14th EDITION ELEMENTARY STATISTICS
ELEMENTARY STATISTICS 14th EDITION MARIO F. TRIOLA
Content Management: Suzanna Bainbridge, Amanda Brands Content Production: Robert Carroll, Jean Choe, Peggy McMahon Product Management: Karen Montgomery Product Marketing: Alicia Wilson Rights and Permissions: Pavithra Gunasekaran, Integra Please contact https://support.pearson.com/getsupport/s/ with any queries on this content. Cover Image by Bim/Getty Images Microsoft and/or its respective suppliers make no representations about the suitability of the information contained in the documents and related graphics published as part of the services for any purpose. All such documents and related graphics are provided “as is” without warranty of any kind. Microsoft and/or its respective suppliers hereby disclaim all warranties and conditions with regard to this information, including all warranties and conditions of merchantability, whether express, implied or statutory, fitness for a particular purpose, title and non-infringement. In no event shall Microsoft and/or its respective suppliers be liable for any special, indirect or consequential damages or any damages whatsoever resulting from loss of use, data or profits, whether in an action of contract, negligence or other tortious action, arising out of or in connection with the use or performance of information available from the services. The documents and related graphics contained herein could include technical inaccuracies or typographical errors. Changes are periodically added to the information herein. Microsoft and/or its respective suppliers may make improvements and/or changes in the product(s) and/or the program(s) described herein at any time. Partial screen shots may be viewed in full within the software version specified. Microsoft® and Windows® are registered trademarks of the Microsoft Corporation in the U.S.A. and other countries. This book is not sponsored or endorsed by or affiliated with the Microsoft Corporation. Copyright © 2022, 2018, 2014 by Pearson Education, Inc. or its affiliates, 221 River Street, Hoboken, NJ 07030. All Rights Reserved. Manufactured in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms, and the appropriate contacts within the Pearson Education Global Rights and Permissions department, please visit www.pearsoned.com/permissions/. Acknowledgments of third-party content appear on the appropriate page within the text, or in the Credits at the end of the book which constitutes an extension of this copyright page. PEARSON, ALWAYS LEARNING, MyMathLab, and MYLAB are exclusive trademarks owned by Pearson Education, Inc., or its affiliates in the U.S. and/or other countries. Unless otherwise indicated herein, any third-party trademarks, logos, or icons that may appear in this work are the property of their respective owners, and any references to third-party trademarks, logos, icons, or other trade dress are for demonstrative or descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement, authorization, or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and Pearson Education, Inc., or its affiliates, authors, licensees, or distributors. Library of Congress Cataloging-in-Publication Data Names: Triola, Mario F., author. Title: Elementary statistics / Mario F. Triola. Description: 14th edition, annotated instructor’s edition. | Hoboken : Pearson, [2022] | Includes index. | Summary: “Step-by-step guide to the important concepts of Statistics”-- Provided by publisher. Identifiers: LCCN 2020040438 | ISBN 9780136803201 (hardcover) Subjects: LCSH: Statistics--Textbooks. Classification: LCC QA276.12 .T76 2022 | DDC 519.5--dc23 LC record available at https://lccn.loc.gov/2020040438 ScoutAutomatedPrintCode Student Edition ISBN-10: 0137320809 ISBN-13: 9780137320806
To Ginny Marc, Dushana, and Marisa Scott, Anna, Siena, and Kaia
Mario F. Triola is a Professor Emeritus of Mathematics at Dutchess Community College, where he has taught statistics for over 30 years. Marty is the author of Essentials of Statistics, 6th edition, Elementary Statistics Using Excel™, 7th edition, Elementary Statistics Using the TI@83>84 Plus Calculator, 5th edition, and he is a coauthor of Biostatistics for the Biological and Health Sciences, 2nd edition, Statistical Reasoning for Everyday Life, 5th edition, and Business Statistics. Elementary Statistics is currently available as an International Edition, and it has been translated into several foreign languages. Marty designed the original Statdisk statistical software, and he has written several manuals and workbooks for technology supporting statistics education. He has been a speaker at many conferences and colleges. Marty’s consulting work includes the design of casino slot machines and fishing rods. He has worked with attorneys in determining probabilities in paternity lawsuits, analyzing data in medical malpractice lawsuits, identifying salary inequities based on gender, and analyzing disputed election results. He has also used statistical methods in analyzing medical school surveys, and in analyzing survey results for the New York City Transit Authority, and analyzing COVID-19 virus data for government officials. Marty has testified as an expert witness in the New York State Supreme Court. The Text and Academic Authors Association has awarded Marty a “Texty” for Excellence for his work on Elementary Statistics. As of this writing, Marty’s Elementary Statistics book has been the #1 statistics book in the United States for the past 25 consecutive years. ABOUT THE AUTHOR vii Celebrating the past 25 years as the #1 statistics textbook author!
