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Introduction

to Statistics and Data Analysis

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Introduction

to Statistics and Data Analysis

Third Edition

Roxy Peck

California Polytechnic State University,San Luis Obispo

Chris Olsen

George Washington High School,Cedar Rapids,IA

Jay Devore

California Polytechnic State University,San Luis Obispo

Australia • Brazil • Canada • Mexico • Singapore • Spain • United Kingdom • United States

Introduction to Statistics and Data Analysis,

Third Edition

Roxy Peck,Chris Olsen,Jay Devore

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©2008,2005 Duxbury, an imprint of Thomson Brooks/Cole,a part of The Thomson Corporation. Thomson,the Star logo,and Brooks/Cole are trademarks used herein under license. ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon may be reproduced or used in any form or by any means - graphic,electronic,or mechanical,including photo- copying,recording,taping,Web distribution,information storage and retrieval systems,or in any other manner - without the writ- ten permission of the publisher.

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Library of Congress Control Number:2006933904

Student Edition:

ISBN-13:978-0-495-11873-2

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For permission to use material from this text or product,submit a request online at http://www.thomsonrights.com. Any additional questions about permissions can be submitted by e-mail to thomsonrights@thomson.com. !To my nephews,Jesse and Luke Smidt,who bet I wouldn't put their names in this book. R. P. !To my wife,Sally,and my daughter,Anna C. O. !To Carol,Allie,and Teri. J. D.

ROXY PECKis Associate Dean of the

College of Science and Mathemat ics

and Professor of Statistics at California

Polytechnic State University, San Luis

Obispo. Roxy has been on the faculty

at Cal Poly since 1979, serving for six years as Chair ofthe Statistics Department before becoming Associate Dean. She received an M.S. in Mathematics and a Ph.D. in Applied Statistics from the University of California, Riverside. Roxy is na- tionally known in the area of statistics educat ion, and in 2003 she receiv ed the Amer ican Statist ical Association's Founder's Award, recognizing her con- tributions to K-12 and undergraduate statistics edu- cation. She is a Fellow of the American Statistical

Association and an elected member of the Interna-

tional Statistics Institute. Roxy has recently com- pleted five years as the Chief Reader for the Ad- vanced Placement Statistics Exam and cur rently chairs the Amer ican Statist ical Association's J oint Committee with the National Council of Teachers of Mathematics on Curriculum in Statistics and Proba- bility for Grades K-12. In addition to her texts in in- cal Case Studies: A Collaboration Between Academe and Industryand a member of the editorial board for Statistics: A Guide to the Unknown, 4th edition. Out- side the classroom and the office, Roxy likes to travel and spends her spare time reading mystery novels. She also collects Navajo rugs and heads to New Mex- ico whenever she can find the time.

CHRIS OLSENhas taught stat istics

at George Washington High School in

Cedar Rapids, Iowa, for over 25 years.

Chris is a past member of the A d-

vanced Placement Statist ics Test De- velopment Committee and the author of the Teacher's Guide for Advanced Placement Sta- tistics. He has been a table leader at the AP Statistics reading for 6 years and since the summer of 1996 has been a consultant to the College Board. Chris leads workshops and institutes for AP Statistics teachers in the United States and internationally. Chris was the Iowa recipient of the Presidential Award for Ex- cellence in Science and Mathematics Teaching in

1986. He was a regional winner of the IBM Com-

puterTeacher oftheYearaw ardin1988 andreceiv ed ematics in 1999. Chris is a frequent contributor to the AP Statistics Electronic Discussion Group and has reviewed materials for The Mathematics Teacher, the AP Central web site, The American Statistician, and the Journal of the American Statistical Associa- tion. He currently writes a column for Statsmaga- zine. Chris graduated from Iowa State Univ ersity with a major in mathematics and, while acquiring graduate degrees at the University of Iowa, concen- trated on statistics, computer programming, psycho- metrics, and test development. Currently, he divides his duties between teaching and evaluation; in addi- tion to teaching, he is the assessment facilitator for the Cedar Rapids, Iowa, Community Schools. In his spare time he enjoys reading and hiking. He and his wife have a daughter, Anna, who is a graduate stu- dent in Civil Engineering at Cal Tech.

