Case Studies and Examples* Chapter Case Study 1.1 Case Study 1.2 Case Study 1.3 Case Study 1.4 Case Study 1.5 Case Study 1.6 Case Study 1.7 Who Are Those Speedy Drivers? Safety in the Skies? Did Anyone Ask Whom You’ve Been Dating? Who Are Those Angry Women? Does Prayer Lower Blood Pressure? Does Aspirin Reduce Heart Attack Rates? Does the Internet Increase Loneliness and Depression? Chapter Example 2.1 Seatbelt Use by Twelfth-Graders 19 Example 2.2 Lighting the Way to Nearsightedness 20 Example 2.3 Humans Are Not Good Randomizers 22 Example 2.4 Revisiting Nightlights and Nearsightedness 23 Example 2.5 Right Handspans 25 Example 2.6 Ages of Death of U.S First Ladies 27 Example 2.7 Histograms for Ages of Death of U.S First Ladies 30 Example 2.8 Big Music Collections 32 Example 2.9 Median and Mean Quiz Scores 37 Example 2.10 Median and Mean Number of CDs Owned 38 Example 2.11 Will “Normal” Rainfall Get Rid of Those Odors? 38 Example 2.12 Range and Interquartile Range for Fastest Speed Ever Driven 41 Example 2.13 Fastest Driving Speeds for Men 42 Example 2.14 Five-Number Summary and Outlier Detection for the Cambridge University Crew Team 43 Example 2.15 Five-Number Summary and Outlier Detection for Music CDs 44 Example 2.16 Tiny Boatmen 48 Example 2.17 The Shape of British Women’s Heights 49 Example 2.18 Calculating a Standard Deviation 51 Example 2.19 Women’s Heights and the Empirical Rule 53 Chapter Example 3.1 Do First Ladies Represent Other Women? 72 Example 3.2 Do Penn State Students Represent Other College Students? 72 Example 3.3 The Importance of Religion for Adult Americans 77 Example 3.4 Would You Eat Those Modified Tomatoes? 77 Example 3.5 Cloning Human Beings 78 Example 3.6 Representing the Heights of British Women 83 Example 3.7 A Los Angeles Times National Poll on the Millennium 88 Example 3.8 The Nationwide Personal Transportation Survey 89 Example 3.9 Which Scientists Trashed the Public? 92 Example 3.10 A Meaningless Poll 93 Example 3.11 Haphazard Sampling 94 Case Study 3.1 The Infamous Literary Digest Poll of 1936 94 Example 3.12 Laid Off or Fired? 96 Example 3.13 Most Voters Don’t Lie but Some Liars Don’t Vote 96 Example 3.14 Why Weren’t You at Work Last Week? 97 Example 3.15 Is Happiness Related to Dating? 98 Example 3.16 When Will Adolescent Males Report Risky Behavior? 98 Example 3.17 Politics Is All in the Wording 99 Example 3.18 Teenage Sex 100 Example 3.19 The Unemployed 100 Case Study 3.2 No Opinion of Your Own? Let Politics Decide 103 Chapter Example 4.1 What Confounding Variables Lurk Behind Lower Blood Pressure? 120 Example 4.2 The Fewer the Pages, the More Valuable the Book? 121 Case Study 4.1 Lead Exposure and Bad Teeth 122 Case Study 4.2 Kids and Weight Lifting 124 Example 4.3 Randomly Assigning Children to Weight-Lifting Groups 127 Case Study 4.3 Quitting Smoking with Nicotine Patches 129 *Examples marked by an asterisk are revisited for further discussion later in the chapter Case Study 4.4 Baldness and Heart Attacks 133 Example 4.4 Will Preventing Artery Clog Prevent Memory Loss? 137 Example 4.5 Dull Rats 139 Example 4.6 Real Smokers with a Desire to Quit 140 Example 4.7 Do Left-Handers Die Young? 