Elementary Statistics PICTURING THE WORLD Ron Larson The Pennsylvania State University The Behrend College EIGHTH EDITION
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CONTENTS v Introduction to Statistics Where You’ve Been Where You’re Going 1 1.1 An Overview of Statistics 2 1.2 Data Classification 9 Case Study: Reputations of Companies in the U.S. 16 1.3 Data Collection and Experimental Design 17 Activity: Random Numbers 27 Uses and Abuses: Statistics in the Real World 28 Chapter Summary 29 Review Exercises 30 Chapter Quiz 32 Chapter Test 33 Real Statistics—Real Decisions: Putting it all together 34 History of Statistics—Timeline 35 Technology: UsingTechnology in Statistics 36 Descriptive Statistics 38 Where You’ve Been Where You’re Going 39 2.1 Frequency Distributions and Their Graphs 40 2.2 More Graphs and Displays 55 2.3 Measures of Central Tendency 67 Activity: Mean Versus Median 81 2.4 Measures of Variation 82 Activity: Standard Deviation 100 Case Study: Business Size 101 2.5 Measures of Position 102 Uses and Abuses: Statistics in the Real World 114 Chapter Summary 115 Review Exercises 116 Chapter Quiz 120 Chapter Test 121 Real Statistics—Real Decisions: Putting it all together 122 Technology: Parking Tickets 123 UsingTechnology to Determine Descriptive Statistics 124 Cumulative Review: Chapters 1 & 2 126 1 2 PART 1 DESCRIPTIVE STATISTICS CONTENTS Preface xi Acknowledgments xv Index of Applications xvi
Probability 128 Where You’ve Been Where You’re Going 129 3.1 Basic Concepts of Probability and Counting 130 Activity: Simulating the Stock Market 146 3.2 Conditional Probability and the Multiplication Rule 147 3.3 The Addition Rule 157 Activity: Simulating the Probability of Rolling a 3 or 4 166 Case Study: United States Congress 167 3.4 Additional Topics in Probability and Counting 168 Uses and Abuses: Statistics in the Real World 178 Chapter Summary 179 Review Exercises 180 Chapter Quiz 184 Chapter Test 185 Real Statistics—Real Decisions: Putting it all together 186 Technology: Simulation: Composing Mozart Variations with Dice 187 Discrete Probability Distributions 188 Where You’ve Been Where You’re Going 189 4.1 Probability Distributions 190 4.2 Binomial Distributions 201 Activity: Binomial Distribution 214 Case Study: Distribution of Number of Hits in Baseball Games 215 4.3 More Discrete Probability Distributions 216 Uses and Abuses: Statistics in the Real World 223 Chapter Summary 224 Review Exercises 225 Chapter Quiz 228 Chapter Test 229 Real Statistics—Real Decisions: Putting it all together 230 Technology: Using Poisson Distributions as Queuing Models 231 3 4 PART 2 PROBABILITY AND PROBABILITY DISTRIBUTIONS vi CONTENTS
CONTENTS vii Normal Probability Distributions 232 Where You’ve Been Where You’re Going 233 5.1 Introduction to Normal Distributions and the Standard Normal Distribution 234 5.2 Normal Distributions: Finding Probabilities 246 5.3 Normal Distributions: Finding Values 252 Case Study: Birth Weights in America 260 5.4 Sampling Distributions and the Central Limit Theorem 261 Activity: Sampling Distributions 274 5.5 Normal Approximations to Binomial Distributions 275 Uses and Abuses: Statistics in the Real World 284 Chapter Summary 285 Review Exercises 286 Chapter Quiz 290 Chapter Test 291 Real Statistics—Real Decisions: Putting it all together 292 Technology: Age Distribution in California 293 Cumulative Review: Chapters 3–5 294 5 PART 3 STATISTICAL INFERENCE Confidence Intervals 296 Where You’ve Been Where You’re Going 297 6.1 Confidence Intervals for the Mean (S Known) 298 6.2 Confidence Intervals for the Mean (S Unknown) 310 Activity: Confidence Intervals for a Mean 318 Case Study: Marathon Training 319 6.3 Confidence Intervals for Population Proportions 320 Activity: Confidence Intervals for a Proportion 329 6.4 Confidence Intervals for Variance and Standard Deviation 330 Uses and Abuses: Statistics in the Real World 336 Chapter Summary 337 Review Exercises 338 Chapter Quiz 340 Chapter Test 341 Real Statistics—Real Decisions: Putting it all together 342 Technology: United States Foreign Policy Polls 343 UsingTechnology to Construct Confidence Intervals 344 6
viii CONTENTS Hypothesis Testing with One Sample 346 Where You’ve Been Where You’re Going 347 7.1 Introduction to Hypothesis Testing 348 7.2 Hypothesis Testing for the Mean (S Known) 363 7.3 Hypothesis Testing for the Mean (S Unknown) 377 Activity: HypothesisTests for a Mean 386 Case Study: Human BodyTemperature: What's Normal? 387 7.4 Hypothesis Testing for Proportions 388 Activity: HypothesisTests for a Proportion 393 7.5 Hypothesis Testing for Variance and Standard Deviation 394 A Summary of HypothesisTesting 402 Uses and Abuses: Statistics in the Real World 404 Chapter Summary 405 Review Exercises 406 Chapter Quiz 410 Chapter Test 411 Real Statistics—Real Decisions: Putting it all together 412 Technology: The Case of the Vanishing Women 413 UsingTechnology to Perform HypothesisTests 414 Hypothesis Testing with Two Samples 416 Where You’ve Been Where You’re Going 417 8.1 Testing the Difference Between Means (Independent Samples, S1 and S2 Known) 418 8.2 Testing the Difference Between Means (Independent Samples, S1 and S2 Unknown) 428 Case Study: How Protein Affects Weight Gain in Overeaters 436 8.3 Testing the Difference Between Means (Dependent Samples) 437 8.4 Testing the Difference Between Proportions 447 Uses and Abuses: Statistics in the Real World 454 Chapter Summary 455 Review Exercises 456 Chapter Quiz 460 Chapter Test 461 Real Statistics—Real Decisions: Putting it all together 462 Technology: Tails over Heads 463 UsingTechnology to PerformTwo-Sample HypothesisTests 464 Cumulative Review: Chapters 6–8 466 7 8
CONTENTS ix Correlation and Regression 468 Where You’ve Been Where You’re Going 469 9.1 Correlation 470 Activity: Correlation by Eye 485 9.2 Linear Regression 486 Activity: Regression by Eye 496 Case Study: Correlation of Body Measurements 497 9.3 Measures of Regression and Prediction Intervals 498 9.4 Multiple Regression 509 Uses and Abuses: Statistics in the Real World 514 Chapter Summary 515 Review Exercises 516 Chapter Quiz 520 Chapter Test 521 Real Statistics—Real Decisions: Putting it all together 522 Technology: Nutrients in Breakfast Cereals 523 Chi-Square Tests and the F-Distribution 524 Where You’ve Been Where You’re Going 525 10.1 Goodness-of-Fit Test 526 10.2 Independence 536 Case Study: Food Safety Survey 548 10.3 Comparing Two Variances 549 10.4 Analysis of Variance 558 Uses and Abuses: Statistics in the Real World 570 Chapter Summary 571 Review Exercises 572 Chapter Quiz 576 Chapter Test 577 Real Statistics—Real Decisions: Putting it all together 578 Technology: Teacher Salaries 579 Cumulative Review: Chapters 9 & 10 580 9 10 PART 4 MORE STATISTICAL INFERENCE