JAY DEVORE earned his under-

graduate degree in Engineering Sci- ence from the University of California at Berkeley, spent a year at the Univer- sity of Shef field in England, and fin- ished his Ph.D. in statistics at Stanford University. He previously taught at the University of Florida and at Oberlin College and has had visiting appointments at Stanford, Harvard, the University of Washington, and New York University. From 1998 to 2006, Jay served as Chair of the Statistics Depart- ment at California Polytechnic State University, San Luis Obispo. The Statistics Department at Cal Poly has an international reputation for activities in sta- tistics education. In addition to this book, Jay has written several widely used engineering statistics texts and is currently working on a book in applied mathematical statistics. He is the recipient of a dis- tinguished teaching award from Cal Poly and is a Fellow of the American Statistical Association. In his spare time, he enjoys reading, cooking and eating good food, tennis, and travel to faraway places. He is especially proud of hiswife, Carol, a retired elemen- tary school teacher, his daughter Allison, who works for the Center for Women and Excellence in Boston, and his daughter Teri, who is finishing a graduate program in education at NYU.

About the Authors

vii

Contents

1The Role of Statistics and the Data Analysis Process1

1.1Three Reasons to Study Statistics1

1.2The Nature and Role of Variability4

1.3Statistics and the Data Analysis Process7

1.4Types of Data and Some Simple Graphical Displays12

Activity 1.1Head Sizes: Understanding Variability22

Activity 1.2Estimating Sizes23

Activity 1.3A Meaningful Paragraph24

2Collecting Data Sensibly27

2.1Statistical Studies: Observation and Experimentation27

2.2Sampling32

2.3Simple Comparative Experiments42

2.4More on Experimental Design51

2.5More on Observational Studies: Designing Surveys (Optional)56

2.6Interpreting and Communicating the Results of

Statistical Analyses61

Activity 2.1Designing a Sampling Plan63

Activity 2.2An Experiment to Test for the Stroop Effect64 Activity 2.3McDonald's and the Next 100 Billion Burgers64