140 Chapter Example 5.1 Height and Handspan 152 Example 5.2 Driver Age and the Maximum Legibility Distance of Highway Signs 153 Example 5.3 The Development of Musical Preferences 154 Example 5.4 Heights and Foot Lengths of College Women 156 Example 5.5 Describing Height and Handspan with a Regression Line 158 Example 5.6 Regression for Driver Age and the Maximum Legibility Distance of Highway Signs 161 Example 5.7 Prediction Errors for the Highway Sign Data 162 Example 5.8 Calculating the Sum of Squared Errors 164 Example 5.9 The Correlation Between Handspan and Height 166 Example 5.10 The Correlation Between Age and Sign Legibility Distance 167 Example 5.11 Left and Right Handspans 167 Example 5.12 Verbal SAT and GPA 168 Example 5.13 Age and Hours of Television Viewing per Day 168 Example 5.14 Hours of Sleep and Hours of Study 169 Example 5.15 Height and Foot Length of College Women 172 Example 5.16 Earthquakes in the Continental United States 172 Example 5.17 Does It Make Sense? Height and Lead Feet 173 Example 5.18 Does It Make Sense? U.S Population Predictions 174 Case Study 5.1 A Weighty Issue 179 Chapter Example 6.1 Smoking and the Risk of Divorce 195 Example 6.2 Tattoos and Ear Pierces 196 Example 6.3 Gender and Reasons for Taking Care of Your Body 197 Example 6.4 Smoking and Relative Risk of Divorce 198 Example 6.5 Percent Increase in the Risk of Divorce for Smokers 199 Example 6.6 The Risk of a Shark Attack 201 Example 6.7 Disaster in the Skies? Case Study 1.2 Revisited 202 Example 6.8 Dietary Fat and Breast Cancer 202 Case Study 6.1 Is Smoking More Dangerous for Women? 203 Example 6.9 Educational Status and Driving after Substance Use 204 Example 6.10 Blood Pressure and Oral Contraceptive Use 205 Example 6.11 A Table of Expected Counts 209 Example 6.12 Does Order Influence Who Wins an Election? 211 Example 6.13 Breast Cancer Risk Stops Hormone Replacement Therapy Study 212 Example 6.14 Aspirin and Heart Attacks 214 Case Study 6.2 Drinking, Driving, and the Supreme Court 216 Chapter Case Study 7.1 A Hypothetical Story: Alicia Has a Bad Day 230 Example 7.1 Probability of Male Versus Female Births 232 Example 7.2 A Simple Lottery 233 Example 7.3 The Probability That Alicia Has to Answer a Question 233 Example 7.4 The Probability of Lost Luggage 234 Example 7.5 Nightlights and Myopia Revisited 235 Example 7.6 Days per Week of Drinking Alcohol 238 Example 7.7 Probabilities for Some Lottery Events 239 Example 7.8 The Probability of Not Winning the Lottery 239 Example 7.9 Mutually Exclusive Events for Lottery Numbers 240 Example 7.10 Winning a Free Lunch 241 Example 7.11 The Probability That Alicia Has to Answer a Question 241 Example 7.12 Probability That a Teenager Gambles Depends upon Gender 242 Example 7.13 Probability a Stranger Does Not Share Your Birth Date 243 Example 7.14 Roommate Compatibility 244 Example 7.15 Probability of Either Two Boys or Two Girls in Two Births 245 Example 7.16 Probability That a Randomly Selected Ninth-Grader Is a Male and a Weekly Gambler 246 Example 7.17 Probability That Two Strangers Both Share Your Birth Month 246 Example 7.18 Probability Alicia Is Picked for the First Question Given That She’s Picked to Answer a Question 247 Example 7.19 The Probability of Guilt and Innocence Given a DNA Match 248 Example 7.20 Winning the Lottery 251 Example 7.21 Prizes in Cereal Boxes 252 Example 7.22 Family Composition 253 Example 7.23 Optimism for Alicia—She Is Probably Healthy 254 Example 7.24 Two-Way Table for Teens and Gambling 255 Example 7.25 Alicia’s Possible Fates 256 Example 7.26 The Probability That Alicia Has a Positive Test 257 Example 7.27 Tree Diagram for Teens and Gambling 257 Example 7.28 Getting All the Prizes 259 Example 7.29 Finding Gifted