Introduction to Statistics - Saint Paul Public Schools

1 Introductionto Statistics and Data AnalysisThis page intentionally left blank Introductionto Statistics and Data AnalysisThird EditionRoxy PeckCalifornia Polytechnic State University, San Luis ObispoChris OlsenGeorge Washington High School, Cedar Rapids, IAJay DevoreCalifornia Polytechnic State University, San Luis ObispoAustralia Brazil Canada Mexico Singapore Spain United Kingdom United StatesIntroduction to Statistics and Data Analysis,Third EditionRoxy Peck, Chris Olsen, Jay DevoreAcquisitions Editor: Carolyn CrockettDevelopment Editor: Danielle DerbentiAssistant Editor: Beth GershmanEditorial Assistant: Ashley SummersTechnology Project Manager: Colin BlakeMarketing Manager: Joe RogoveMarketing Assistant: Jennifer LiangMarketing Communications Manager: Jessica PerryProject Manager, Editorial Production: Jennifer RisdenCreative Director: Rob HugelArt Director: Vernon BoesPrint Buyer: Karen HuntPermissions Editor: Isabel AlvesProduction Service: Newgen AustinText Designer: Stuart PatersonPhoto Researcher: Gretchen MillerCopy Editor: Nancy DicksonIllustrator: Jade Myers; Newgen IndiaCover Designer: Stuart PatersonCover Image: Paul Chesley/Getty ImagesCover Printer: Courier Corporation/KendallvilleCompositor: Newgen IndiaPrinter: Courier Corporation/Kendallville 2008, 2005 Duxbury, an imprint of Thomson Brooks/Cole, apart of The Thomson Corporation.

2 Thomson, the Star logo, andBrooks/Cole are trademarks used herein under RIGHTS RESERVED. No part of this work covered by thecopyright hereon may be reproduced or used in any form or byany means graphic, electronic, or mechanical, including photo-copying, recording, taping, Web distribution, information storageand retrieval systems, or in any other manner without the writ-ten permission of the in the United States of America1 2 3 4 5 6 7 11 10 09 08 07 ExamView and ExamView Pro are registered trademarks of FSCreations, Inc. Windows is a registered trademark of theMicrosoft Corporation used herein under license. Macintosh andPower Macintosh are registered trademarks of Apple Computer,Inc. Used herein under of Congress Control Number: 2006933904 Student Edition:ISBN-13: 978-0-495-11873-2 ISBN-10: 0-495-11873-7 Thomson Higher Education10 Davis DriveBelmont, CA 94002-3098 USAFor more information about our products, contact us at:Thomson Learning Academic Resource Center1-800-423-0563 For permission to use material from this text or product, submit arequest online at additional questions about permissions can be submitted bye-mail to To my nephews, Jesse and Luke Smidt, who bet I wouldn t put their names in this P.

3 To my wife, Sally, and my daughter, AnnaC. O. To Carol, Allie, and PECK is Associate Dean of theCollege of Science and Mathematicsand Professor of Statistics at CaliforniaPolytechnic State University, San LuisObispo. Roxy has been on the facultyat Cal Poly since 1979, serving for sixyears as Chair of the Statistics Department beforebecoming Associate Dean. She received an inMathematics and a in Applied Statistics fromthe University of California, Riverside. Roxy is na-tionally known in the area of Statistics education,and in 2003 she received the American StatisticalAssociation s Founder s Award, recognizing her con-tributions to K 12 and undergraduate Statistics edu-cation. She is a Fellow of the American StatisticalAssociation and an elected member of the Interna-tional Statistics Institute.

4 Roxy has recently com-pleted five years as the Chief Reader for the Ad-vanced Placement Statistics Exam and currentlychairs the American Statistical Association s JointCommittee with the National Council of Teachers ofMathematics on Curriculum in Statistics and Proba-bility for Grades K 12. In addition to her texts in in-troductory Statistics , Roxy is also co-editor ofStatisti-cal Case Studies: A Collaboration Between Academeand Industryand a member of the editorial board forStatistics: A Guide to the Unknown, 4th edition. Out-side the classroom and the office, Roxy likes to traveland spends her spare time reading mystery also collects Navajo rugs and heads to New Mex-ico whenever she can find the OLSEN has taught Statistics at George Washington High School inCedar Rapids, Iowa, for over 25 is a past member of the Ad-vanced Placement Statistics Test De-velopment Committee and the authorof the Teacher s Guide for Advanced Placement Sta-tistics.

5 He has been a table leader at the AP Statisticsreading for 6 years and since the summer of 1996 hasbeen a consultant to the College Board. Chris leadsworkshops and institutes for AP Statistics teachersin the United States and internationally. Chris wasthe Iowa recipient of the Presidential Award for Ex-cellence in Science and Mathematics Teaching in1986. He was a regional winner of the IBM Com-puter Teacher of the Year award in 1988 and receivedthe Siemens Award for Advanced Placement in math-ematics in 1999. Chris is a frequent contributor tothe AP Statistics Electronic Discussion Group andhas 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 Universitywith a major in mathematics and, while acquiringgraduate degrees at the University of Iowa, concen-trated on Statistics , computer programming, psycho-metrics, and test development.