Nonparametric Tests (Online Only)* Where You’ve Been Where You’re Going 11.1 The Sign Test 11.2 The Wilcoxon Tests Case Study: College Ranks 11.3 The Kruskal-Wallis Test 11.4 Rank Correlation 11.5 The Runs Test Uses and Abuses: Statistics in the Real World Chapter Summary Review Exercises Chapter Quiz Chapter Test Real Statistics—Real Decisions: Putting it all together Technology: U.S. Income and Economic Research * Available in MyMathLab for School Appendices APPENDIX A Alternative Presentation of the Standard Normal Distribution A1 Standard Normal DistributionTable (0-to-z) A1 Alternative Presentation of the Standard Normal Distribution A2 APPENDIX B Tables A7 Table 1 Random Numbers A7 Table 2 Binomial Distribution A8 Table 3 Poisson Distribution A11 Table 4 Standard Normal Distribution A16 Table 5 t-Distribution A18 Table 6 Chi-Square Distribution A19 Table 7 F-Distribution A20 Table 8 Critical Values for the SignTest A25 Table 9 Critical Values for the Wilcoxon Signed-RankTest A25 Table 10 Critical Values for the Spearman Rank Correlation Coefficient A26 Table 11 Critical Values for the Pearson Correlation Coefficient A26 Table 12 Critical Values for the Number of Runs A27 APPENDIX C Normal Probability Plots A28 APPENDIX D Key Formulas A31 Answers to the Try It Yourself Exercises A35 Answers to the Odd-Numbered Exercises A44 Index I1 Credits P1 11 x CONTENTS
PREFACE xi Welcome to Elementary Statistics: Picturing the World, Eighth Edition. You will find that this textbook is written with a balance of rigor and simplicity. It combines step-by-step instructions, real-life examples and exercises, carefully developed features, and technology that makes statistics accessible to all. I am grateful for the overwhelming acceptance of the first seven editions. It is gratifying to know that my vision of combining theory, pedagogy, and design to exemplify how statistics is used to picture and describe the world has helped students learn about statistics and make informed decisions. What’s New in This Edition The goal of the Eighth Edition was a thorough update of the key features, examples, and exercises: Examples This edition has 213 examples, nearly 50% of which are new or revised. Also, several of the examples now show an alternate solution or a check using technology. Try It Yourself Over 40% of the 213 Try It Yourself exercises are new or revised. Picturing the World Over 70% of these are new or revised. Screen Displays In the examples, technology tips, and other features that show screen displays from Minitab®, Excel®, the TI-84 Plus, and StatCrunch®, the displays were revised as appropriate to make them more visually appealing, easy to follow, and reflective of the most up-to-date version of the software. Exercises Over 30% of the more than 2300 exercises are new or revised. Extensive Chapter Feature Updates A full 50% of the following key features are new or revised, making this edition fresh and relevant to today’s students: • Where You’ve Been and Where You’re Going • Uses and Abuses: Statistics in the Real World • Real Statistics—Real Decisions: Putting it all together • Chapter Technology Project References to Co-Requisite Help Margin notes have been included at point-of-use locations throughout this edition to remind students that they can get help reviewing a particular area of mathematics in the Integrated Review in MyMathLab for School. Applet Activities Revisions have been made to the applet activities throughout the text to reflect changes to the corresponding online applets they reference. Applet activities are discussed further on the next page. Study Strategies At the bottom of each chapter summary page in Chapters 1 through 10, there are study strategies that students can use to help improve their performance in college. These include tips on improving reading skills, avoiding procrastination, preparing for a test, taking notes, and other areas. Features of the Eighth Edition Guiding Student Learning Where You’ve Been and Where You’re Going Each chapter begins with a two-page visual description of a real-life problem. Where You’ve Been connects the chapter to topics learned in earlier chapters. Where You’re Going gives students an overview of the chapter. What You Should Learn Each section is organized by learning objectives, presented in everyday language in What You Should Learn. The same objectives are then used as subsection titles throughout the section. Definitions and Formulas are clearly presented in easy-to-locate boxes. They are often followed by Guidelines, which explain In Words and In Symbols how to apply the formula or understand the definition. Margin Features help reinforce understanding: • Study Tips show how to read a table, interpret a result, help drive home an important interpretation, or connect different concepts. • Tech Tips show how to use Minitab, Excel, the TI-84 Plus, or StatCrunch to solve a problem. • References to Co-Requisite Help point students to extra math help. • Picturing the World is a “mini case study” in each section that illustrates the important concept or concepts of the section. Each Picturing the World concludes with a question and can be used for general class discussion or group work. The answers to these questions are included in the Annotated Instructor’s Edition. Examples and Exercises Examples Every concept in the text is clearly illustrated with one or more step-by-step examples. Most examples have an interpretation step that shows the student how the solution may be interpreted within the real-life context of the example and promotes critical thinking and writing skills. Each example, which is numbered and titled for easy reference, is followed by a similar exercise called Try It Yourself so students can immediately practice the skill learned. The answers to these exercises are in the back of the book and the worked-out solutions are available in MyMathLab for School in the Student Solutions Manual. Technology Examples Many sections contain an example that shows how technology can be used to calculate formulas, perform tests, or display data. Screen displays from Minitab, Excel, the TI-84 Plus, and StatCrunch are shown. Additional screen displays are presented at the ends of selected chapters, and detailed instructions are given in separate technology manuals available with the book. Exercises The exercises give students practice in performing calculations, making decisions, providing explanations, and applying results to a real-life setting. The section exercises are divided into three parts:
xii • Building Basic Skills and Vocabulary are short-answer, true-or-false, and vocabulary exercises carefully written to nurture student understanding. • Using and Interpreting Concepts are skill or word problems that move from basic skill development to more challenging and interpretive problems. • Extending Concepts go beyond the material presented in the section. They tend to be more challenging and are not required as prerequisites for subsequent sections. Technology Answers Answers in the back of the book are found using calculations by hand and by tables. Answers found using technology (usually the TI-84 Plus) are also included when there are discrepancies due to rounding. Review and Assessment Chapter Summary Each chapter concludes with a Chapter Summary that answers the question What did you learn? The objectives listed are correlated to Examples in the section as well as to the Review Exercises. Chapter Review Exercises A set of Review Exercises follows each Chapter Summary. The order of the exercises follows the chapter organization. Answers to all odd-numbered exercises are given in the back of the book. Chapter Quizzes Each chapter has a Chapter Quiz. The answers to all quiz questions are provided in the back of the book. For additional help, see the step-by-step video solutions available in MyMathLab for School. Chapter Tests Each chapter has a Chapter Test. The questions are in random order. The answers to all test questions are provided in the Annotated Instructor’s Edition. Cumulative Review There is a Cumulative Review after Chapters 2, 5, 8, and 10. Exercises in the Cumulative Review are in random order and may incorporate multiple ideas. Answers to all odd-numbered exercises are given in the back of the book. Statistics in the Real World Uses and Abuses: Statistics in the Real World Each chapter discusses how statistical techniques should be used, while cautioning students about common abuses. The discussion includes ethics, where appropriate. Exercises help students apply their knowledge. Applet Activities Selected sections contain activities that encourage interactive investigation of concepts in the lesson with exercises that ask students to draw conclusions. The applets are available in MyMathLab for School and at www.pearson.com/math-stats-resources. Chapter Case Study Each chapter has a full-page Case Study featuring actual data from a real-world context and questions that illustrate the important concepts of the chapter. Real Statistics—Real Decisions: Putting it all together This feature encourages students to think critically and make informed decisions about real-world data. Exercises guide students from interpretation to drawing of conclusions. Chapter Technology Project Each chapter has a Technology project using Minitab, Excel, and the TI-84 Plus that gives students insight into how technology is used to handle large data sets or real-life questions. Continued Strong Pedagogy from the Seventh Edition Versatile Course Coverage The table of contents was developed to give instructors many options. For instance, the Extending Concepts exercises, applet activities, Real Statistics— Real Decisions, and Uses and Abuses provide sufficient content for the text to be used in a two-semester course. More commonly, I expect the text to be used in a three-credit semester course or a four-credit semester course that includes a lab component. In such cases, instructors will have to pare down the text’s 46 sections. Graphical Approach As with most introductory statistics texts, this text begins the descriptive statistics chapter (Chapter 2) with a discussion of different ways to display data graphically. A difference between this text and many others is that it continues to incorporate the graphical display of data throughout the text. For example, see the use of stem-and-leaf plots to display data on page 387. This emphasis on graphical displays is beneficial to all students, especially those utilizing visual learning strategies. Balanced Approach The text strikes a balance among computation, decision making, and conceptual understanding. I have provided many Examples, Exercises, and Try It Yourself exercises that go beyond mere computation. Variety of Real-Life Applications I have chosen real-life applications that are representative of the varied experiences of students taking introductory statistics courses. I want statistics to come alive and appear relevant to students so they understand the importance of and rationale for studying statistics. I wanted the applications to be authentic—but they also need to be accessible. See the Index of Applications on page xvi. Data Sets and Source Lines The data sets in the book were chosen for interest, variety, and their ability to illustrate concepts. Most of the 250-plus data sets contain real data with source lines. The remaining data sets contain simulated data that are representative of real-life situations. All data sets containing 20 or more entries are available in a variety of formats in MyMathLab for School or at www.pearson.com/math-stats-resources. In the exercise sets, the data sets that are available electronically are indicated by the icon . Flexible Technology Although most formulas in the book are illustrated with “hand” calculations, I assume that most students have access to some form of technology, such as Minitab, Excel, StatCrunch, or the TI-84 Plus. Because technology varies widely, the text is flexible. It can be used in courses with no more technology than a scientific calculator—or it can be used in courses that require sophisticated technology tools. Whatever your use of technology, I am sure you agree with me that the goal of the course is not computation. Rather, it is to help students gain an understanding of the basic concepts and uses of statistics. Prerequisites Algebraic manipulations are kept to a minimum—often I display informal versions of formulas using words in place of or in addition to variables. Choice of Tables My experience has shown that students find a cumulative distribution function (CDF) table easier to use than a “0-to-z” table. Using the CDF table to find the area under the standard normal curve is a topic of Section 5.1 on