CONTENTS 1 INTRODUCTION TO STATISTICS 1 1-1 Statistical and Critical Thinking 3 1-2 Types of Data 14 1-3 Collecting Sample Data 26 1-4 Ethics in Statistics (download only) 36 2 EXPLORING DATA WITH TABLES AND GRAPHS 43 2-1 Frequency Distributions for Organizing and Summarizing Data 45 2-2 Histograms 55 2-3 Graphs That Enlighten and Graphs That Deceive 62 2-4 Scatterplots, Correlation, and Regression 73 3 DESCRIBING, EXPLORING, AND COMPARING DATA 86 3-1 Measures of Center 88 3-2 Measures of Variation 104 3-3 Measures of Relative Standing and Boxplots 121 4 PROBABILITY 142 4-1 Basic Concepts of Probability 144 4-2 Addition Rule and Multiplication Rule 158 4-3 Complements, Conditional Probability, and Bayes’ Theorem 171 4-4 Counting 180 4-5 Simulations for Hypothesis Tests 190 5 DISCRETE PROBABILITY DISTRIBUTIONS 203 5-1 Probability Distributions 205 5-2 Binomial Probability Distributions 218 5-3 Poisson Probability Distributions 232 6 NORMAL PROBABILITY DISTRIBUTIONS 244 6-1 The Standard Normal Distribution 246 6-2 Real Applications of Normal Distributions 260 6-3 Sampling Distributions and Estimators 272 6-4 The Central Limit Theorem 283 6-5 Assessing Normality 294 6-6 Normal as Approximation to Binomial (download only) 303 7 ESTIMATING PARAMETERS AND DETERMINING SAMPLE SIZES 310 7-1 Estimating a Population Proportion 312 7-2 Estimating a Population Mean 329 7-3 Estimating a Population Standard Deviation or Variance 345 7-4 Bootstrapping: Using Technology for Estimates 355 8 HYPOTHESIS TESTING 372 8-1 Basics of Hypothesis Testing 374 8-2 Testing a Claim About a Proportion 390 8-3 Testing a Claim About a Mean 404 8-4 Testing a Claim About a Standard Deviation or Variance 416 8-5 Resampling: Using Technology for Hypothesis Testing 425 ix
x Contents 9 INFERENCES FROM TWO SAMPLES 440 9-1 Two Proportions 442 9-2 Two Means: Independent Samples 454 9-3 Matched Pairs 469 9-4 Two Variances or Standard Deviations 480 9-5 Resampling: Using Technology for Inferences 490 10 CORRELATION AND REGRESSION 506 10-1 Correlation 508 10-2 Regression 529 10-3 Prediction Intervals and Variation 544 10-4 Multiple Regression 552 10-5 Nonlinear Regression 564 11 GOODNESS-OF-FIT AND CONTINGENCY TABLES 576 11-1 Goodness-of-Fit 578 11-2 Contingency Tables 590 12 ANALYSIS OF VARIANCE 610 12-1 One-Way ANOVA 612 12-2 Two-Way ANOVA 626 13 NONPARAMETRIC TESTS 642 13-1 Basics of Nonparametric Tests 644 13-2 Sign Test 646 13-3 Wilcoxon Signed-Ranks Test for Matched Pairs 657 13-4 Wilcoxon Rank-Sum Test for Two Independent Samples 664 13-5 Kruskal-Wallis Test for Three or More Samples 671 13-6 Rank Correlation 677 13-7 Runs Test for Randomness 686 14 STATISTICAL PROCESS CONTROL 700 14-1 Control Charts for Variation and Mean 702 14-2 Control Charts for Attributes 713 15 HOLISTIC STATISTICS 724 APPENDIX A TABLES AND FORMULAS 731 APPENDIX B DATA SETS 749 APPENDIX C WEBSITES AND BIBLIOGRAPHY OF BOOKS 765 APPENDIX D ANSWERS TO ODD-NUMBERED SECTION EXERCISES 766 (and all Quick Quizzes, all Review Exercises, and all Cumulative Review Exercises) Credits 815 Subject Index 823 Applications Index 835
The ancient Chinese philosopher Lao Tzu famously wrote: A journey of a thousand miles must begin with a single step. This textbook will lead you, step-by-step, on a journey through the important concepts of statistics and if you’re reading this, you’ve already taken the first step! Thankfully, our journey will be much less physically taxing than a “journey of a thousand miles” and will only require use of your feet for determining skewness (see page 57). We are now on the leading edge of a major revolution in technology, and the content of this text is key to that revolution. Artificial intelligence, machine learning, and deep learning are studied in data science, and the study of data science requires study of the discipline of statistics. Data science is now experiencing unprecedented growth. Projections indicate a 33% increased demand for statisticians in a few short years, and there is a projected shortage of workers with statistical skills. Also, as in past decades, statistics continues to be essential to a wide variety of disciplines, including medicine, polling, journalism, law, physical science, education, business, and economics. It is a gross understatement to suggest that it is now very wise to initiate a study of statistics. Goals of This Fourteenth Edition ■ Foster personal growth of students through critical thinking, use of technology, collaborative work, and development of communication skills. ■ Incorporate the latest and best methods used by professional statisticians. ■ Include features that address all of the recommendations included in the Guidelines for Assessment and Instruction in Statistics Education (GAISE) as recommended by the American Statistical Association. ■ Provide an abundance of new and interesting data sets, examples, and exercises, such as those involving biometric security, cybersecurity, drones, and Internet traffic. ■ Present topics used in data science and many other applications, and include very large data sets that have become so important in our current culture. ■ Enhance teaching and learning with the most extensive and best set of supplements and digital resources. Audience, Prerequisites Elementary Statistics is written for high school students preparing for any college major or career path. Algebra is used minimally. It is recommended that students have completed at least an elementary algebra course prior to taking Elementary Statistics. In many cases, underlying theory is included, but this book does not require the mathematical rigor more appropriate for mathematics majors. Instead of being a “cookbook” devoid of any theory, this book includes the mathematics underlying important statistical methods, but the focus is on understanding and applying those methods along with interpreting results in a meaningful way. PREFACE xi
