Sullivan’s Pathway to Making an Informed Decision Begin your journey… Making an Informed Decision projects at the start of each chapter allow you to work with data in order to make informed decisions that impact your life. Putting It Together overviews show how material you are about to cover relates to prior material. Preparation is key… Preparing for This Section lists all of the skills needed to be successful. Preparing for This Section Quizzes are available online to help you check your mastery. Each Objective is listed at the beginning of the section and then repeated in the text for easy reference. Look at the model then practice, practice, practice… Step-by-Step Annotated Examples illustrate new concepts and methods in 3 steps: 1. Problem 2. Approach 3. Solution Examples point to Now Work Exercises so you can solve similar exercises on your own. Exercise Sets… Putting It Together exercises use skills you’ve acquired in various chapters. (See facing page) You Explain It! exercises ask you to provide an interpretation of statistical results. Check where you’ve been and test your mastery… Putting It Together Sections require you to decide which technique to use when performing inference. (See facing page) End-of-Chapter Objectives are listed with page references for easy review. Chapter Tests provide an opportunity to test your knowledge. Apply yourself… In-Class Activities in the Student Activity Workbook allow you to experience statistics in a fun and exciting way by experiencing the process firsthand. End-of-Chapter Case Studies tie statistical concepts together within an interesting application. Sullivan’s Guide to Putting It Together Putting It Together Sections Objective Page(s) 5.6 Putting It Together: Which Method 1 Determine the appropriate probability rule to use 308–309 Do I Use? 2 Determine the appropriate counting technique to use 309–311 9.5 Putting It Together: Which Method 1 Determine the appropriate confidence interval to construct 461–462 Do I Use? 10.6 Putting It Together: Which Method 1 Determine the appropriate hypothesis test to perform (one sample) 514 Do I Use? 11.5 Putting It Together: Which Method 1 Determine the appropriate hypothesis test to perform (two samples) 576–577 Do I Use? Section(s) Putting It Together Exercises Skills Utilized Covered Page(s) 1.2.23 Passive Smoke Variables, observational studies, designed experiments 1.1, 1.2 21 1.4.37 Comparing Sampling Methods Simple random sampling and other sampling techniques 1.3, 1.4 38 1.4.38 Thinking about Randomness Random sampling 1.3, 1.4 38 1.5.35 Speed Limit Population, variables, level of measurement, sampling, bias 1.1–1.5 44 1.6.33 Mosquito Control Population, variables, design of experiments 1.1, 1.6 56 2.1.30 Online Homework Variables, designed experiments, bar graphs 1.1, 1.2, 1.6, 2.1 78–79 2.2.51 Time Viewing a Webpage Graphing data 2.2 99–100 2.3.23 Shark! Graphing data 2.3 109 3.1.43 Shape, Mean, and Median Discrete vs. continuous data, histograms, shape of a distribution, 1.1, 1.4, 2.2, 3.1 140 mean, median, mode, bias 3.5.17 Paternal Smoking Observational studies, designed experiments, lurking variables, 1.2, 1.6, 3.1, 3.2, 180–181 mean, median, standard deviation, quartiles, boxplots 3.4, 3.5 4.2.28 Housing Prices Scatter diagrams, correlation, linear regression 4.1, 4.2 219 4.2.29 Smoking and Birth Weight Observational study vs. designed experiment, prospective studies, 1.2, 4.1, 4.2 219–220 scatter diagrams, linear regression, correlation vs. causation, lurking variables 4.3.31 Building a Financial Model Scatter diagrams, correlation, linear regression, residual analysis 4.1, 4.2, 4.3 232–233 5.1.54 Drug Side Effects Variables, graphical summaries of data, experiments, probability 1.1, 1.6, 2.1, 5.1 268 5.2.47 Red Light Cameras