xiii pages 237–241. Because some teachers prefer to use the “0-to-z” table, an alternative presentation of this topic is provided in Appendix A. Page Layout Statistics instruction is more accessible when it is carefully formatted on each page with a consistent open layout. This text is the first college-level statistics book to be written so that, when possible, its features are not split from one page to the next. Although this process requires extra planning, the result is a presentation that is clean and clear. Meeting the Standards MAA, AMATYC, NCTM Standards This text answers the call for a student-friendly text that emphasizes the uses of statistics. My goal is not to produce statisticians but to produce informed consumers of statistical reports. For this reason, I have included exercises that require students to interpret results, provide written explanations, find patterns, and make decisions. GAISE Recommendations Funded by the American Statistical Association, the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Project developed six recommendations for teaching introductory statistics in a college course. These recommendations are: • Emphasize statistical literacy and develop statistical thinking. • Use real data. • Stress conceptual understanding rather than mere knowledge of procedures. • Foster active learning in the classroom. • Use technology for developing conceptual understanding and analyzing data. • Use assessments to improve and evaluate student learning. The examples, exercises, and features in this text embrace all of these recommendations. MyMathLab for School Resources for Success MyMathLab for School is available to accompany Pearson’s market-leading text options, including Elementary Statistics: Picturing The World, 8e (access code required). MyMathLabTM for School 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®, a web-based statistical software program, students learn the skills they need to interact with data in the real world. MyMathLab for School supports all learners, regardless of their ability and background, to provide an equal opportunity for success. Accessible resources support learners for a more equitable experience no matter their abilities. And options to personalize learning and address individual gaps helps to provide each learner with the specific resources they need to achieve success. 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. StatCrunch® is integrated directly into MyMathLab for School. StatCrunch® is a powerful web-based statistical software that allows users to perform complex analyses, share data sets, and generate compelling reports of their data. The vibrant online community offers tens of thousands of shared data sets for students to analyze. • Collect Users can upload their own data to StatCrunch or search a large library of publicly shared data sets, spanning almost any topic of interest. Data sets from the text and from online homework exercises can also be accessed and analyzed in StatCrunch. An online survey tool allows users to quickly collect data via web-based surveys. • Crunch A full range of numerical and graphical methods allows users to analyze and gain insights from any data set. Interactive graphics help users understand statistical concepts, and are available for export to enrich reports with visual representations of data. • Communicate Reporting options help users create a wide variety of visually appealing representations of their data. StatCrunch can be accessed on your laptop, smartphone, or tablet when you visit the StatCrunch website from your device’s browser. For more information, visit the StatCrunch website, or contact your Pearson representative. Exercises with Immediate Feedback The exercises in MyMathLab for School reflect the approach and learning style of this text, and regenerate algorithmically to give student unlimited opportunity for practice and mastery. Most exercises include learning aids, such as guided solutions and sample problems, and they offer helpful feedback when students enter incorrect answers. Personalized Homework With Personalized Homework, students take a quiz or test and receive a subsequent homework assignment that is personalized based on their performance. This way, students can focus on just the topics they have not yet mastered. Integrated Review Elementary Statistics, Picturing the World with Integrated Review can be used in corequisite courses, or simply to help students who enter without a full understanding of prerequisite skills and concepts. MyMathLab for School courses provide the full suite of supporting resources for the Statistics course, plus additional assignments and for study aids from select intermediate algebra topics for students who will benefit from remediation. Assignments for the integrated review content are pre-assigned in MyMathLab for School, making it easier than ever to create your course. Mindset videos and assignable, open-ended exercises foster a growth mindset in students. This material encourages them to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities—so often a hurdle for math students.