xii Preface Hallmark Features Great care has been taken to ensure that each chapter of Elementary Statistics will help students understand the concepts presented. The following features are designed to help meet that objective of conceptual understanding. Real Data Thousands of hours have been devoted to finding data that are real, meaningful, and interesting to students. 94% of the examples are based on real data, and 93% of the exercises are based on real data. Some exercises refer to the 46 data sets listed in Appendix B, and 20 of those data sets are new to this edition. Exercises requiring use of the Appendix B data sets are located toward the end of each exercise set and are marked with a special data set icon . These data sets are also available in MyMathLab for School, including data sets for StatCrunch. Appendix B includes descriptions of the 46 data sets that can be downloaded from www.TriolaStats.com in formats for Excel™, Minitab™, JMP, SPSS, and TI-83>84™ Plus calculators. (Because TI-83>84 Plus calculators have limited memory, several larger data sets have been truncated for TI users, and answers have been annotated when appropriate.) Readability Great care, enthusiasm, and passion have been devoted to creating a book that is readable, understandable, interesting, and relevant. Students pursuing any field of study are sure to find applications related to their future work. Website This textbook is supported by www.pearsonhighered.com/triola and the author’s website www.TriolaStats.com which are continually updated to provide the latest digital resources for the Triola Statistics Series, including: ■ Statdisk: A free and robust browser-based statistical program designed specifically for this book. This is the only statistics textbook with dedicated and comprehensive statistics software. ■ Downloadable Appendix B data sets in a variety of technology formats. ■ Downloadable textbook supplements including Section 1-4 Ethics in Statistics, Section 6-6 Normal as Approximation to Binomial, Glossary of Statistical Terms, and Formulas and Tables. ■ Interactive flow charts for key statistical procedures. ■ Online instructional videos created specifically for the 14th Edition that provide step-by-step technology instructions. ■ Contact link providing one-click access for instructors and students to contact the author, Marty Triola, with questions and comments. Chapter Features Chapter Opening Features ■ Chapters begin with a Chapter Problem that uses real data and motivates the chapter material. ■ Chapter Objectives provide a summary of key learning goals for each section in the chapter.
Preface xiii Exercises Many exercises require the interpretation of results. Great care has been taken to ensure their usefulness, relevance, and accuracy. Exercises are arranged in order of increasing difficulty and exercises are also divided into two groups: (1) Basic Skills and Concepts and (2) Beyond the Basics. Beyond the Basics exercises address more difficult concepts or require a stronger mathematical background. In a few cases, these exercises introduce a new concept. End-of-Chapter Features ■ Chapter Quick Quiz provides 10 review questions that require brief answers. ■ Review Exercises offer practice on the chapter concepts and procedures. ■ Cumulative Review Exercises reinforce earlier material. ■ Technology Project provides an activity that can be used with a variety of technologies. ■ Big (or Very Large) Data Projects encourage use of large data sets. ■ From Data to Decision is a capstone problem that requires critical thinking and writing. ■ Cooperative Group Activities encourage active learning in groups. Other Features Margin Essays There are 134 margin essays designed to highlight real-world topics and foster student interest. 36 of them are new to this edition. There are also many Go Figure items that briefly describe interesting numbers or statistics. Flowcharts The text includes flowcharts that simplify and clarify more complex concepts and procedures. Animated versions of the text’s flowcharts are available within MyMathLab for School. Formulas and Tables This downloadable resource, organized by chapter, gives students a quick reference for studying, or can be printed for use when taking tests (if allowed by the instructor). It also includes the most commonly used tables. This is available for download at www.TriolaStats.com, pearson.com/math-stats-resources, or from the MyMathLab for School course. Technology Integration As in the preceding edition, there are many displays of screens from technology throughout the book, and some exercises are based on displayed results from technology. Where appropriate, sections end with a new Tech Center subsection that includes new technology specific videos and detailed instructions for Statdisk, Minitab®, Excel®, StatCrunch, or a TI@83>84 Plus® calculator. (Throughout this text, “TI@83>84 Plus” is used to identify a TI-83 Plus or TI-84 Plus calculator). The end-of-chapter features include a Technology Project. The Statdisk statistical software package is designed specifically for this textbook and contains all Appendix B data sets. Statdisk is free to users of this book and it can be downloaded at www.Statdisk.org. Changes to This 14th Edition New Features New Content: This 14th edition includes an abundance of new exercises, new examples, and Chapter Problems, as summarized in the following table. Number New to 14th Edition Use Real Data Exercises 1822 64% (1172) 93% (1703) Examples 213 58% (124) 94% (201) Chapter Problems 14 100% (14) 100% (14)
xiv Preface New Data Sets: This book includes a rich data set library in Appendix B so that professors and students have ready access to real and interesting data. Appendix B has been expanded from 32 data sets to 46 data sets. Twenty of those data sets are new, including Internet Traffic, Queues, Car Data, Commute Times, Candies, Taxi Data, and Disney World Wait Times. Larger Data Sets: The largest data set in the previous edition had 600 cases. The data set library in this 14th edition includes data sets with 6068, 3982, 5755, 8959, and 1000 cases. In addition, there are big data sets with 465,506 cases and 31,784 cases. Working with such larger data sets is essential to students progressing into the age of big data and data science. New Types of Exercises: To foster the development of critical thinking, the Cumulative Review Exercises near the end of Chapters 9, 10, and 11 consist of open-ended questions in which students are presented with a data set, and they are asked to pose a key question relevant to the data, identify a procedure for addressing that question, then analyzing the data to form a conclusion. New Margin Essays: This 14th edition of Elementary Statistics includes 36 new margin essays. Big (or Very Large) Data Projects: New to this edition, these projects are located near the end of each chapter and ask students to think critically while using large data sets. New Chapter Problem Icon: Examples that relate to the Chapter Problem are now highlighted with this icon CP to show how different statistical concepts and procedures can be applied to the real-world issue highlighted in the chapter. Organization Changes New Technology: The previous edition of Elementary Statistics introduced the resampling method of bootstrapping in Section 7-4. This 14th edition of Elementary Statistics includes these methods of resampling using bootstrapping and randomization: Bootstrap One Proportion Bootstrap Two Proportions Bootstrap One Mean Bootstrap Two Means Bootstrap Matched Pairs ------------------------------------------- Randomization One Proportion Randomization Two Proportions Randomization One Mean Randomization Two Means Randomization Matched Pairs Randomization Correlation New Section 4-5: Simulations for Hypothesis Tests New Resampling Methods: Resampling methods are new to Sections 8-2, 8-3, 8-4, 8-5, 9-5, and 10-1. New Section 8-5: Resampling: Using Technology for Hypothesis Testing New Section 9-5: Resampling: Using Technology for Inferences New Subsection 10-1, Part 3: Randomization Test for Correlation New Chapter 15: Holistic Statistics