Variables, relative frequency distributions, bar graphs, mean, 1.1, 2.1, 3.1, 3.2, 279–280 standard deviation, probability, Simpson’s Paradox 4.4, 5.1, 5.2 5.2.48 Exam Scores Relative frequency distributions, mean, median, standard deviation, 2.2, 3.1, 3.2, 5.1, 5.2 280 interquartile range, classical probability, Addition Rule for Disjoint Events 6.1.37 Sullivan Statistics Survey Mean, standard deviation, probability, probability distributions 3.1, 3.2, 5.1, 6.1 333 7.2.52 Birth Weights Relative frequency distribution, histograms, mean and standard 2.1, 2.2, 3.3, 7.2 380 deviation from grouped data, normal probabilities 8.1.33 Playing Roulette Probability distributions, mean and standard deviation of a random 6.1, 8.1 413 variable, sampling distributions 9.1.45 Hand Washing Observational studies, bias, confidence intervals 1.2, 1.5, 9.1 438–439 9.2.53 Smoking Cessation Study Experimental design, confidence intervals 1.6, 9.1, 9.2 453 10.2.40 Lupus Observational studies, retrospective vs. prospective studies, bar 1.2, 2.1, 9.1, 10.2 495 graphs, confidence intervals, hypothesis testing 10.2.41 Naughty or Nice? Experimental design, determining null and alternative hypotheses, 1.6, 6.2, 10.1, 10.2 495–496 binomial probabilities, interpreting P-values 10.3.38 Analyzing a Study Statistical process, confidence intervals, hypothesis testing, 1.1, 1.2, 9.1, 10.1, 506 Case-control studies 10.2 10.5.21 Ideal Number of Children Relative frequency histogram, mode, mean, standard deviation, 2.2, 3.1, 3.2, 516 Central Limit Theorem, hypothesis testing 8.1,10.2 11.1.41 Salk Vaccine Completely randomized design, hypothesis testing 1.6, 11.1 543 11.2.18 Glide Testing Matched pairs design, hypothesis testing 1.6, 11.2 553 11.3.25 Online Homework Completely randomized design, confounding, hypothesis testing 1.6, 11.3 565 12.1.29 The V-2 Rocket in London Mean of discrete data; expected value; Poisson probability 6.1, 6.3, 12.1 598 distribution; goodness-of-fit Section(s) Putting It Together Exercises Skills Utilized Covered Page(s) 12.1.30 Weldon’s Dice Addition Rule for Disjoint Events, Classical Probability, 5.1, 5.2, 12.1 598 Goodness-of-Fit 12.2.21 Women, Aspirin, and Heart Population; sample; variables; observational study vs. designed 1.1, 1.2, 1.6, 612–613 Attacks experiment; experimental design; compare two proportions; 11.1, 12.2 chi-square test of homogeneity 13.1.27 Psychological Profiles Standard deviation; sampling methods; Two-sample t-test; Central 1.4, 3.2, 8.1, 636 Limit Theorem; One-way Analysis of Variance 11.2, 13.1 13.2.17 Time to Complete a Degree Observational studies; sample mean; sample standard deviation; 1.2, 3.1, 3.2, 9.2, 644–645 Confidence intervals for a mean; One-way Analysis of Variance; 13.1, 13.2 Tukey’s test 13.4.22 Students at Ease Population; Designed experiments versus observational studies, 1.1, 1.2, 3.1, 668–669 Variables; sample means; sample standard deviation; Two sample 3.2, 11.3, t-tests; One-way ANOVA, Interaction effects; Non-sampling error 13.1, 13.4 14.2.17 Plasma Television Prices Scatter diagrams; correlation coefficient; linear relations; 4.1, 4.2, 4.3, 698 least-squares regression; residual analysis; confidence and 14.1, 14.2 prediction intervals; lurking variables 14.3.35 Purchasing Diamonds Level of measurement; correlation matrix; multiple regression; 1.1, 14.3 726–727 confidence and prediction intervals New to this edition is the Student Activity Workbook. The Activity Workbook includes many tactile activities for the classroom. In addition, the workbook includes activities based on statistical applets. Below is a list of the applet activities. Applet Section Activity Name Description Mean versus 3.1 Understanding Measures Observe the effect of outliers on mean and median. Use Applet to construct