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Introduction
to Statistics and Data Analysis
This page intentionally left blank
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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Printer:Courier Corporation/K endallville
©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.
Printed in the United States of America
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and ExamView Pro are registered trademarks of FSCreations,Inc. Windo ws is a registered trademark of the Microsoft Corporation used herein under license. Macintosh and Power Macintosh are registered trademarks of Apple Computer,
Inc. Used herein under license.
Library of Congress Control Number:2006933904
Student Edition:
ISBN-13:978-0-495-11873-2
ISBN-10:0-495-11873-7
Thomson Higher Education
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Belmont,CA 94002-3098
USA For more information about our products,contact us at:
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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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