Preface xv Removed Section: The content of Section 6-6 (Normal as Approximation to Binomial) has been removed from the text and is now available for download (www.TriolaStats.com, pearson.com/math-stats-resources, or MyMathLab for School). Removed Section: Ethics in Statistics has been moved from Chapter 15 to Section 1-4, and is available for download (www.TriolaStats.com, pearson.com/math-stats- resources, or MyMathLab for School). Technology Changes New to Statdisk: The previous version of Statdisk for Elementary Statistics included bootstrap resampling, but the new version of Statdisk for the 14th edition also includes all of the bootstrapping and randomization methods listed above under “New Technology.” Statdisk Online: Statdisk is now a browser-based program that can be used on any device with a modern web browser, including laptops (Windows, macOS), Chromebooks, tablets and smartphones. Statdisk Online includes all of the statistical functions from earlier versions of Statdisk and is continually adding new functions and features. New Technology: Where it is appropriate, the end-of-section Tech Centers include R and Google Sheets™ as an additional technology. (The technologies of Statdisk, Excel, StatCrunch, Minitab, and TI-83>84 Plus calculators continue to be included in the Tech Centers.) Flexible Syllabus This book’s organization reflects the preferences of most statistics instructors, but there are two common variations: ■ Early Coverage of Correlation and Regression: Some instructors prefer to cover the basics of correlation and regression early in the course. Section 2-4 includes basic concepts of scatterplots, correlation, and regression without the use of formulas and greater depth found in Sections 10-1 (Correlation) and 10-2 (Regression). ■ Minimum Probability: Some instructors prefer extensive coverage of probability, while others prefer to include only basic concepts. Instructors preferring minimum coverage can include Section 4-1 while skipping the remaining sections of Chapter 4, as they are not essential for the chapters that follow. Many instructors prefer to cover the fundamentals of probability along with the basics of the addition rule and multiplication rule (Section 4-2). GAISE This book reflects recommendations from the American Statistical Association and its Guidelines for Assessment and Instruction in Statistics Education (GAISE). Those guidelines suggest the following objectives and strategies. 1. Emphasize statistical literacy and develop statistical thinking: Each section exercise set begins with Statistical Literacy and Critical Thinking exercises. Many of the book’s exercises are designed to encourage statistical thinking rather than the blind use of mechanical procedures. 2. Use real data: 94% of the examples and 93% of the exercises use real data. 3. Stress conceptual understanding rather than mere knowledge of procedures: Instead of seeking simple numerical answers, most exercises and examples involve conceptual understanding through questions that encourage practical interpretations of results. Also, each chapter includes a From Data to Decision project. 4. Foster active learning in the classroom: Each chapter ends with several Cooperative Group Activities.
xvi Preface 5. Use technology for developing conceptual understanding and analyzing data: Computer software displays are included throughout the book. Special Tech Center subsections include instruction for using the software. Each chapter includes a Technology Project. When there are discrepancies between answers based on tables and answers based on technology, Appendix D provides both answers. The website www.TriolaStats.com includes free text-specific software (Statdisk), data sets formatted for several different technologies, and instructional videos for technologies. MyMathLab for School also includes support videos for different statistical software applications. 6. Use assessments to improve and evaluate student learning: Assessment tools include an abundance of section exercises, Chapter Quick Quizzes, Chapter Review Exercises, Cumulative Review Exercises, Technology Projects, Big (or Very Large) Data Projects, From Data to Decision projects, and Cooperative Group Activities. Acknowledgments I would like to thank the thousands of statistics professors and students who have contributed to the success of this book. I thank the reviewers for their suggestions for this fourteenth edition: Mary Kay Abbey, Vance Granville Community College; Kristin Cook, College of Western Idaho; Celia Cruz, Lehman College of CUNY; Don Davis, Lakeland Community College; Jean Ellefson, Alfred University; Matthew Harris, Ozarks Tech Community College; Stephen Krizan, Sait Polytechnic; Adam Littig, Los Angeles Valley College; Dr. Rick Silvey, University of Saint Mary – Leavenworth; Sasha Verkhovtseva, Anoka Ramsey Community College; William Wade, Seminole Community College. Special thanks to Laura Iossi of Broward College for her comprehensive work in reviewing and contributing to this edition and the 13th. Other recent reviewers have included Raid W. Amin, University of West Florida; Robert Black, United States Air Force Academy; James Bryan, Merced College; Donald Burd, Monroe College; Keith Carroll, Benedictine University; Monte Cheney, Central Oregon Community College; Christopher Donnelly, Macomb Community College; Billy Edwards, University of Tennessee—Chattanooga; Marcos Enriquez, Moorpark College; Angela Everett, Chattanooga State Technical Community College; Joe Franko, Mount San Antonio College; Rob Fusco, Broward College; Sanford Geraci, Broward College; Eric Gorenstein, Bunker Hill Community College; Rhonda Hatcher, Texas Christian University; Laura Heath, Palm Beach State College; Richard Herbst, Montgomery County Community College; Richard Hertz; Diane Hollister, Reading Area Community College; Michael Huber, George Jahn, Palm Beach State College; Gary King, Ozarks Technical