ESP Participants 260 Example 7.30 Two George D Brysons 264 Example 7.31 Identical Cars and Matching Keys 264 Example 7.33 Winning the Lottery Twice 265 Example 7.34 Unusual Hands in Card Games 266 Case Study 7.2 Doin’ the iPod ® Shuffle 268 Chapter Example 8.1 Random Variables at an Outdoor Graduation or Wedding 280 Example 8.2 It’s Possible to Toss Forever 281 Example 8.3 Probability an Event Occurs Three Times in Three Tries 281 Example 8.4 Waiting on Standby 282 Example 8.5 Probability Distribution Function for Number of Courses 283 Example 8.6 Probability Distribution Function for Number of Girls 284 Example 8.7 Graph of pdf for Number of Girls 285 Example 8.8 Cumulative Distribution for the Number of Girls 286 Example 8.9 A Mixture of Children 287 Example 8.10 Probabilities for Sum of Two Dice 287 Example 8.11 Gambling Losses 289 Example 8.12 California Decco Lottery Game 290 Example 8.13 Stability or Excitement—Same Mean, Different Standard Deviations 291 Example 8.14 Mean Hours of Study for the Class Yesterday 293 Example 8.15 Probability of Two Wins in Three Plays 296 Example 8.16 Excel Calculations for Number of Girls in Ten Births 297 Example 8.17 Guessing Your Way to a Passing Score 297 Example 8.18 Is There Extraterrestrial Life? 299 Case Study 8.1 Does Caffeine Enhance the Taste of Cola? 299 Example 8.19 Time Spent Waiting for the Bus 301 Example 8.20 Probability That the Waiting Time is Between and Minutes 301 Example 8.21 College Women’s Heights 303 Example 8.22 The z-Score for a Height of 62 Inches 304 Example 8.23 Probability That Height is Less Than 62 Inches 306 Example 8.24 Probability That Z Is Greater Than 1.31 307 Example 8.25 Probability That Height Is Greater Than 68 Inches 308 Example 8.26 Probability That Z Is Between ؊2.59 and 1.31 308 Example 8.27 Probability That a Vehicle Speed Is Between 60 and 70 mph 309 Example 8.28 The 75th Percentile of Systolic Blood Pressures 310 Example 8.29 The Number of Heads in 30 Flips of a Coin 312 Example 8.30 Political Woes 313 Example 8.31 Guessing and Passing a True-False Test 313 Example 8.32 Will Meg Miss Her Flight? 317 Example 8.33 Can Alison Ever Win? 317 Example 8.34 Donations Add Up 318 Example 8.35 Strategies for Studying When You Are Out of Time 319 Chapter Example 9.1 Example 9.2 Example 9.3 Example 9.4 The “Freshman 15” 334 Opinions About Genetically Modified Food 339 Probability of Quitting with a Nicotine Patch 339 How Much More Likely Are Smokers to Quit with a Nicotine Patch? 340 Example 9.5 Age of First Intercourse for Females 341 Example 9.6 Which Hand Is Bigger? 341 Example 9.7 Do Girls and Boys Have First Intercourse at the Same Age on Average? 342 Example 9.8 Mean Hours of Sleep for College Students 345 Example 9.9 Possible Sample Proportions Favoring a Candidate 351 Example 9.10 Caffeinated or Not? 352 Example 9.11 Men, Women, and the Death Penalty 356 Example 9.12 Hypothetical Mean Weight Loss 360 Example 9.13 Suppose There Is No “Freshman 15” 364 Example 9.14 Who Are the Speed Demons? 367 Example 9.15 Unpopular TV Shows 369 Example 9.16 Standardized Mean Weights 371 Example 9.17 The Long Run for the Decco Lottery Game 374 Example 9.18 California Decco Losses 375 Example 9.19 Winning the Lottery by Betting on Birthdays 377 Example 9.20 Constructing a Simple Sampling Distribution for the Mean Movie Rating 378 Case Study 9.1 Do Americans Really Vote When They Say They Do? 382 Chapter 10 Example 10.1 Teens and Interracial Dating: Case Study 1.3 Revisited 405 Example 10.2 The Pollen Count Must Be High Today 409 Example 10.3 Is There Intelligent Life on Other Planets? 