Activity 2.4Video Games and Pain Management65

Graphing Calculator Explorations69

3Graphical Methods for Describing Data75

3.1Displaying Categorical Data: Comparative Bar Charts

and Pie Charts76

3.2Displaying Numerical Data: Stem-and-Leaf Displays87

Contents

viii!Contents

3.3Displaying Numerical Data: Frequency Distributions

and Histograms97

3.4Displaying Bivariate Numerical Data117

3.5Interpreting and Communicating the Results of

Statistical Analyses127

Activity 3.1Locating States134

Activity 3.2Bean Counters!134

Graphing Calculator Explorations141

4Numerical Methods for Describing Data147

4.1Describing the Center of a Data Set148

4.2Describing Variability in a Data Set159

4.3Summarizing a Data Set: Boxplots169

4.4Interpreting Center and Variability: Chebyshev's Rule,

the Empirical Rule, and zScores176

4.5Interpreting and Communicating the Results of

Statistical Analyses186

Activity 4.1Collecting and Summarizing Numerical Data190

Activity 4.2Airline Passenger Weights190

Activity 4.3Boxplot Shapes190

Graphing Calculator Explorations195

5Summarizing Bivariate Data199

5.1Correlation200

5.2Linear Regression: Fitting a Line to Bivariate Data210

5.3Assessing the Fit of a Line221

5.4Nonlinear Relationships and Transformations238

5.5Logistic Regression (Optional)255

5.6Interpreting and Communicating the Results

of Statistical Analyses264 Activity 5.1Exploring Correlation and Regression267

Activity 5.2Age and Flexibility268

Graphing Calculator Explorations272

6Probability 279

6.1Chance Experiments and Events279

6.2Definition of Probability288

!Contentsix

6.3Basic Properties of Probability295

6.4Conditional Probability302

6.5Independence313

6.6Some General Probability Rules323

6.7Estimating Probabilities Empirically Using Simulation335

Activity 6.1Kisses347

Activity 6.2A Crisis for European Sports Fans?347

Activity 6.3The "Hot Hand" in Basketball347

Graphing Calculator Explorations351

7Random V ariables and Probability Distributions357

7.1Random Variables358

7.2Probability Distributions for Discrete Random Variables361

7.3Probability Distributions for Continuous Random Variables367

7.4Mean and Standard Deviation of a Random Variable372

7.5Binomial and Geometric Distributions386

7.6Normal Distributions397

7.7Checking for Normality and Normalizing Transformations414

7.8Using the Normal Distribution to Approximate a

Discrete Distribution425

Activity 7.1Rotten Eggs?429

Graphing Calculator Explorations434

8Sampling V ariability and Sampling Distributions445

8.1Statistics and Sampling Variability446

8.2The Sampling Distribution of a Sample Mean450

8.3The Sampling Distribution of a Sample Proportion461

Activity 8.1Do Students Who Take the SATs Multiple Times Have an Advantage in College Admissions?468

Graphing Calculator Explorations471

9Estimation Using a Single Sample475

9.1Point Estimation476

9.2Large-Sample Confidence Interval for a Population Proportion482

9.3Confidence Interval for a Population Mean495

x!Contents

9.4Interpreting and Communicating the Results of

Statistical Analyses508

Activity 9.1Getting a Feel for Confidence Level514 Activity 9.2An Alternative Confidence Interval for a

PopulationProportion 515

Activity 9.3Verifying Signatures on a Recall Petition516

Activity 9.4A Meaningful Paragraph516

Graphing Calculator Explorations521

10Hypothesis T esting Using a Single Sample525

10.1Hypotheses and Test Procedures526

10.2Errors in Hypotheses Testing531

10.3Large-Sample Hypothesis Tests for a Population Proportion537

10.4Hypotheses Tests for a Population Mean550

10.5Power and Probability of Type II Error562

10.6Interpreting and Communicating the Results of

Statistical Analyses571

Activity 10.1Comparing the tandzDistributions574

Activity 10.2A Meaningful Paragraph575

Graphing Calculator Explorations580

11Comparing T wo Populations or Treatments583

11.1Inferences Concerning the Difference Between Two Population

or Treatment Means Using Independent Samples583

11.2Inferences Concerning the Difference Between Two Population

or Treatment Means Using Paired Samples606

11.3Large Sample Inferences Concerning a Difference Between Two

Population or Treatment Proportions619

11.4Interpreting and Communicating the Results of

Statistical Analyses629

Activity 11.1Helium-Filled Footballs632

Activity 11.2Thinking About Data Collection633

Activity 11.3A Meaningful Paragraph633

Graphing Calculator Explorations641

!Contentsxi

12The Analysis of Categorical Data and Goodness-of-

FitTests 647

12.1Chi-Square Tests for Univariate Data647

12.2Tests for Homogeneity and Independence in a Two-

way Table660

12.3Interpreting and Communicating the Results of

Statistical Analyses677

Activity 12.1Pick a Number, Any Number...680

Activity 12.2Color and Perceived Taste680

Graphing Calculator Explorations685

13Simple Linear Regression and Correlation:

Inferential Methods689

13.1Simple Linear Regression Model690

13.2Inferences About the Slope of the Population Regression Line702

13.3Checking Model Adequacy713

13.4Inferences Based on the Estimated Regression Line

(Optional)725

13.5Inferences About the Population Correlation Coefficient

(Optional)734

13.6Interpreting and Communicating the Results of

Statistical Analyses737

Activity 13.1Are Tall Women from "Big" Families?739

Graphing Calculator Exploration746

14Multiple Regression Analysis749

14.1Multiple Regression Models750

14.2Fitting a Model and Assessing Its Utility763

14.3Inferences Based on an Estimated Model14-1

14.4Other Issues in Multiple Regression14-13

14.5Interpreting and Communicating the Results of

Statistical Analyses14-26

Activity 14.1Exploring the Relationship Between Number of

Predictors and Sample Size780

Sections and/or chapter numbers in color can be found at www.thomsonedu.com/statistics/peck xii!Contents Sections and/or chapter numbers in color can be found at www.thomsonedu.com/statistics/peck

15Analysis of Variance783

15.1Single-Factor ANOVA and the FTest784

15.2Multiple Comparisons800

15.3TheFTest for a Randomized Block Experiment15-1

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