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Statistics through applications PDF

579 Pages·2011·30.578 MB·English
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STATISTICS THROUGH APPLICATIONS This page intentionally left blank STATISTICS THROUGH APPLICATIONS SECOND EDITION DAREN S. STARNES THE LAWRENCEVILLE SCHOOL DANIEL S. YATES STATISTICS CONSULTANT DAVID S. MOORE PURDUE UNIVERSITY W. H. FREEMAN AND COMPANY / NEW YORK Executive Publisher: Craig Bleyer Publisher: Ruth Baruth Executive Editor: Ann Heath Senior Developmental Editor: Shona Burke Executive Marketing Manager: Cindi Weiss Marketing Manager: Nicole Sheppard Klophaus Media Editor: Laura Capuano Associate Editor: Katrina Wilhelm Editorial Assistant: Catriona Kaplan Project Editor: Jane O’Neill Text and Cover Designer: Blake Logan Photo Editor: Cecilia Varas Photo Researcher: Elyse Rieder Senior Illustration Coordinator: Bill Page Illustrations: Network Graphics Production Coordinator: Paul Rohloff Composition: Aptara Printing and Binding: RR Donnelley TI-84TM and TI-NspireTM screen shots are used with permission of the publisher: ©1996, Texas Instruments Incorporated. TI-84TM and TI-NspireTM Graphic Calculators are registered trademarks of Texas Instruments Incorporated. Minitab is a registered trademark of Minitab, Inc. Microsoft © and Windows© are registered trademarks of the Microsoft Corporation in the United States and other countries. Excel screen shots are reprinted with permission from the Microsoft Corporation. Fathom Dynamic Statistics is a trademark of KCP Technologies. Library of Congress Control Number: 2009936387 ISBN-13: 9-781-4292-1974-7 ISBN-10: 1-4292-1974-2 © 2011, 2005 by W. H. Freeman and Company All rights reserved Printed in the United States of America First Printing No part of this book may be reproduced by any mechanical, photographic, or electronic process, or in the form of a phonographic recording, nor may it be stored in a retrieval system, transmitted, or otherwise copied for public or private use, without the written permission of the publisher. W. H. Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com CONTENTS About the Authors vii CHAPTER 4 DESCRIBING Preface ix RELATIONSHIPS 141 4.1 Scatterplots and CHAPTER 1 STATISTICS: THE ART Correlation 142 AND SCIENCE OF DATA 1 4.2 Regression and Prediction 168 1.1 Where Do Data Come From? 2 Chapter 4 Review 194 1.2 Drawing Conclusions from Chapter 4 Review Exercises 195 Data 18 Chapter 1 Review 28 Chapter 1 Review Exercises 29 Part B Producing Data 199 CHAPTER 5 SAMPLING AND SURVEYS 201 Part A Analyzing Data 33 5.1 Samples, Good and CHAPTER 2 DESCRIBING Bad 202 DISTRIBUTIONS OF DATA 35 5.2 What Do Samples 2.1 Displaying Distributions Tell Us? 219 with Graphs 36 5.3 Sample Surveys in the 2.2 Describing Distributions Real World 236 with Numbers 59 Chapter 5 Review 252 2.3 Use and Misuse of Statistics 82 Chapter 5 Review Exercises 253 Chapter 2 Review 94 Chapter 2 Review Exercises 96 CHAPTER 6 DESIGNING EXPERIMENTS 257 CHAPTER 3 MODELING 6.1 Experiments, Good DISTRIBUTIONS OF DATA 101 and Bad 258 3.1 Measuring Location in a 6.2 Experiments in the Distribution 102 Real World 273 3.2 Normal Distributions 116 6.3 Data Ethics 292 Chapter 3 Review 136 Chapter 6 Review 305 Chapter 3 Review Exercises 137 Chapter 6 Review Exercises 306 vi Contents Chapter 9 Review 464 Part C Chance 309 Chapter 9 Review Exercises 466 CHAPTER 7 PROBABILITY: WHAT ARE THE CHANCES? 311 CHAPTER 10 INFERENCE IN PRACTICE 469 7.1 Randomness, Probability, and Simulation 312 10.1 Chi-Square Tests: Goodness of Fit 7.2 Probability Rules 329 and Two-Way Tables 470 7.3 Conditional Probability 10.2 Inference about a Population and Independence 348 Mean 493 Chapter 7 Review 364 Chapter 10 Review 516 Chapter 7 Review Exercises 365 Chapter 10 Review Exercises 517 Notes and Data Sources N-1 CHAPTER 8 PROBABILITY Solutions to Odd-Numbered Exercises S-1 MODELS 369 Index I-1 8.1 Probability Distributions 370 Tables T-1 8.2 Counting and Probability 387 Table A Standard Normal 8.3 Binomial Distributions 399 Probabilities T-1 Chapter 8 Review 413 Table B Random Digits T-2 Chapter 8 Review Exercises 414 Table C t Distribution Critical Values T-3 Table D Critical Values of z* T-4 Table E Chi-Square Critical Values T-4 Part D Inference 417 Additional Topics on CD-ROM and at www.whfreeman.com/sta2e CHAPTER 9 INTRODUCTION S.1 Measuring TO INFERENCE 419 S.2 The Consumer Price Index and 9.1 What Is a Confi dence Government Statistics Interval? 