412 Example 10.4 50% Confidence Interval for Proportion Believing That Intelligent Life Exists Elsewhere 413 Example 10.5 College Men and Ear Pierces 415 Example 10.6 Would You Return a Lost Wallet? 415 Example 10.7 Winning the Lottery and Quitting Work 421 Example 10.8 The Gallup Poll Margin of Error for n ؍1000 422 Example 10.9 Allergies and Really Bad Allergies 423 Example 10.10 Snoring and Heart Attacks 425 Example 10.11 Do You Always Buckle Up When Driving? 426 Example 10.12 Which Drink Tastes Better? 429 Case Study 10.1 Extrasensory Perception Works with Movies 429 Case Study 10.2 Nicotine Patches versus Zyban ® 430 Case Study 10.3 What a Great Personality 431 Chapter 11 Example 11.1 Pet Ownership and Stress 446 Example 11.2 Mean Hours per Day That Penn State Students Watch TV 448 Example 11.3 Do Men Lose More Weight by Diet or by Exercise? 449 Example 11.4 Finding the t* Values for 24 Degrees of Freedom and 95% or 99% Confidence Intervals 451 Example 11.5 Are Your Sleeves Too Short? The Mean Forearm Length of Men 454 Example 11.6 How Much TV Do Penn State Students Watch? 455 Example 11.7 What Type of Students Sleep More? 457 Example 11.8 Approximate 95% Confidence Interval for TV Time 460 Example 11.9 Screen Time—Computer Versus TV 463 Example 11.10 Meditation and Anxiety 465 Example 11.11 The Effect of a Stare on Driving Behavior 468 Example 11.12 Parental Alcohol Problems and Child Hangover Symptoms 471 Example 11.13 Confidence Interval for Difference in Mean Weight Losses by Diet or Exercise 472 Example 11.14 Pooled t-Interval for Difference Between Mean Female and Male Sleep Times 474 Example 11.15 Sleep Time with and Without the Equal Variance Assumption 476 Case Study 11.1 Confidence Interval for Relative Risk: Case Study 4.4 Revisited 478 Chapter 12 Example 12.1 Example 12.2 Example 12.3 Example 12.4 Example 12.5 Example 12.6 Example 12.7 Example 12.8 Are Side Effects Experienced by Fewer Than 20% of Patients? 497 Does a Majority Favor the Proposed Blood Alcohol Limit? 498 Psychic Powers 499 Stop the Pain before It Starts 500 A Jury Trial 504 Errors in the Courtroom 504 Errors in Medical Tests 505 Calcium and the Relief of Premenstrual Symptoms 506 Example 12.9 Medical Tests Revisited 507 *Example 12.10 The Importance of Order in Voting 512 *Example 12.11 Do Fewer Than 20% Experience Medication Side Effects? 516 Example 12.12 A Test for Extrasensory Perception 519 Example 12.13 A Two-Sided Test: Are Left and Right Foot Lengths Equal? 520 Example 12.14 Making Sure Students Aren’t Guessing 521 Example 12.15 What Do Men Care About in a Date? 522 Example 12.16 Power and Sample Size for a Survey of Students 524 *Example 12.17 The Prevention of Ear Infections 528 Example 12.18 How the Same Sample Proportion Can Produce Different Conclusions 533 Example 12.19 Birth Month and Height 536 Chapter 13 *Example 13.1 Normal Human Body Temperature 553 Example 13.2 The Effect of Alcohol on Useful Consciousness 562 *Example 13.3 The Effect of a Stare on Driving Behavior 565 Example 13.4 A Two-Tailed Test of Television Watching for Men and Women 568 Example 13.5 Misleading Pooled t-Test for Television Watching for Men and Women 572 Example 13.6 Legitimate Pooled t-Test for Comparing Male and Female Sleep Time 573 Example 13.7 Mean Daily Television Hours of Men and Women 575 Example 13.8 Ear Infections and Xylitol 576 Example 13.9 Kids and Weight Lifting 579 Example 13.10 Loss of Cognitive Functioning 580 Example 13.11 Could Aliens Tell That Women Are Shorter? 