Community College; Kate Kozak, Coconino Community College; Dan Kumpf, Ventura College; Ladorian Latin, Franklin University; Mickey Levendusky, Pima County Community College; Mitch Levy, Broward College; Tristan Londre, Blue River Community College; Alma Lopez, South Plains College; Kim McHale, Heartland Community College; Carla Monticelli, Camden County Community College; Ken Mulzet, Florida State College at Jacksonville; Julia Norton, California State University Hayward; Michael Oriolo, Herkimer Community College; Jeanne Osborne, Middlesex Community College; Joseph Pick, Palm Beach State College; Ali Saadat, University of California—Riverside; Radha Sankaran, Passaic County Community College; Steve Schwager, Cornell University; Pradipta Seal, Boston University; Kelly Smitch, Brevard College; Sandra Spain, Thomas Nelson Community College; Ellen G. Stutes, Louisiana State University, Eunice; Sharon Testone, Onondaga Community College; Chris Vertullo, Marist College; Dave Wallach, University of Findlay; Cheng Wang, Nova Southeastern University; Barbara Ward,
Preface xvii Belmont University; Richard Weil, Brown College; Lisa Whitaker, Keiser University; Gail Wiltse, St. John River Community College; Claire Wladis, Borough of Manhattan Community College; Rick Woodmansee, Sacramento City College; Yong Zeng, University of Missouri at Kansas City; Jim Zimmer, Chattanooga State Technical Community College; Cathleen Zucco-Teveloff, Rowan University; Mark Z. Zuiker, Minnesota State University, Mankato. This fourteenth edition of Elementary Statistics is truly a team effort, and I consider myself fortunate to work with the dedication and commitment of the Pearson team. I thank Suzy Bainbridge, Amanda Brands, Deirdre Lynch, Peggy McMahon, Vicki Dreyfus, Jean Choe, Robert Carroll, Joe Vetere, and Rose Kernan of RPK Editorial Services. I extend special thanks to Marc Triola, M.D., New York University School of Medicine, for his outstanding work on creating the new 14th edition of the Statdisk software. I thank Scott Triola for his very extensive help throughout the entire production process for this 14th edition. I thank the following for their help in checking the accuracy of text and answers in this 14th edition: James Lapp, Paul Lorczak, and Dirk Tempelaar. M.F.T. Madison, Connecticut September 2020
MyMathLab for School is available to accompany Pearson’s market-leading text options, including Elementary Statistics, 14e by Mario F. Triola (access code required). MyLab™ is the teaching and learning platform that empowers you to reach every student. MyMathLab for School combines trusted author content—including full eText and assessment with immediate feedback—with digital tools and a flexible platform to personalize the learning experience and improve results for each student. Integrated with StatCrunch®, Pearson’s web-based statistical software program, students learn the skills they need to interact with data in the real world. Real-World Data Examples - Help students understand how statistics applies to everyday life through the extensive current, real-world data examples and exercises provided throughout the text. Expanded objective-based exercise coverage - Exercises in MyMathLab for School are designed to reinforce and support students’ understanding of key statistical topics. Enhanced video program to meet Introductory Statistics needs: • New! Animated Flow Charts - Animated flow charts have been updated with a modern, interactive interface with assignable auto-graded assessment questions in MyMathLab for School. • New! Tech-Specific Video Tutorials - These short, topical videos show how to use common statistical software to complete exercises. • Updated! Chapter Review Exercise Videos - Watch the Chapter Review Exercises come to life with new review videos that help students understand key chapter concepts. Resources for Success mymathlabforschool.com xviii
Supplements Student Resources Each student learns at a different pace. Personalized learning pinpoints the precise areas where each student needs practice, giving all students the support they need — when and where they need it — to be successful. Student’s Solutions Manual, by James Lapp (Colorado Mesa University), provides detailed, worked-out solutions to all odd-numbered text exercises. Available for download in MyMathLab for School. Student Workbook for the Triola Statistics Series, by Laura Iossi (Broward College) offers additional examples, concept exercises, and vocabulary exercises for each chapter. Available for download in MyMathLab for School. Can also be purchased separately. The following technology manuals include instructions, examples from the main text, and interpretations to complement those given in the text. They are all available for download in MyMathLab for School. Excel Student Laboratory Manual and Workbook, (Download Only) by Laurel Chiappetta (University of Pittsburgh). MINITAB Student Laboratory Manual and Workbook, (Download Only) by Mario F. Triola. Graphing Calculator Manual for the TI-83 Plus, TI-84 Plus, TI-84 Plus C and TI-84 Plus CE, (Download Only) by Kathleen McLaughlin (University of Connecticut) & Dorothy Wakefield (University of Connecticut Health Center). Statdisk Student Laboratory Manual and Workbook (Download Only), by Mario F. Triola. Instructor Resources Your course is unique. So whether you’d like to build your own assignments, teach multiple sections, or set prerequisites, MyMathLab for School gives you the flexibility to easily create your course to fit your needs. Annotated Instructor’s Edition, by Mario F. Triola, contains answers to exercises in the margin, plus recommended assignments, and teaching suggestions. (ISBN-13: 9780136803065; ISBN-10: 0136803067) Instructor’s Solutions Manual (Download Only), by James Lapp (Colorado Mesa University), contains solutions to all the exercises. These files are available to qualified instructors through Pearson Education’s online catalog at www.pearsonhighered.com/irc or within MyMathLab for School. Insider’s Guide to Teaching with the Triola Statistics Series, (Download Only) by Mario F. Triola, contains sample syllabi and tips for incorporating projects, as well as lesson overviews, extra examples, minimum outcome objectives, and recommended assignments for each chapter. TestGen® Computerized Test Bank (www.pearsoned. com/testgen), enables instructors to build, edit, print, and administer tests using a computerized bank of questions developed to cover all the objectives of the text. TestGen is algorithmically based, allowing instructors to create multiple but equivalent versions of the same question or test with the click of a