Personal Inventory Assessments are a collection of online exercises designed to promote self reflection and metacognition in students. These 33 assessments include topics such as a Stress Management Assessment, Diagnosing Poor Performance and Enhancing Motivation, and Time Management Assessment. 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. MyMathLab for School Features Performance Analytics enable instructors to see and analyze student performance across multiple courses. Based on their current course progress, the student’s performance is identified as above, at, or below expectations through a variety of graphs and visualizations. Conceptual Question Library There are 1000 questions in the Assignment Manager that require students to apply their statistical understanding. PowerPoint Presentations include lecture content and key graphics from the textbook. Accessible PowerPoint slides are also available and are built to align with WCAG 2.0 AA standards and Section 508 guidelines. TestGen® (www.pearsoned.com/testgen) enables instructors to build, edit, print, and administer tests using a computerized bank of questions developed to cover the objectives of the text. Test Bank features printable PDF containing all the test exercises available in TestGen. 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 (https://www.pearson.com/accessibility-guidelines.html). Minitab Minitab™ makes learning statistics easy and provide students with a skill-set that is in demand in today’s data driven workforce. Bundling Minitab software with educational materials ensures students have access to the software they need in the classroom, around campus, and at home. And having 12-month access to Minitab ensures students can use the software for the duration of their course. ISBN 13: 978-0-13-445640-9 ISBN 10: 0-13-445640-8 (access card only; not sold as stand alone) JMP Student Edition JMP® Student Edition is an easy-to-use, streamlined version of JMP desktop statistical discovery software from SAS Institute, Inc. and is available for bundling with the text. ISBN-13: 978-0-13-467979-2 ISBN-10: 0-13-467979-2 XLSTAT XLSTAT™ is an Excel add-in that enhances the analytical capabilities of Excel. XLSTAT is used by leading businesses and universities around the world. It is available to bundle with this text. For more information, go to www.pearsonhighered.com/xlstat. ISBN-13: 978-0-321-75932-0; ISBN-10: 0-321-75932-X xiv
xv I owe a debt of gratitude to the many reviewers who helped me shape and refine Elementary Statistics: Picturing the World, Eighth Edition. Reviewers of the Current Edition Chris Bendixen, Lake Michigan College Seunghee Lee, Pellissippi State Community College Nancy Liu, Miami Dade College Lohuwa Mamadu, University of South Florida Ashley Nicoloff, Glendale Community College Jason Samuels, Borough of Manhattan Community College Reviewers of the Previous Editions Rosalie Abraham, Florida Community College at Jacksonville Ahmed Adala, Metropolitan Community College Olcay Akman, College of Charleston Polly Amstutz, University of Nebraska, Kearney John J. Avioli, Christopher Newport University Karen Benway, University of Vermont David P. Benzel, Montgomery College John Bernard, University of Texas—Pan American B.K. Brinkley, Tidewater Community College G. Andy Chang, Youngstown State University Keith J. Craswell, Western Washington University Carol Curtis, Fresno City College Christine Curtis, Hillsborough Community College–Dale Mabry Dawn Dabney, Northeast State Community College Cara DeLong, Fayetteville Technical Community College Ginger Dewey, York Technical College David DiMarco, Neumann College Gary Egan, Monroe Community College Charles Ehler, Anne Arundel Community College Carrie Elledge, San Juan College Harold W. Ellingsen, Jr., SUNY—Potsdam Michael Eurgubian, Santa Rosa Jr. College Jill Fanter, Walters State Community College Patricia Foard, South Plains College Douglas Frank, Indiana University of Pennsylvania Frieda Ganter, California State University David Gilbert, Santa Barbara City College Donna Gorton, Butler Community College Larry Green, Lake Tahoe Community College Sonja Hensler, St. Petersburg Jr. College Sandeep Holay, Southeast Community College, Lincoln Campus Lloyd Jaisingh, Morehead State Nancy Johnson, Manatee Community College Martin Jones, College of Charleston David Kay, Moorpark College Mohammad Kazemi, University of North Carolina—Charlotte Jane Keller, Metropolitan Community College Susan Kellicut, Seminole Community College Hyune-Ju Kim, Syracuse University Rita Kolb, Cantonsville Community College Rowan Lindley, Westchester Community College Jeffrey Linek, St. Petersburg Jr. College Benny Lo, DeVry University, Fremont Diane Long, College of DuPage Austin Lovenstein, Pulaski Technical College Rhonda Magel, North Dakota State University Jason Malozzi, Lower Columbia College Mike McGann, Ventura Community College Cynthia McGinnis, Northwest Florida State College Vicki McMillian, Ocean County College Lynn Meslinsky, Erie Community College Larry Musolino, Pennsylvania State University Lyn A. Noble, Florida Community College at Jacksonville— South Campus Julie Norton, California State University—Hayward Lynn Onken, San Juan College Lindsay Packer, College of Charleston Nishant Patel, Northwest Florida State Jack Plaggemeyer, Little Big Horn College Eric Preibisius, Cuyamaca Community College Melonie Rasmussen, Pierce College Cyndi Roemer, Union County College Neal Rogness, Grand Valley State University Jean Rowley, American Public University and DeVry University Elisabeth Schuster, Benedictine University Jean Sells, Sacred Heart University John Seppala, Valdosta State University Carole Shapero, Oakton Community College Abdullah Shuaibi, Harry S. Truman College Aileen Solomon, Trident Technical College Sandra L. Spain, Thomas Nelson Community College Michelle Strager-McCarney, Penn State—Erie, The Behrend College Jennifer Strehler, Oakton Community College Deborah Swiderski, Macomb Community College William J. Thistleton, SUNY—Institute of Technology, Utica Millicent Thomas, Northwest University Agnes Tuska, California State University—Fresno Clark Vangilder, DeVry University Ting-Xiu Wang, Oakton Community Heidi Webb, Horry Georgetown Technical College Dex Whittinghall, Rowan University Cathleen Zucco-Teveloff, Rider University Many thanks to Betsy Farber for her significant contributions to previous editions of the text. I would also like to thank the staff of Larson Texts, Inc., who assisted with the production of the book. On a personal level, I am grateful to my spouse, Deanna Gilbert Larson, for her love, patience, and support. Also, a special thanks goes to R. Scott O’Neil. I have worked hard to make this text a clean, clear, and enjoyable one from which to teach and learn statistics. Despite my best efforts to ensure accuracy and ease of use, many users will undoubtedly have suggestions for improvement. I welcome your suggestions. Ron Larson, odx@psu.edu ACKNOWLEDGMENTS