582 Example 13.12 Normal Body Temperature 583 Example 13.13 The Hypothesis-Testing Paradox 583 Example 13.14 Planning a Weight-Loss Study 584 Chapter 14 Example 14.1 Residuals in the Handspan and Height Regression 602 Example 14.2 Mean and Deviation for Height and Handspan Regression 604 Example 14.3 Relationship Between Height and Weight for College Men 606 Example 14.4 R for Heights and Weights of College Men 608 Example 14.5 Driver Age and Highway Sign-Reading Distance 608 Example 14.6 Hypothesis Test for Driver Age and Sign-Reading Distance 610 Example 14.7 95% Confidence Interval for Slope Between Age and Sign-Reading Distance 611 Example 14.8 Estimating Mean Weight of College Men at Various Heights 617 Example 14.9 Checking the Conditions for the Weight and Height Problem 620 Case Study 14.1 A Contested Election 623 Chapter 15 Example 15.1 Ear Infections and Xylitol Sweetener 636 Example 15.2 With Whom Do You Find It Easiest to Make Friends? 637 Example 15.3 Calculation of Expected Counts and Chi-Square for the Xylitol and Ear Infection Data 639 Example 15.4 p-Value Area for the Xylitol Example 641 Example 15.5 Using Table A.5 for the Xylitol and Ear Infection Problem 642 Example 15.6 A Moderate p-Value 643 Example 15.7 A Tiny p-Value 643 Example 15.8 Making Friends 644 Example 15.9 Gender, Drinking, and Driving 647 Example 15.10 Age and Tension Headaches 648 Example 15.11 Sheep, Goats, and ESP 649 Example 15.12 Butterfly Ballots 650 Example 15.13 The Pennsylvania Daily Number 654 Case Study 15.1 Do You Mind If I Eat the Blue Ones? 657 Chapter 16 Example 16.1 Example 16.2 Example 16.3 Example 16.4 Classroom Seat Location and Grade Point Average 670 Application of Notation to the GPA and Classroom Seat Sample 672 Assessing the Necessary Conditions for the GPA and Seat Location Data 673 Occupational Choice and Testosterone Level 674 Example 16.5 The p-Value for the Testosterone and Occupational Choice Example 676 Example 16.6 Pairwise Comparisons of GPAs Based on Seat Locations 677 Example 16.7 Comparison of Weight-Loss Programs 680 Example 16.8 Analysis of Variation Among Weight Losses 681 Example 16.9 Top Speeds of Supercars 683 Example 16.10 95% Confidence Intervals for Mean Car Speeds 684 Example 16.11 Drinks per Week and Seat Location 685 Example 16.12 Kruskal–Wallis Test for Alcoholic Beverages per Week by Seat Location 687 Example 16.13 Mood’s Median Test for the Alcoholic Beverages and Seat Location Example 688 Example 16.14 Happy Faces and Restaurant Tips 690 Example 16.15 You’ve Got to Have Heart 691 Example 16.16 Two-Way Analysis of Variance for Happy Face Example 692 Chapter 17 Example 17.1 Example 17.2 Example 17.3 Example 17.4 Example 17.5 Example 17.6 Example 17.7 Example 17.8 Example 17.9 Playing the Lottery 710 Surgery or Uncertainty? 710 Fish Oil and Psychiatric Disorders 711 Go, Granny, Go or Stop, Granny, Stop? 713 When Smokers Butt Out, Does Society Benefit? 714 Is It Wining or Dining That Helps French Hearts? 716 Give Her the Car Keys 717 Lifestyle Statistics from the Census Bureau 718 In Whom Do We Trust? 