button. Instructors can also modify test bank questions or add new questions. The software and testbank are available for download from Pearson Education’s online catalog at www.pearsonhighered.com. Test Forms (Download Only) are also available from the online catalog. PowerPoint® Lecture Slides: Free to qualified adopters, this classroom lecture presentation software is geared specifically to the sequence and philosophy of Elementary Statistics. Key graphics from the book are included to help bring the statistical concepts alive in the classroom. These files are available to qualified instructors through Pearson Education’s online catalog at www.pearsonhighered.com/irc or within MyMathLab for School. Accessibility Accessibility—Pearson works continuously to ensure our products are as accessible as possible to all students. Currently we work toward achieving WCAG 2.0 AA for our existing products (2.1 AA for future products) and Section 508 standards, as expressed in the Pearson Guidelines for Accessible Educational Web Media. Resources for Success mymathlabforschool.com xix
MyLab™ is the teaching and learning platform that empowers you to reach every student. MyMathLab for School combines trusted author content — including full eText and assessment with immediate feedback — with digital tools and a flexible platform to personalize the learning experience and improve results for each student. Integrated with StatCrunch®, Pearson’s web-based statistical software program, students learn the skills they need to interact with data in the real world. Learn more about MyMathLab for School. Preparedness One of the biggest challenges in many mathematics and statistics courses is making sure students are adequately prepared with the prerequisite skills needed to successfully complete their course work. Pearson offers a variety of content and course options to support students with just-in-time remediation and key-concept review. • MyMathLab for School with Integrated Review can be used for just-in-time prerequisite review or co-requisite courses. These courses provide videos on review topics, along with pre-made, assignable skills-check quizzes and personalized review homework assignments. • In recent years many new course models have emerged, as institutions “redesign” to help improve retention and results. At Pearson, we’re focused on creating solutions tailored to support your plans and programs. In addition to the new Integrated Review courses, we offer new All-in-One solutions, non-STEM pathways, and STEM-track options. Used by nearly one million students a year, MyMathLab for School is the world’s leading online program for teaching and learning statistics. mymathlabforschool.com ® Get the Most Out of MyMathLab® for School xx
1 other topics, this survey asked respondents to identify their preferred learning tools, and YouTube was identified as one of the top tools by both Gen-Z and millennials. Figure 1-1 includes a graph that depicts the percentage of Gen-Z and millennials who identified YouTube as a preferred learning tool. Critical Thinking Figure 1-1 on the next page makes it appear that Gen-Z is more than twice as likely to prefer YouTube as a learning tool compared to millennials. A quick glance might also Surveys provide data that enable us to better understand the world in which we live and identify changes in the opinions, habits, and behaviors of others. Survey data guide public policy, influence business and educational practices, and affect many aspects of our daily lives. A recent Pearson survey, conducted by The Harris Poll, examined how technology has shaped students’ learning habits and compared the responses from Gen-Z (ages 14–23) and millennials (ages 24–40). Among 1-1 Statistical and Critical Thinking 1-2 Types of Data 1-3 Collecting Sample Data 1-4 Ethics in Statistics (available at www.TriolaStats.com) Is YouTube Becoming a More Important Learning Tool? CHAPTER PROBLEM INTRODUCTION TO STATISTICS 1
give the impression that most millennials do not prefer YouTube as a learning tool. But wait! Look carefully at Figure 1-1 and see that the vertical axis has a scale that ranges from 52% to 60%. The graph in Figure 1-1 is misleading because it uses the scale of 52% to 60% instead of a scale that begins with 0%. As a result, the difference between the two bars is visually exaggerated in Figure 1-1. In Figure 1-2, the same data are shown in the graph, but we use a scale that begins with 0%. Figure 1-2 shows that the Gen-Z prefers YouTube as a learning tool only slightly more than millennials (actually 4% more to be exact). Figure 1-1 is misleading, whereas Figure 1-2 depicts the data fairly. We might now consider how these survey data can be used to improve the learning experience for Elementary Statistics! Figure 1-2 shows that the majority of both Gen-Z and millennials prefer YouTube as a learning tool and this percentage has increased from one generation to the next. Knowing that YouTube and other videos are increasingly preferred learning tools, the author has created a YouTube channel with custom instructional videos to support this textbook (visit www.TriolaStats.com for the link). In addition, MyLab includes additional instructional videos and interactive content to support students. The flaw shown in Figure 1-1 is among the most commonly used tactics to present misleading arguments, so it is especially important to recognize. Here are brief descriptions of common flaws: Flaw 1: Misleading Graphs The bar chart in Figure 1-1 is very deceptive. By using a vertical scale that does not start at zero, the difference between the two percentages is grossly exaggerated. Deceptive graphs are discussed in more detail in Section 2-3. Flaw 2: Bad Sampling Method Figure 1-1 and Figure 1-2 are based on data from the Pearson survey cited earlier. This study included 2587 respondents from a nationally representative sample, and the sampling method appears to be sound based on the description provided in the report. However, many other surveys obtain participants by using methods that are inappropriate and may lead to biased results, such as these: • Voluntary response sample: Participants decide themselves whether to participate. Example: A survey question is posted on a website, and then Internet users decide whether to respond. With a voluntary response sample, it often happens that those with a strong interest in the topic are more likely to participate, so the results are very questionable. • Convenience sample: Participants are selected because they are easy to reach and are readily available. Example: A student conducts a survey of fellow students relaxing in the cafeteria. When