xvi INDEX OF APPLICATIONS Biology and Life Sciences Adult femur lengths, A30 Adult weights, 67, 68, 69 Age and vocabulary, 482, 483 Ages of dogs, 13 American alligator tail lengths, 127 Bacteria, 495 Birth weights and gestation periods, 260 Black bear weights, 51, 341 Black cherry tree volume, 512 Blood types, 130, 155, 160 Body measurements, 497 BRCA1 gene, 153 Brown trout, 218 Calves born on a farm, 191 Cloning, 212 Diameters of white oak trees, 265 Dog lifespan, 565 Elephant weight, 512 Elk population in Pennsylvania, 18 Endangered and threatened species, 573 Eye color, 141, 153 Female body temperature, 271 Female fibula lengths, 50 Female heights, 88, 108, 249 Fijian banded iguana lengths, 53 Fish measurements, 511 Fisher’s Iris data set, 60 Flowers, 13 Fork length of yellowfin tuna, 433 Genders of children, 180 Genetics, 144, 213 Gestational lengths of horses, 121 Heights of children, 456 Heights and trunk diameters of trees, 505, 507 Human body temperature, 358, 387 Incubation period for ostrich eggs, 467 Incubation period for swan eggs, 361 Infant crawling age and average monthly temperature, 499 Infant weight, 106 Length and girth of harbor seals, 492 Life spans of fruit flies, 112 Life spans of houseflies, 64 Litter size of Florida panthers, 332 Male body temperature, 271 Male heights, 51, 79, 88, 108 Mean birth weight, 466 Metacarpal bone length and height of adults, 581 Milk produced by cows, 233 North Atlantic right whale dive duration, 385 Rabbits, 218 Reaction times to auditory stimulus, 52 Rolling a tongue, 180 Salmon swimming, 137, 149 Sex of children, 143 Shoe size and height, 492 Stomach contents of blue crabs, 433 Trimethylamine, 17 Vulnerable, endangered, or critically endangered species, 9 Water footprint for a kilogram of wheat, 258 Weights of boys, 74 Weights of cats, 254 Weights of dogs, 254 Weights of grapefruits, 456 Weights of newborns, 235 Weights of oranges, 456 Weights of teenagers, 258 Weights of toddlers, 317 Business Accounting department advisory committee, 171 Advertising sales, 225 Advertising time and sales, 501 Annual revenues, 6 Attracting more customers, 19 Bank employee procedure preference, 542, 546 Bankruptcies, 222 Better Business Bureau complaints, 59 Board of Directors, 176 Book prices, 306 Business executives and selfleadership traits, 153 Cauliflower yield, 512 Cell phone prices, 315, 316 CEO compensations, 31 Charges for satellite television, 118 Company sales, 66 Cost of cellphone repairs, 360 Customer ratings, bed-in-a-box 425 Customer transactions, 433 Distribution of sales, 570 Effectiveness of advertising, 568 Employees and revenue of hotel and gaming companies, 492 Existing home sales, 70 Failure rate of businesses, 216, 217 Farming and agriculture, 289 Fortune 500 companies, 191 Fortune 500 revenues, 30 Gas grill ratings, 411 Gasoline prices, 444, 446 Hotel room rates, 401, 411, 467, 574 Hourly earnings at a consulting firm, 110 Hours spent on calls by a business, 190 Marketing plan, 419 Meal prices at a resort, 411 Milk production, 517, 518 Mobile device repair costs, 315, 316 Monthly sales, 562 Natural gas expenditures, 580 Natural gas marketed productions and exports, 506, 507 Net income of farms, 489 Net profit for Procter & Gamble, 114 Net sales, 521 New vehicle sales, 506, 507 No longer needing a physical store, 32 Number of calls by a business, 190 Numbers of manufacturing businesses, 101 Office positions, 184 Office rental rates, 86, 92 Potato yield, 519 President contract, 32 Prices for computer monitors, 268 Printing company departments, 31 Product ratings, 445 Profit and loss analysis, 199 Rental rates, 122 Repair cost for paint damage, 358 Repair costs for washing machines, 425 Repeat customers, 360 Reputations of companies in the U.S., 16 Response times for customer service representatives, 13 Retail prices of minivans, 456 Retail prices of motorcycles, 456 Sale per customer, 118 Sales for a representative, 52, 192, 193, 194, 195, 530 Sales volumes, 159 Service at electronics store, 33 Shipping errors, 360 Sizes of firms, 180 Smartphone sales, 64 Sorghum yield, 512 Soybean harvest, 26 Starting salaries for Standard & Poor’s companies, 7 Sweet potato yield, 580 Telemarketing and Internet fraud, 578 Telephone sales, 220 Television ratings, 410 Tomato prices, 63 Toothpaste costs, 565 Video game prices, 306 Website costs, 335 Wheat production, 574 Yearly commission earned, 114 Combinatorics Access codes, 133, 143, 184 Arranging letters in a word, 175 Birthday problem, 156 Building access code, 185 Code, 169 Committee makeup, 174 Debit card personal identification numbers, 32 Identification number, 139 License plates, 133, 180 Lock box codes, 141 Passwords, 174, 186 Personal identification number, 186 Security code, 174, 183 Sudoku, 168 Telephone numbers, 181 Computers and Technology Active users on social networking sites, 63 Battery life of tablets, 360 Byte, 175 Calling a number, 216 Cell phone screen times, 41, 43, 44, 45, 46, 47, 48, 72 Collection of personal data by smart speakers, 320, 322 Customizing a tablet, 141 Data collected by companies, 290 Data use, 317 Digital device fatigue, 205 Digital device use, 126 Disappearance of Facebook, 282 Going online, 204 Identity theft, 201 Internet access, 182 Internet use, 5 Laptop repairs, 569 Life span of home theater systems, 350, 355 Lifetimes of smartphones, 234 Listening time on a single charge, 384 Mobile payment application users, 34 Online dating app, 328 Phishing, 226 Phone screen sizes, 65 Pinterest, 328 Privacy of personal information, 321 Private internet browsing, 325 Reddit, 221 Reliance on human memory to manage passwords, 291 Robots and computers doing jobs, 409 Smart watch or fitness tracker owners, 33 Snapchat, 328 Social media, 2, 78, 202 Technical failure while working at home, 390 Technology seminar, 183 Testing smartphones, 37 Text messages sent, 55, 56, 57 Time spent checking email, 340 Time spent online, 361 Time spent on social media, 300 Wireless devices, 228 YouTube watching times, 51
