4 Independence ....................................................................................................................................... 266 5.5 Bayes’ Theorem .................................................................................................................................... 272 5.6 Counting Techniques ........................................................................................................................... 276 Discovering Technology ....................................................................................................................... 282 Chapter 5 Review .................................................................................................................................. 287 Additional Exercises ............................................................................................................................. 290 Discovery Project .................................................................................................................................. 293 Chapter 6: Discrete Probability Distributions: About the Future 6.1 Types of Random Variables ................................................................................................................. 299 6.2 Discrete Random Variables ................................................................................................................. 302 6.3 The Discrete Uniform Distribution ..................................................................................................... 312 6.4 The Binomial Distribution .................................................................................................................... 315 6.5 The Poisson Distribution ..................................................................................................................... 325 6.6 The Hypergeometric Distribution ....................................................................................................... 329 Discovering Technology ....................................................................................................................... 334 Chapter 6 Review .................................................................................................................................. 346 Additional Exercises ............................................................................................................................. 348 Discovery Project .................................................................................................................................. 351 Chapter 7: Continuous Random Variables 7.1 The Uniform Distribution..................................................................................................................... 357 7.2 The Normal Distribution ...................................................................................................................... 361 7.3 Assessing Normality Graphically ........................................................................................................ 365 7.4 The Standard Normal Distribution ..................................................................................................... 372 7.5 Approximations to Other Distributions ............................................................................................. 386 Discovering Technology ....................................................................................................................... 395v Chapter 7 Review .................................................................................................................................. 405 Additional Exercises ............................................................................................................................. 407 Discovery Project .................................................................................................................................. 410 Chapter 8: Samples and Sampling Distributions 8.1 Random Samples and Sampling Distributions ................................................................................. 415 8.2 The Distribution of the Sample Mean and the Central Limit Theorem ......................................... 420 8.3 The Distribution of the Sample Proportion ....................................................................................... 432 8.4 Sampling Methods ................................................................................................................................ 439 Discovering Technology ....................................................................................................................... 446 Chapter 8 Review .................................................................................................................................. 450 Additional Exercises ............................................................................................................................. 452 Discovery Project .................................................................................................................................. 456 Chapter 9: Estimation with Confidence Intervals: Single Sample 9.1 Estimating the Population Mean, s Known ...................................................................................... 461 9.2 Estimating the Population Mean, s Unknown .................................................................................. 469 9.3 Estimating the Population Proportion ............................................................................................... 477 9.4 Estimating the Population Standard Deviation or Variance ........................................................... 484 Discovering Technology ....................................................................................................................... 489 Chapter 9 Review .................................................................................................................................. 499 Additional Exercises ............................................................................................................................. 502 Discovery Project .................................................................................................................................. 504 Chapter 10: Hypothesis Testing: Single Sample 10.1 Introduction to Hypothesis Testing .................................................................................................. 510 10.2 Testing a Hypothesis about a Population Mean, s Known ........................................................... 517 10.3 Testing a Hypothesis about a Population Mean, s Unknown ...................................................... 532 10.4 The Relationship Between Confidence Interval Estimation and Hypothesis Testing ................ 543 10.5 Testing a Hypothesis about a Population Proportion .................................................................... 547 10.6 Testing a Hypothesis about a Population Variance ........................................................................ 556 Discovering Technology ....................................................................................................................... 561 Chapter 10 Review ................................................................................................................................ 568 Additional Exercises ............................................................................................................................. 569 Discovery Project .................................................................................................................................. 573 Chapter 11: Inferences about Two Samples 11.1 Comparing Two Population Means, s 1 and s 2 Known .................................................................. 579 11.2 Comparing Two Population Means, s 1 and s 2 Unknown ............................................................. 587vi 11.3 Paired Difference Test ....................................................................................................................... 598 11.4 Comparing Two Population Proportions ......................................................................................... 607 11.5 Comparing Two Population Variances ............................................................................................. 614 Discovering Technology ....................................................................................................................... 624 Chapter 11 Review ................................................................................................................................ 635 Additional Exercises ............................................................................................................................. 639 Discovery Project .................................................................................................................................. 645 Chapter 12: Analysis of Variance (ANOVA) 12.1 Introduction to Analysis of Variance (ANOVA) ................................................................................ 651 12.2 Assumptions in an ANOVA Test ........................................................................................................ 663 12.3 The F-Distribution and the F-Test ..................................................................................................... 672 12.4 Multiple Comparison Procedures..................................................................................................... 680 12.5 Two-Way ANOVA: The Randomized Block Design .......................................................................... 690 12.6 Two-Way ANOVA: The Factorial Design ........................................................................................... 701 Discovering Technology ....................................................................................................................... 717 Chapter 12 Review ................................................................................................................................ 733 Additional Exercises ............................................................................................................................. 737 Discovery Project .................................................................................................................................. 744 Chapter 13: Regression, Inference, and Model Building 13.1 The Simple Linear Regression Model ............................................................................................... 