data median of Center sets for a given relationship between the mean and median. Standard 3.2 Exploring Standard Deviation Create data set with given standard deviation to learn properties of this measure deviation of dispersion. Correlation by 4.1 Limitations of the Linear Explore the properties of Pearson’s linear correlation coefficient. Eye Correlation Coefficient Regression by 4.2 Minimizing the Sum of the Experiment with identifying the line of best fit using the sum of squared residuals. Eye Squared Residuals Regression by 4.2 Investigating Outliers and Explore the role outliers and influential points play in determining the Eye Influential Points least-squares regression line. Simulating 5.1 Demonstrating the Law of Simulate flipping a fair and a biased coin to help understand the Law of Large Flipping a Coin Large Numbers Numbers and the interpretation of probability. Binomial 6.2 Exploring a Binomial Explore a binomial distribution through multiple methods. Use a card simulation Distribution Distribution from Multiple to construct a probability distribution for a binomial situation. Then use an applet Perspectives and compare the two distributions obtained. Finally develop a mathematical model. Sampling 8.1 Sampling from Normal and Obtain samples from normal, uniform, and skewed distributions and analyze Distributions Non-normal Populations center, spread, and shape of distribution of sample means. Sampling 8.2 Describing the Distribution Obtain samples from binary population and analyze center, spread, and shape of Distributions of the Sample Proportion distribution of sample proportions. Confidence 9.1 Exploring the Effects of Explore the roles of confidence level and sample size when estimating a Intervals for a Confidence Level, Sample proportion. Proportion Size, and Shape Confidence 9.2 Exploring the Effects of Explore the roles of confidence level and sample size when estimating a mean. Intervals for a Confidence Level and Mean Sample Size Hypothesis Tests 10.2 Understanding Type I Error Explore effect of sample size on probability of making a type I error in hypothesis for a Proportion Rates tests for a proportion. Hypothesis Tests 10.3 Understanding Type I Error Explore effect of sample size on probability of making a type I error in hypothesis for a Mean Rates tests for a mean. Randomization 11.1 Making an Inference about Simulate randomly assigning treatments between two samples to approximate the Test for Two Two Proportions P-value of the hypothesis test. Proportions Randomization 14.1 Using a Randomization Test Simulate randomly assigning observations for bivariate data to approximate the Test for for Correlation P-value for testing whether a significant relation exists between the explanatory Correlation and response variables. FOURTH Statistics EDITION Informed Decisions Using Data Michael Sullivan, III Joliet Junior College Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Editor in Chief, Mathematics and Statistics Deirdre Lynch Acquisitions Editor Christopher Cummings NOTICE: Senior Content Editor Joanne Dill Editorial Assistant Sonia Ashraf This work is Development Editor Lenore Parens protected by U.S. Senior Managing Editor Karen Wernholm copyright laws and Associate Managing Editor Tamela Ambush is provided solely for Marketing Manager Erin Lane Marketing Assistant Kathleen DeChavez the use of college Digital Assets Manager Marianne Groth instructors in review- Supplements Production Coordinator Katherine Roz ing course materials Media Producer Vicki Dreyfus QA Manager, Assessment Content Marty Wright for classroom use. 