6 Currently, he divideshis duties between teaching and evaluation; in addi-tion to teaching, he is the assessment facilitator forthe Cedar Rapids, Iowa, Community Schools . In hisspare time he enjoys reading and hiking. He and hiswife have a daughter, Anna, who is a graduate stu-dent in Civil Engineering at Cal DEVORE earned his under-graduate degree in Engineering Sci-ence from the University of Californiaat Berkeley, spent a year at the Univer-sity of Sheffield in England, and fin-ished his in Statistics at StanfordUniversity. He previously taught at the University ofFlorida and at Oberlin College and has had visitingappointments at Stanford, Harvard, the Universityof Washington, and New York University. From 1998to 2006, Jay served as Chair of the Statistics Depart-ment at California Polytechnic State University, SanLuis Obispo.

7 The Statistics Department at Cal Polyhas an international reputation for activities in sta-tistics education. In addition to this book, Jay haswritten several widely used engineering statisticstexts and is currently working on a book in appliedmathematical Statistics . He is the recipient of a dis-tinguished teaching award from Cal Poly and is aFellow of the American Statistical Association. Inhis spare time, he enjoys reading, cooking and eatinggood food, tennis, and travel to faraway places. He isespecially proud of his wife, Carol, a retired elemen-tary school teacher, his daughter Allison, who worksfor the Center for Women and Excellence in Boston,and his daughter Teri, who is finishing a graduateprogram in education at NYU. About the AuthorsviiContents1 The Role of Statistics and the Data Analysis Reasons to Study Nature and Role of and the Data Analysis of Data and Some Simple Graphical Displays12 Activity Sizes: Understanding Variability22 Activity Sizes23 Activity Meaningful Paragraph242 Collecting Data Studies: Observation and Comparative on Experimental on Observational Studies: Designing Surveys (Optional) and Communicating the Results of Statistical Analyses61 Activity a Sampling Plan63 Activity Experiment to Test for the Stroop Effect64 Activity s and the Next 100 Billion Burgers64 Activity Games and Pain Management65 Graphing Calculator Explorations693 Graphical Methods for Describing Categorical Data: Comparative Bar Charts and Pie Numerical Data: Stem-and-Leaf Displays87 Contentsviii Numerical Data.

8 Frequency Distributions and Bivariate Numerical and Communicating the Results of Statistical Analyses127 Activity States134 Activity Counters!134 Graphing Calculator Explorations1414 Numerical Methods for Describing the Center of a Data Variability in a Data a Data Set: Center and Variability: Chebyshev s Rule, the Empirical Rule, and and Communicating the Results of Statistical Analyses186 Activity and Summarizing Numerical Data190 Activity Passenger Weights190 Activity Shapes190 Graphing Calculator Explorations1955 Summarizing Bivariate Regression: Fitting a Line to Bivariate the Fit of a Relationships and Regression (Optional) and Communicating the Results of Statistical Analyses264 Activity Correlation and Regression267 Activity and Flexibility268 Graphing Calculator Explorations2726 Experiments and of Probability288 Properties of General Probability Probabilities Empirically Using Simulation335 Activity Crisis for European Sports Fans?

9 347 Activity Hot Hand in Basketball347 Graphing Calculator Explorations3517 Random Variables and Probability Distributions for Discrete Random Distributions for Continuous Random and Standard Deviation of a Random and Geometric for Normality and Normalizing the Normal Distribution to Approximate a Discrete Distribution425 Activity Eggs?429 Graphing Calculator Explorations4348 Sampling Variability and Sampling and Sampling Sampling Distribution of a Sample Sampling Distribution of a Sample Proportion461 Activity Students Who Take the SATs Multiple Times Have an Advantage in College Admissions?468 Graphing Calculator Explorations4719 Estimation Using a Single Confidence Interval for a Population Interval for a Population Mean495x and Communicating the Results of Statistical Analyses508 Activity a Feel for Confidence Level514 Activity Alternative Confidence Interval for aPopulation Proportion515 Activity Signatures on a Recall Petition516 Activity Meaningful Paragraph516 Graphing Calculator Explorations52110 Hypothesis Testing Using a Single and Test in Hypotheses Hypothesis Tests for a Population Tests for a Population and Probability of Type II and Communicating the Results of Statistical Analyses571 Activity the tandzDistributions574 Activity Meaningful Paragraph575 Graphing Calculator Explorations58011 Comparing Two Populations or Concerning the Difference Between Two Populationor Treatment Means Using

10 Independent Concerning the Difference Between Two Populationor Treatment Means Using Paired Sample Inferences Concerning a Difference Between TwoPopulation or Treatment and Communicating the Results of Statistical Analyses629 Activity Footballs632 Activity About Data Collection633 Activity Meaningful Paragraph633 Graphing Calculator Explorations641 Contentsxi12 The Analysis of Categorical Data and Goodness-of-Fit Tests for Univariate for Homogeneity and Independence in a Two-way and Communicating the Results of Statistical Analyses677 Activity a Number, Any and Perceived Taste680 Graphing Calculator Explorations68513 Simple Linear Regression and Correlation: Inferential Linear Regression About the Slope of the Population Regression Model Based on the Estimated Regression Line (Optional) About the Population Correlation Coefficient (Optional) and Communicating the Results of Statistical Analyses737 Activity Tall Women from Big Families?