420 9.2 What Is a Signifi cance Test? 438 9.3 Use and Abuse of Statistical Inference 453 ABOUT THE AUTHORS DAREN S. STARNES holds the endowed Master Teacher chair in Mathematics at The Lawrenceville School near Princeton, New Jersey. He earned his MA in Mathematics from the University of Michigan. In 1997, he received a GTE GIFT Grant to integrate AP Statistics and AP Environmental Science. He was named a Tandy Technology Scholar in 1999. Daren has led numerous one-day and weeklong AP Statistics institutes for new and experienced AP teachers, and he has been a reader, table leader, and question leader for the AP Statistics exam. In 2001–2002, he served as coeditor of the Technology Tips column in the NCTM journal The Mathematics Teacher. Since 2004, Daren has served on the ASA/NCTM Joint Committee on the Curriculum in Statistics and Probability (which he chaired in 2009). While on the committee, he edited the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Pre-K–12 Report and coauthored (with Roxy Peck) Making Sense of Statistical Studies, a capstone module in statistical thinking for high school students. Daren is also coauthor of the popular text The Practice of Statistics, second and third editions. DANIEL S. YATES has taught AP Statistics in the Electronic Classroom (a distance learning facility affi liated with Henrico County Public Schools in Richmond, Virginia). Before he was a high school teacher, Dan was on the mathematics faculty at Virginia Tech and Randolph-Macon College. He has a PhD in Mathematics Education from Florida State University. He has served as President of the Greater Richmond Council of Teachers of Mathematics and the Virginia Council of Teachers of Mathematics. Named a Tandy Technology Scholar in 1997, Dan is a 2000 recipient of the College Board/Siemens Foundation Advanced Placement Teaching Award. Although recently retired from classroom teaching, he stays in step with trends in teaching by frequently conducting College Board workshops for new and experienced AP Statistics teachers and by monitoring and participating in the AP Statistics electronic discussion group. Dan is coauthor of The Practice of Statistics, fi rst, second, and third editions. DAVID S. MOORE is Shanti S. Gupta Distinguished Professor of Statistics at Purdue University and 1998 President of the American Statistical Association. David is an elected fellow of the American Statistical Association and of the Institute of Mathematical Statistics and an elected member of the International Statistical Institute. He has served as program director for statistics and probability at the National Science Foundation. David has devoted his attention to the teaching of statistics. He was the content developer for the Annenberg/Corporation for Public Broadcasting college-level telecourse Against All Odds: Inside Statistics and for the series of video modules Statistics: Decisions Through Data, intended to aid the teaching of statistics in schools. He is the author of infl uential articles on statistics education and of several leading textbooks, including Introduction to the Practice of Statistics (written with George P. McCabe and Bruce Craig), The Basic Practice of Statistics, Statistics: Concepts and Controversies, The Practice of Business Statistics, The Practice of Statistics in the Life Sciences (written with Brigitte Baldi), and most recently Essential Statistics. vii This page intentionally left blank PREFACE Statistics Through Applications, second edition (STA 2e), is investigate, discuss, and make use of statistical ideas and designed to support a fi rst course in statistics that empha- methods. Examples and