INDEX OF APPLICATIONS xvii Demographics Age, 30, 62, 70, 78, 89, 94, 111, 131, 136, 138, 180, 411, 482, 530, 532 Age distribution, 142, 163, 293, 572 Annual arrests, 197 Annual income by state, 93 Asthma prevalence by state, 272 Birthdays, 162, 185 Births by day of the week, 535 Bisexual identification, 326 Book reading by U.S. adults, 135 Cell phones per household, 225 Census, 1, 4 Census Bureau geographical regions, 15 Characteristics of people who use yoga and people who do not use yoga, 417, 449, 450 Children per household, 90 Cost of raising a child, 372 Daily activities, 453 Dogs per household, 199 18- to 22-year old U.S. population, 21 Fastest growing U.S. states, 1 Favorite day of the week, 65 Favorite season, 65 Favorite store, 26 Fertility rates by state, 272 Gun ownership, 282 Hiding purchases from spouse or partner, 278 Household food purchasing, 30 Household income, 5, 433, 458, 461, 575 Household sizes, 294 Hunger and homelessness, 325 Immigration, 220 Incomes of adults in Nevada, 7 Level of education, 126, 143 LGBT identification, 326 Life expectancies, 127 Living with a partner, 328 Magazine subscriptions per household, 117 Marital status, 30 Marriage, 213 National identity and birthplace, 327 Nationality, 6, 13 News sources, 323 People who smoke, 145 Per capita disposable income, 291 Per capita milk consumption, 244 Pet ownership, 63, 96 Physician demographics, 33 Population densities of the 50 U.S. states, 288 Population of Iowa, 42 Population of the U.S. by age group, 142 Population of West Ridge County, 21, 22, 23 Populations of counties in Montana, 78 Populations of the 50 U.S. states, 197 Populations of U.S. cities, 9 Providing support to parents, 30 Renters behind on rent payments, 361 Retirement ages, 53 Richest people, 15 Spending on Christmas gifts, 117 States with the greatest numerical population increases, 1 Televisions per household, 119, 198 Top-earning states, 127 Unemployment rates, 117 U.S. population, 1, 229 Value of home and lifespan, 482 Young adults, 452 Earth Science Acid rain, 522 Air concentration of fine particulate matter in U.S. cities, 407 Air concentration of nitrogen dioxide in U.S. cities, 407 Air pollution, 32 Archaeology, 93 Archaeology club members, 175 Carbon monoxide levels, 384 Classification of elements, 120 Clear days, 209 Climate change, 294 Cloudy days, 209 Conductivity of river water, 381 Conservation, 273 Cyanide presence in drinking water, 342 Days of rain, 189, 191, 193 Density of elements, 94 Earth’s temperature, 406 Greenhouse gases from U.S. energy sources, 287, 288 Hurricanes, 199, 221 Ice thickness, 63 Lead levels, 379, 384 Lightning strikes, 228 Old Faithful eruptions, 46, 96, 273, 472, 475, 477, 480, 488, 489, 499 pH level of river water, 381 pH level of soil, 554 Pollution indices, 116 Precipitation, 6, 12, 221, 335, 426 Protecting the environment, 392 Rain, 140 Snowfall, 197, 270 Sodium chloride concentrations of seawater, 307 Surface concentration of carbonyl sulfide on the Indian Ocean, 287, 288 Temperature, 11, 12, 30, 49, 426 Tornadoes, 127, 306 Water pollution, 175 Water quality, 335 Weather forecasting, 130, 189 Wildland fires, 516 Wind energy, 425 Economics and Finance Account balance, 77 Allowance, 572 Amount spent at a store, 6 Annual rate of return for large growth mutual funds, 255 ATM cash withdrawals, 54 Broker records, 37 Child support payments, 265 Confidence in U.S. economy, 18 Credit card balance, 77 Credit card debt, 384, 422 Credit card purchases, 113 Credit cards, 193 Credit scores, 460 Crude oil imports, 66 Cryptocurrency, 291 Dow Jones Industrial Average, 272, 442 Earnings and dividends, 483 Electric bill, 118, 575 Federal income tax, 404 Financial plans for retirement, 31 Financial risk managers, 284 Fund assets, 506, 507 Gold prices, 306 Gross domestic product, 376 Gross domestic product and carbon dioxide emissions, 471, 474, 479, 480, 487, 489, 499, 500, 501, 503, 508, 509 Gross domestic product from manufacturing sector, 65 Individual stock price, 145 Investment committee, 177 Loan application approval, 178 Mean utility bill, 96, 108 Money management, 534 Mortgage rates, 317 Popular investment types, 33 Preferences on how to pay for goods, 533 Renewable energy prices, 271 Retirement savings, 5, 152 Savings account, 11 Simulating the stock market, 146 Standard & Poor’s 500, 272 Stock offerings, 504, 507 Stock price, 180, 306, 520 Stock risk, 554 Tax fraud, 325 Tax preparation, 526, 527, 529 Tax refunds, 391 Tax return audits, 229 U.S. trade deficits, 79 Use of a mobile device to manage a bank account, 289 Utility bills, 249 Education Abilities in music and mathematics, 153 Academic scholarship, 181 Achievement and school location, 544 ACT composite scores, 250, 289 ACT English score, 426 ACT math score, 8, 426 ACT reading score, 286, 426 ACT science score, 426 Actuarial exam, 211 Advanced Dental Admission Test, 258 Ages of college professors, 121 Ages of enrolled students, 303, 308 Ages of high school students, 284 Alumni contributions, 471, 475, 477, 488 Attitudes about safety at schools, 543 Bachelor of Science degree, 7, 30 Bachelor’s degrees, 281, 390 Branch campuses, 13 Business degrees, 152 Campus security response times, 50 Chairs in a classroom, 310 Changes needed in U.S. schools, 142 Choosing a college, 545 Class levels, 76 Class project, 175 Class schedule, 180 Class size, 116, 117, 385 College acceptance, 212 College board, 7 College costs, 97, 412 College credits, 75 College debt, 360 College education, 534 College programs, 282 College students and drinking, 229 College students with jobs, 246 College success, 412 College visits, 545 Completing an exam, 197 Continuing education, 544 COVID-19 pandemic impacting ability to complete degree, 126 Dormitory room charges, 118 Earned degrees conferred, 58, 184 Educational attainment, 64, 576 Engineering degrees, 65, 164 Enrollment levels, 185, 225 Exam scores, 63, 225, 334, 418 Expression of political views on college campuses, 281 Extracurricular activities, 350, 355, 356 Faculty classroom hours, 385 Failing a distance learning course, 276, 278 Federal student loans in repayment, 229 Final grade, 77, 78, 510, 511 Freshman orientation, 229 Full-time teaching experience, 573 Getting the classes you want, 142 Grade point averages, 26, 33, 62, 71, 76, 78, 98, 119, 316, 471, 480, 514, 563, 569 Grades, 80, 109, 119, 141, 162 GRE scores, 259 High school bell schedule, 14 High school grade point averages and SAT and ACT scores, 32 High school graduation rate, 361, 376 History class grades, 259