using sample data to learn something about a population, it is extremely important to obtain sample data that are representative of the population from which the data are drawn. As we proceed through this chapter and discuss types of data and sampling methods, we should focus on these key concepts: • Sample data must be collected in an appropriate way, such as through a process of random selection. • If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical torturing can salvage them. It is all too easy to analyze sample data without thinking critically about how the data were collected. We could then develop conclusions that are fundamentally wrong and misleading. Instead, we should develop skills in statistical thinking and critical thinking so that we can distinguish between collections of sample data that are good and those that are seriously flawed. FIGURE 1-1 YouTube as a Preferred Learning Tool FIGURE 1-2 Same as Figure 1-1 but with scale beginning with 0% 2 CHAPTER 1 Introduction to Statistics
1-1 Statistical and Critical Thinking 3 Here is the single most important concept presented in this chapter: When using methods of statistics with sample data to form conclusions about a population, it is absolutely essential to collect sample data in a way that is appropriate. Here are the chapter objectives: 1-1 Statistical and Critical Thinking • Analyze sample data relative to context, source, and sampling method. • Understand the difference between statistical significance and practical significance. • Define and identify a voluntary response sample and know that statistical conclusions based on data from such a sample are generally not valid. 1-2 Types of Data • Distinguish between a parameter and a statistic. • Distinguish between quantitative data and categorical (or qualitative or attribute) data. • Distinguish between discrete data and continuous data. • Determine whether basic statistical calculations are appropriate for a particular data set. 1-3 Collecting Sample Data • Define and identify a simple random sample. • Understand the importance of sound sampling methods and the importance of good design of experiments. 1-4 Ethics in Statistics (available at www.TriolaStats.com) • Analyze ethical issues in statistics, including those related to data collection, analysis, and reporting. CHAPTER OBJECTIVES Key Concept In this section we begin with a few very basic definitions, and then we consider an overview of the process involved in conducting a statistical study. This process consists of “prepare, analyze, and conclude.” “Preparation” involves consideration of the context, the source of data, and sampling method. In future chapters we construct suitable graphs, explore the data, and execute computations required for the statistical method being used. In future chapters we also form conclusions by determining whether results have statistical significance and practical significance. Statistical thinking involves critical thinking and the ability to make sense of results. Statistical thinking demands so much more than the ability to execute complicated calculations. Through numerous examples, exercises, and discussions, this text will help you develop the statistical thinking skills that are so important in today’s world. 1-1 Statistical and Critical Thinking
4 CHAPTER 1 Introduction to Statistics DEFINITIONS Data are collections of observations, such as measurements, genders, or survey responses. (A single data value is called a datum, a term rarely used. The term “data” is plural, so it is correct to say “data are . . .” not “data is . . .”) Statistics is the science of planning studies and experiments; obtaining data; and organizing, summarizing, presenting, analyzing, and interpreting those data and then drawing conclusions based on them. A population is the complete collection of all measurements or data that are being considered. A census is the collection of data from every member of the population. A sample is a subcollection of members selected from a population. Because populations are often very large, a common objective of the use of statistics is to obtain data from a sample and then use those data to form a conclusion about the population. We begin with some very basic definitions. Watch What You Post Online EXAMPLE 1 In a survey of 410 human resource professionals, 148 of them said that job candidates were disqualified because of information found on social media postings (based on data from The Society for Human Resource Management). In this case, the population and sample are as follows: Population: All human resource professionals Sample: The 410 human resource professionals who were surveyed The objective is to use the sample as a basis for drawing a conclusion about the population of all human resource professionals, and methods of statistics are helpful in drawing such conclusions. YOUR TURN. Do part (a) of Exercise 2 “Reported Versus Measured.” We now proceed to consider the process involved in a statistical study. See Figure 1-3 for a summary of this process and note that the focus is on critical thinking, not mathematical calculations. Thanks to wonderful developments in technology, we have powerful tools that effectively do the number crunching so that we can focus on understanding and interpreting results. Prepare Context Figure 1-3 suggests that we begin our preparation by considering the context of the data, so let’s start with context by considering the data in Table 1-1. Table 1-1 includes shoe print lengths and heights of eight males. Forensic scientists measure shoe print lengths at burglary scenes and other crime scenes in order to estimate the height of the criminal. The format of Table 1-1 suggests the following goal: Determine whether there is a relationship between shoe print lengths P C te T Go Figure 78%: The percentage of female veterinarian students who are women, according to The Herald in Glasgow, Scotland. Importance of Accurate Census Results The United States Constitution requires a census every ten years. Some factors affected by census results: Apportionment of congressional seats; distribution of billions of dollars of federal funds to states for transportation, schools, and hospitals; locations of sites for businesses and stores. Although accuracy of census results is extremely important, it is becoming more difficult to collect accurate census data due to the growing diversity of cultures and languages and increased distrust of the government. No amount of statistical analysis can salvage poor data, so it is critical that the census data is collected in an appropriate manner. T S t c t f b