exercises have been carefully sizes statistical thinking. The focus of this text is on statistical selected to pique students’ interest and curiosity. Although ideas and reasoning and on their relevance to such fi elds as the text has a fairly relaxed style and demands only an medicine, education, environmental science, business, algebra background, its emphasis on ideas and reasoning psychology, sports, politics, and entertainment. asks more of the student than many texts that emphasize In its publication Principles and Standards for procedures over concepts. School Mathematics, the National Council of Teachers Students learn to think about data by working with data. of Mathematics (NCTM) identifi es “Data Analysis and Consequently, we have included many elementary graphical Probability” as one of fi ve content standards. Here is the and numerical techniques in STA 2e. We have not, however, precise statement of this NCTM standard: allowed techniques to dominate concepts. Our intention is to invite discussion and even argument about statistical ideas Instructional programs from prekindergarten rather than to focus exclusively on computation (though through grade 12 should enable all students to— some computation remains essential). The coverage in STA 2e is considerably broader than that of some traditional • formulate questions that can be addressed with statistics texts, as the table of contents reveals. data and collect, organize, and display relevant data to answer them; • select and use appropriate statistical methods to THE STRUCTURE OF STA 2e analyze data; STA 2e contains 10 chapters organized in four parts: • develop and evaluate inferences and predictions analyzing data, producing data, chance, and inference. Each that are based on data; chapter consists of two or three sections, each devoted to a single coherent set of ideas. Sections are further divided into • understand and apply basic concepts of probability.1 small subsections of material that can be fully addressed in More recently, the American Statistical Association (ASA) a standard 45- or 50-minute high school period. Exercises published its Guidelines for Assessment and Instruction appear at the end of each subsection, section, and chapter. in Statistics Education (GAISE) Pre-K–12 Report to Summaries at the end of each section and chapter help elaborate on the NCTM Data Analysis and Probability students distill what they have learned. standard. The joint curriculum committee of the ASA and the Mathematical Association of America (MAA) THE SECOND EDITION recommends that any fi rst course in statistics “emphasize In revising Statistics Through Applications, we have the elements of statistical thinking” and feature “more attempted to build on the elements that made the fi rst data and concepts, fewer recipes and derivations.”2STA 2e edition successful: incorporates the recommendations made by the NCTM, ASA, and MAA by taking a conceptual and verbal approach • Clear explanations of statistical ideas and rather than a methods-oriented one. terminology are presented. Statistics Through Applications is ideally suited for • Hands-on Activities that allow students to explore a non-AP-level introduction to statistics for high school statistical concepts begin each section. students. It may be used effectively in either a one- or a • Abundant examples from a variety of fi elds two-semester course. illustrate important statistical ideas. • Varied exercises (with descriptive titles) refl ect the THE NATURE OF STA 2e usefulness of statistics in many different subject areas. Statistics Through Applications is written to be read by • Numerous cartoons enliven the pages. students. It is somewhat informal, with thought-provoking stories (“nuggets”) in the margins and cartoons and photo- • More than 30 short marginal nuggets offer graphs interspersed throughout. Activities, Applications, interesting and often amusing anecdotes about and Data Explorations give students an opportunity to statistics and its impact. ix

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