719 Supplemental Topic *Example S1.1 *Example S1.2 Example S1.3 Example S1.4 Example S1.5 Example S1.6 Example S1.7 Random Security Screening S1-3 Betting Birthdays for the Lottery S1-3 Customers Entering a Small Shop S1-8 Earthquakes in the Coming Year S1-10 Emergency Calls to a Small Town Police Department S1-10 Are There Illegal Drugs in the Next 5000 Cars? S1-11 Calling On the Back of the Class S1-13 Supplemental Topic Example S2.1 Example S2.2 *Example S2.3 Example S2.4 Example S2.5 Example S2.6 Normal Human Body Temperature S2-5 Heights of Male Students and Their Fathers S2-6 Estimating the Size of Canada’s Population S2-9 Calculating T ؉ for a Sample of Systolic Blood Pressures S2-13 Difference Between Student Height and Mother’s Height for College Women S2-14 Comparing the Quality of Wine Produced in Three Different Regions S2-17 Supplemental Topic *Example S3.1 Predicting Average August Temperature S3-3 *Example S3.2 Blood Pressure of Peruvian Indians S3-4 Supplemental Topic *Example S4.1 *Example S4.2 Example S4.3 Example S4.4 Example S4.5 Sleep Hours Based on Gender and Seat Location S4-2 Pulse Rates, Gender, and Smoking S4-6 Nature Versus Nurture in IQ Scores S4-14 Happy Faces and Restaurant Tips Revisited S4-16 Does Smoking Lead to More Errors? S4-18 Supplemental Topic Example S5.1 Stanley Milgram’s “Obedience and Individual Responsibility” Experiment S5-3 Example S5.2 Janet’s (Hypothetical) Dissertation Research S5-12 Example S5.3 Jake’s (Hypothetical) Fishing Expedition S5-14 Example S5.4 The Debate Over Passive Smoking S5-15 Example S5.5 Helpful and Harmless Outcomes from Hormone Replacement Therapy S5-18 Case Study S5.1 Science Fair Project or Fair Science Project? S5-19 Mind on Statistics Third Edit ion Jessica M Utts University of California, Davis Robert F Heckard Pennsylvania State University Australia • Brazil • Canada • Mexico • Singapore Spain • United Kingdom • United States Mind on Statistics, Third Edition Jessica M Utts and Robert F Heckard Senior Acquisitions Editor: Carolyn Crockett Development Editor: Danielle Derbenti Senior Assistant Editor: Ann Day Technology Project Manager: Fiona Chong Marketing Manager: Joseph Rogove Marketing Assistant: Brian R Smith Marketing Communications Manager: Darlene AmidonBrent Project Manager, Editorial Production: Sandra Craig Creative Director: Rob Hugel Art Director: Lee Friedman Print Buyer: Barbara Britton Permissions Editor: Kiely Sisk Production Service: Martha Emry Text Designer: tani hasegawa Photo Researcher: Stephen Forsling Copy Editor: Barbara Willette Illustrator: Lori Heckelman Cover Designer: Lee Friedman Cover Image: © Jack Hollingsworth/Corbis Cover Printer: Phoenix Color Corp Compositor: G & S Book Services Printer: R.R Donnelley/Willard © 2007 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 Thomson Higher Education 10 Davis Drive Belmont, CA 94002-3098 USA 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 photocopying, recording, taping, web distribution, information storage and retrieval systems, or in any other manner— without the written permission of the publisher Printed in the United States of America 09 08 07 06 05 © 2007 Thomson Learning, Inc All Rights Reserved Thomson Learning WebTutor™ is a trademark of Thomson Learning, Inc Library of Congress Control Number: 2005931910 ISBN 0-534-99864-X For more information about our products, contact us at: Thomson Learning Academic Resource Center 1-800-423-0563 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 Bill Harkness— energetic, generous, and innovative educator, guide, and friend—who launched our careers in statistics and continues