1-1 Statistical and Critical Thinking 5 TABLE 1-1 Shoe Print Lengths and Heights of Men Shoe Print (cm) 27.6 29.7 29.7 31.0 31.3 31.4 31.8 34.5 Height (cm) 172.7 175.3 177.8 175.3 180.3 182.3 177.8 193.7 Source of the Data The second step in our preparation is to consider the source (as indicated in Figure 1-3). The data in Table 1-1 are from Data Set 9 “Foot and Height” in Appendix B, where the source is identified. The source certainly appears to be reputable. Conclude 1. Significance • Do the results have statistical significance? • Do the results have practical significance? Analyze 1. Graph the Data 2. Explore the Data • Are there any outliers (numbers very far away from almost all of the other data)? • What important statistics summarize the data (such as the mean and standard deviation described in Chapter 3)? • How are the data distributed? • Are there missing data? • Did many selected subjects refuse to respond? 3. Apply Statistical Methods • Use technology to obtain results. Prepare 1. Context • What do the data represent? • What is the goal of study? 2. Source of the Data • Are the data from a source with a special interest so that there is pressure to obtain results that are favorable to the source? 3. Sampling Method • Were the data collected in a way that is unbiased, or were the data collected in a way that is biased (such as a procedure in which respondents volunteer to participate)? FIGURE 1-3 Statistical and Critical Thinking Survivorship Bias In World War II, statistician Abraham Wald saved many lives with his work on the Applied Mathematics Panel. Military leaders asked the panel how they could improve the chances of aircraft bombers returning after missions. They wanted to add some armor for protection, and they recorded locations on the bombers where damaging holes were found. They reasoned that armor should be placed in locations with the most holes, but Wald said that strategy would be a big mistake. He said that armor should be placed where returning bombers were not damaged. His reasoning was this: The bombers that made it back with damage were survivors, so the damage they suffered could be survived. Locations on the aircraft that were not damaged were the most vulnerable, and aircraft suffering damage in those vulnerable areas were the ones that did not make it back. The military leaders would have made a big mistake with survivorship bias by studying the planes that survived instead of thinking about the planes that did not survive. Sampling Method Figure 1-3 suggests that we conclude our preparation by considering the sampling method. For the data in Table 1-1, individuals were randomly selected, so the sampling method appears to be sound. Sampling methods and the use of random selection will be discussed in Section 1-3, but for now, we stress that a sound sampling method is absolutely essential for good results in a statistical study. It is generally a bad practice to use voluntary response (or self-selected) samples, even though their use is common. and heights of males. This goal suggests a reasonable hypothesis: Males with larger shoe print lengths tend to be taller. (We are using data for males only because 84% of burglaries are committed by males.)
6 CHAPTER 1 Introduction to Statistics The following types of polls are common examples of voluntary response samples. By their very nature, all are seriously flawed because we should not make conclusions about a population on the basis of samples with a strong possibility of bias. ■ Internet polls, in which people online decide whether to respond ■ Mail-in polls, in which people decide whether to reply ■ Telephone call-in polls, in which newspaper, radio, or television announcements ask that you voluntarily call a special number to register your opinion See the following Example 2. DEFINITION A voluntary response sample (or self-selected sample) is one in which the respondents themselves decide whether to be included. Voluntary Response Sample EXAMPLE 2 The ABC television show Nightline asked viewers to call with their opinion about whether the United Nations headquarters should remain in the United States. Viewers then decided themselves whether to call with their opinions, and 67% of 186,000 respondents said that the United Nations should be moved out of the United States. In a separate and independent survey, 500 respondents were randomly selected and surveyed, and 38% of this group wanted the United Nations to move out of the United States. The two polls produced dramatically different results. Even though the Nightline poll involved 186,000 volunteer respondents, the much smaller poll of 500 randomly selected respondents is more likely to provide better results because of the far superior sampling method. YOUR TURN. Do Exercise 1 “Computer Virus.” Analyze Figure 1-3 indicates that after completing our preparation by considering the context, source, and sampling method, we begin to analyze the data. Graph and Explore An analysis should begin with appropriate graphs and explorations of the data. Graphs are discussed in Chapter 2, and important statistics are discussed in Chapter 3. Apply Statistical Methods Later chapters describe important statistical methods, but application of these methods is often made easy with technology (calculators and>or statistical software packages). A good statistical analysis does not require strong computational skills. A good statistical analysis does require using common sense and paying careful attention to sound statistical methods. Conclude Figure 1-3 shows that the final step in our statistical process involves conclusions, and we should develop an ability to distinguish between statistical significance and practical significance. Go Figure 17%: The percentage of U.S. men between 20 and 40 years of age and taller than 7 feet who play basketball in the NBA. si Origin of “Statistics” The word statistics is derived from the Latin word status (meaning “state”). Early uses of statistics involved compilations of data and graphs describing various aspects of a state or country. In 1662, John Graunt published statistical information about births and deaths. Graunt’s work was followed by studies of mortality and disease rates, population sizes, incomes, and unemployment rates. Households, governments, and businesses rely heavily on statistical data for guidance. For example, unemployment rates, inflation rates, consumer indexes, and birth and death rates are carefully compiled on a regular basis, and the resulting data are used by business leaders to make decisions affecting future hiring, production levels, and expansion into new markets.
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