752 13.2 Residual Analysis ................................................................................................................................ 773 13.3 Evaluating the Fit of the Linear Regression Model ......................................................................... 781 13.4 Fitting a Linear Time Trend ............................................................................................................... 790 13.5 Inference Concerning the Slope ....................................................................................................... 795 13.6 Inference Concerning the Model’s Prediction ................................................................................. 808 Discovering Technology ....................................................................................................................... 820 Chapter 13 Review ................................................................................................................................ 830 Additional Exercises ............................................................................................................................. 834 Discovery Project .................................................................................................................................. 840 Chapter 14: Multiple Regression 14.1 The Multiple Regression Model ........................................................................................................ 846 14.2 The Coefficient of Determination and Adjusted R2 ........................................................................ 853 14.3 Inference Concerning the Multiple Regression Model and Its Coefficients ................................ 859 14.4 Inference Concerning the Model’s Prediction ................................................................................. 869 14.5 Models with Qualitative Independent Variables ............................................................................ 875 14.6 Additional Topics in Multiple Regression ........................................................................................ 886 Discovering Technology ....................................................................................................................... 889vii Chapter 14 Review ................................................................................................................................ 897 Additional Exercises ............................................................................................................................. 899 Discovery Project .................................................................................................................................. 905 Chapter 15: Time Series Analysis and Forecasting 15.1 Time Series Components .................................................................................................................. 911 15.2 Moving Averages ................................................................................................................................ 917 15.3 Exponential Smoothing Techniques ................................................................................................ 922 15.4 Forecast Accuracy ............................................................................................................................... 929 15.5 Seasonality .......................................................................................................................................... 935 Discovering Technology ....................................................................................................................... 939 Chapter 15 Review ................................................................................................................................ 959 Additional Exercises ............................................................................................................................. 961 Discovery Project .................................................................................................................................. 962 Chapter 16: Looking for Relationships in Qualitative Data 16.1 The Chi-Square Distribution .............................................................................................................. 967 16.2 The Chi-Square Test for Goodness of Fit ......................................................................................... 971 16.3 The Chi-Square Test for Association ................................................................................................ 980 Discovering Technology ....................................................................................................................... 989 Chapter 16 Review ................................................................................................................................ 999 Additional Exercises ........................................................................................................................... 1000 Discovery Project ................................................................................................................................ 1003 Chapter 17: Nonparametric Statistics 17.1 The Sign Test ..................................................................................................................................... 1009 17.2 The Wilcoxon Signed-Rank Test ...................................................................................................... 1019 17.3 The Wilcoxon Rank-Sum Test .......................................................................................................... 1026 17.4 The Rank Correlation Test ............................................................................................................... 1035 17.5 The Runs Test for Randomness ...................................................................................................... 1041 17.6 The Kruskal–Wallis Test ................................................................................................................... 1046 Discovering Technology ..................................................................................................................... 1051 Chapter 17 Review .............................................................................................................................. 1063 Additional Exercises ........................................................................................................................... 1065 Discovery Project ................................................................................................................................ 1070 Chapter 18: Statistical Process Control 18.1 Basic Charts and Diagrams Used in Quality Control .................................................................... 1076 18.2 Basic Concepts .................................................................................................................................. 1083viii 18.3 Monitoring with x and R Charts .................................................................................................... 1086 18.4 Monitoring with a p Chart ............................................................................................................... 1095 Discovering Technology ..................................................................................................................... 1101 Chapter 18 Review .............................................................................................................................. 1112 Additional Exercises ........................................................................................................................... 1114 Discovery Project ................................................................................................................................ 1117 Appendix A: Statistical Tables ................................................................................................................ 1120 Appendix B: Getting Started with Microsoft Excel (Desktop) ............................................................. 1176 Appendix C: Getting Started with Minitab ............................................................................................ 1184 Appendix D: Getting Started with JMP .................................................................................................. 1189 Answer Key ................................................................................................................................................ 1197 Index ........................................................................................................................................................... 1245ixPreface Preface We have taught Business Statistics for roughly thirty years. We have always wanted to write a textbook that portrays our teaching style – one that introduces the topic being discussed as it relates to the business world and then presents the methodologies in a manner that helps the students know when, where, and how these methodologies are used in the business world. This textbook does just that. As you work your way through the book, you’ll see that in each chapter, the topics are introduced with examples of real-world applications. Then, as subsequent sections are covered in each chapter, the examples are presented and worked through step-by-step in a manner that will keep the students interested. When we set out to write this text, our goal was to discuss topics at a level that would engage the students, present examples that would interest them, and write the book in a relaxed, conversational style—we hope we have accomplished those goals with this text. We have also integrated the TI-84 Plus calculator, Microsoft Excel, Minitab 21, and JMP 16 support in the form of Discovering Technology sections at the end of each chapter, along with Getting Started guides for Excel, Minitab, and JMP. Although the text includes quite a few manual computations with many of its examples, learning to use technology is helpful in analyzing the book’s many business-related data sets and cases (presented as Discovery Projects at the ends of the chapters). In addition, we have included solutions to the odd-numbered exercises and a tear- out formula and table reference that we hope students will find helpful. Further, the material in this text is integrated with the Hawkes Learning Systems: Discovering Business Statistics software. Through the use of this text along with the accompanying software, it is our hope that students will discover the many advantages of statistical thinking and understanding, both in business environments and everyday situations. Quinton J. Nottingham James S. HawkesNext >