to share his vision Brief Contents Statistics Success Stories and Cautionary Tales Relationships Between Quantitative Variables 10 11 12 13 14 15 16 17 iv Turning Data Into Information 12 Sampling: Surveys and How to Ask Questions 70 Gathering Useful Data for Examining Relationships 116 Relationships Between Categorical Variables Probability 150 192 228 Random Variables 278 Understanding Sampling Distributions: Statistics as Random Variables 330 Estimating Proportions with Confidence Estimating Means with Confidence 442 Testing Hypotheses About Proportions Testing Hypotheses About Means Inference About Simple Regression 400 494 550 598 More About Inference for Categorical Variables Analysis of Variance 668 Turning Information Into Wisdom 704 634 Contents Statistics Success Stories and Cautionary Tales 1.1 What Is Statistics? 1.2 Seven Statistical Stories with Morals 1.3 The Common Elements in the Seven Stories Key Terms Exercises Turning Data Into Information 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 12 Raw Data 13 Types of Variables 15 Summarizing One or Two Categorical Variables 19 Exploring Features of Quantitative Data with Pictures Numerical Summaries of Quantitative Variables 36 How to Handle Outliers 47 Features of Bell-Shaped Distributions 49 Skillbuilder Applet: The Empirical Rule in Action 56 24 Key Terms 57 Exercises 58 Sampling: Surveys and How to Ask Questions 70 3.1 3.2 3.3 3.4 3.5 Collecting and Using Sample Data Wisely 71 Margin of Error, Confidence Intervals, and Sample Size Choosing a Simple Random Sample 80 Other Sampling Methods 83 Difficulties and Disasters in Sampling 89 75 v vi Contents 3.6 How to Ask Survey Questions 95 3.7 Skillbuilder Applet: Random Sampling in Action 103 Key Terms 106 Exercises 106 Gathering Useful Data for Examining Relationships 4.1 4.2 4.3 4.4 116 Speaking the Language of Research Studies 117 Designing a Good Experiment 124 Designing a Good Observational Study 133 Difficulties and Disasters in Experiments and Observational Studies 136 Key Terms 141 Exercises 142 Relationships Between Quantitative Variables 150 5.1 5.2 5.3 5.4 5.5 5.6 Looking for Patterns with Scatterplots 152 Describing Linear Patterns with a Regression Line 157 Measuring Strength and Direction with Correlation 165 Regression and Correlation Difficulties and Disasters 171 Correlation Does Not Prove Causation 176 Skillbuilder Applet: Exploring Correlation 178 Key Terms 181 Exercises 181 Relationships Between Categorical Variables 192 6.1 6.2 6.3 6.4 Displaying Relationships Between Categorical Variables 193 Risk, Relative Risks, and Misleading Statistics About Risk 198 The Effect of a Third Variable and Simpson’s Paradox 204 Assessing the Statistical Significance of a ϫ Table 206 Key Terms 216 Exercises 217 Probability 228 7.1 Random Circumstances 229 7.2 Interpretations of Probability 231 ... testing HT Module HT for one population proportion HT Module HT for difference in two population proportions CI Module CI for one population mean CI Module CI for population mean of paired differences... chapter, use the Options button, and click on “Use test and interval based on normal distribution.” Note also that the confidence level can be changed by using the Options button xx Preface: Tools... complete online content for your introductory statistics course It promotes learning through interaction on the Web and can be used as the sole text for a course or in conjunction with a traditional