xviii INDEX OF APPLICATIONS History course final presentations, 185 Hours spent on academic activities outside of class, 182 Hours students slept, 225, 264 Hours studying and test scores, 491 Immigrants with bachelor’s degrees, 212 International mathematics literacy test scores, 408 Length of a guest lecturer’s talk, 109 Library visitation, 30 LSAT scores, 75, 288 Mathematics assessment tests, 401 MCAT scores, 50, 249, 289, 375 Multiple-choice quiz, 202 Music assessment test scores, 460 Music major, 162 New York Grade 6 English Language Arts Operational Test reading subscores, 236 New York Grade 6 Mathematics Operational Test scores, 236 Nursing major, 157 Obstacles that keep students from completing their homework, 25 Off track to graduating because of at least one course failure, 276 Paying for college education, 221, 328, 360, 581 Paying for college expenses with a credit card, 268 Physics class students, 162 Plans after high school, 33 Postgraduate degree, 339 Quantitative reasoning scores, 111 Reading assessment test scores, 401, 460 Residency positions, 151 Room and board expense, 267 Room numbers, 14 SAT critical reading scores, 574 SAT French Subject Test, 271 SAT Italian Subject Test, 271 SAT math scores, 4, 200 SAT multiple choice questions, 212 SAT physics scores, 341 SAT reading and writing score, 33 SAT scores, 54, 98, 106, 244, 250, 316, 442, 467, 514 School-related extracurricular activities, 199 Science achievement test scores, 408 Science assessment tests, 556 Standardized test scores, 155 State mathematics test, 430 Statistics course enrollment, 21 Statistics course scores, 78, 121, 183 Student activities and time use, 116 Student daily life, 412 Student living arrangement and borrowing money for college, 537, 540 Student living arrangement and family college experience, 536, 537, 539 Student loans, A29 Student musicians, 197 Students who earn Bachelor of Science or Bachelor of Arts degrees, 447 Students planning to study visual and performing arts, 453 Students in public schools, 182 Students undecided on an intended college major, 453, 461 Study habits, 31 Study hours, 97, 110 Teaching conference, 162 Teaching experience, 295 Teaching load, 97 Teaching methods, 434, 457 Teaching styles, 33 Test scores, 74, 96, 111, 117, 127, 137, 535, 581 Testing times, 121 Texas Bar Exam, 226 Textbook spending, 51 Time spent on homework, 316 Top ten colleges in terms of value for the money, 13 True/false test, 140, 141 Tuition and fees, 75, 103, 104, 105, 107, 385, 573 U.S. history assessment tests, 556 Using social media to research colleges, 155 What Americans know about science, 2 Engineering Activating temperature of sprinkler systems, 375 Bolt diameters, 334, 335 Bolt widths, 409 Can defects, 163 Carton defects, 163 Chlorine level in a pool, 399 Circumference of soccer balls, 308 Circumference of tennis balls, 308 Defective disks, 177 Defective DVR, 140 Defective parts, 131, 180, 199, 213, 220, 295 Defective units, 177, 183, 184, 222 Diameter of an engine part, 251 Diameter of a gear, 251 Diameters of machine parts, 270 Fishing line strength, 399 Fossil fuels, 221 Glass manufacturer, 221 Golf ball manufacturing, 394 Injection mold, 575 Juice dispensing machine, 308 Landing an astronaut on Mars, 226 Life of appliances, 555 Life span of a backpack, 361 Life span of lawn mowers, 361 Lifetimes of diamond-tipped cutting tools, 270 Light bulb manufacturing, 317, 376 Liquid dispenser, 251 Liquid volume in cans, 116, 117 Living on Mars, 548 Load-bearing capacities of transmission line insulators, 270 Machine part accuracy, 32 Machine settings, 292 Manufacturing defect, 222 Mean life of a compact fluorescent lamp bulb, 376 Mean life of furnaces, 350, 355 Melting points of industrial lubricants, 270 Milk containers, 272 Nail length, 251 Paint can volumes, 272, 308 Parachute failure rate, 352 Power failures, 75 Solar panels, 6 Speed of sound, 483 Statistical process control, 251 Tennis ball manufacturing, 317 Tensile strength, 433, 434 Testing toothbrushes, 126 Time clocks lose, 360 Volume of gasoline, 191 Entertainment Academy Award winners, 112 Albums by The Beatles, 121 American roulette, 200 Amusement park attendance, 360 Arts, 2 Attendance at concerts, 197 Best sellers list, 14 Billboard Hot 100 song lengths, 258 Broadway shows, 15 Celebrities addressing social and political issues, 154 Chess, 360 Comedy series, 13 Fair bet, 199 Finding new music, 176 Game show, 140 Lengths of songs, 113 Live television streaming platforms, 389 Lottery, 142, 173, 175, 176, 178, 211, 222, 226 Monopoly, 148 Motion Picture Association of America ratings, 12 Movie genres, 10 Movie rental late fees, 153 Movies watched in a year, 121 Music, 5 Musical dice game minuet, 187 Number one songs, 75 Planning on summer travel, 320, 322 Raffle, 137, 196, 200 Reading a book, 208, 226 Reviewing a movie, 581 Roller coaster heights, 50, 338, A30 Roller coaster vertical drops, 375 Roulette wheel, 178 Shuffle playback, 176 Singing competition, 175 Song setlist, 175 Spring break destinations, 31 Streaming programming, 389 Television watching, 517, 518 Time The Bachelorette stars stayed with partners, 127 Top-40 radio stations, 119 Top-grossing films, 32 Type of movie rented by age, 543, 546 Types of televised shows, 12 Vacation planning, 14 Video durations, 75 Video game arrangement, 174 Video game scores, 32 Violent video games, 347 Virtual reality device, 210 Winter vacation, 339 Women who are gamers, 360 Food and Nutrition Amounts of caffeine in brewed coffee, 97 Caffeine content of soft drinks, 376 Caloric and sodium content of hot dogs, 492 Calorie, fat, carbohydrate, and protein content, 513 Carbohydrates in chicken sandwiches, 557 Carbohydrates in an energy bar, 406 Carbohydrates in a nutrition bar, 411 Cereal boxes, 341 Cholesterol contents of cheese, 307 Cholesterol contents of chicken sandwiches, 557 Coffee consumption, 532 Corn kernel toxin, 173 Eating habits, 25 Eating healthier foods, 26 Eating at a restaurant, 294 Fast food, 326, 376 Fat content in whole milk, 397 Food storage temperature, 4 Grocery shopping, 262 Ice cream, 272 M&M’s, 226, 530, 531 Meal kits, 411 Meal plan choices of college students, 6 Meat and poultry, 392 Menu selection, 141, 175 Nutrients in breakfast cereals, 523 Ordering pizza, 533 Pepper pungencies, 52 Pizza toppings, 176 Protein powder, 79 Restaurant ratings, 542, 546 Restaurant serving times, 409 Restaurant waiting times, 553 Shelf life of dried fruit, 406 Sodium content of sandwiches, 456 Sports drink, 397 Sugar consumption and cavities, 516 Taste test, 53
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