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Where those designations appear in this book, and Pearson Education was expected to abide aware of a trademark claim, the designations have been printed in initial caps or all caps. by these restrictions Library of Congress Cataloging-in-Publication Data and to honor the Sullivan, Michael, 1967 July 2- intended pedagogi- Statistics: informed decisions using data / Michael Sullivan, III. — 4th ed. cal purposes and p.cm. the needs of other Includes index ISBN 0-321-75727-0 instructors who rely 1. Statistics—Textbooks. I. Title. on these materials. QA276.12.S85 2013 519.5–dc22 2011004653 Copyright © 2013, 2010, 2007, 2004 Pearson Education, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. For information on obtaining permission for use of material in this work, please submit a written request to Pearson Education, Inc., Rights and Contracts Department, 501 Boylston Street, Suite 900, Boston, MA 02116, fax your request to 617-671-3447, or e-mail at http://www.pearsoned.com/legal/permissions.htm. 1 2 3 4 5 6 7 8 9 10—QGD—15 14 13 12 11 ISBN 13: 978-0-321-75727-2 www.pearsonhighered.com ISBN 10: 0-321-75727-0 To My Wife Yolanda and My Children Michael, Kevin, and Marissa This page intentionally left blank Contents Preface to the Instructor xi Supplements xvii Technology Resources xviii Applications Index xxi PART 1 Getting the Information You Need 1 CHAPTER 1 Data Collection 2 1.1 Introduction to the Practice of Statistics 3 1.2 Observational Studies versus Designed Experiments 15 1.3 Simple Random Sampling 22 1.4 Other Effective Sampling Methods 30 1.5 Bias in Sampling 38 1.6 The Design of Experiments 45 Chapter 1 Review 57 Chapter Test 61 Making an Informed Decision: What College Should I Attend? 62 Case Study: Chrysalises for Cash 63 PART 2 Descriptive Statistics 65 CHAPTER 2 Organizing and Summarizing Data 66 2.1 Organizing Qualitative Data 67 2.2 Organizing Quantitative Data: The Popular Displays 81 2.3 Additional Displays of Quantitative Data 101 2.4 Graphical Misrepresentations of Data 110 Chapter 2 Review 118 Chapter Test 122 Making an Informed Decision: Tables or Graphs? 124 Case Study: The Day the Sky Roared 125 CHAPTER 3 Numerically Summarizing Data 127 3.1 Measures of Central Tendency 128 3.2 Measures of Dispersion 141 3.3 Measures of Central Tendency and Dispersion from Grouped Data 158 3.4 Measures of Position and Outliers 164 3.5 The Five-Number Summary and Boxplots 174 v vi CONTENTS Chapter 3 Review 182 Chapter Test 185 Making an Informed Decision: What Car Should I Buy? 187 Case Study: Who Was “A Mourner”? 188 CHAPTER 4 Describing the Relation between Two Variables 190 4.1 Scatter Diagrams and Correlation 191 4.2 Least-Squares Regression 207 4.3 Diagnostics on the Least-Squares Regression Line 221 4.4 Contingency Tables and Association 235 4.5 Nonlinear Regression: Transformations (on CD) 4-1 Chapter 4 Review 245 Chapter Test 250 Making an Informed Decision: Relationships among Variables on a World Scale 251 Case Study: Thomas Malthus, Population, and Subsistence 252 PART 3 Probability and Probability Distributions 253 CHAPTER 5 Probability 254 5.1 Probability Rules 255 5.2 The Addition Rule and Complements 269 5.3 Independence and the Multiplication Rule 280 5.4 Conditional Probability and the General Multiplication Rule 286 5.5 Counting Techniques 296 5.6 Putting It Together: Which Method Do I Use? 308 5.7 Bayes’s Rule (on CD) 5-1 Chapter 5 Review 313 Chapter Test 317 Making an Informed Decision: The Effects of Drinking and Driving 318 Case Study: The Case of the Body in the Bag 319 CHAPTER 6 Discrete Probability Distributions 321 6.1 Discrete Random Variables 322 6.2 The Binomial Probability Distribution 333 6.3 The Poisson Probability Distribution 347 6.4 The Hypergeometric Probability Distribution (on CD) 6-1 Chapter 6 Review 354 Chapter Test 356 Making an Informed Decision: Should We Convict? 357 Case Study: The Voyage of the St. Andrew 358