Introduction to probability and statistics 14th by mendenhall

Giáo trình Introduction to probability and statistics 14th by mendenhall Tài liệu Introduction to probability and statistics 14th by mendenhall Giáo trình Introduction to probability and statistics 14th by mendenhall Tài liệu Introduction to probability and statistics 14th by mendenhall Giáo trình Introduction to probability and statistics 14th by mendenhall Tài liệu Introduction to probability and statistics 14th by mendenhall Giáo trình Introduction to probability and statistics 14th by mendenhall Tài liệu Introduction to probability and statistics 14th by mendenhall Giáo trình Introduction to probability and statistics 14th by mendenhall Tài liệu Introduction to probability and statistics 14th by mendenhall Giáo trình Introduction to probability and statistics 14th by mendenhall Tài liệu Introduction to probability and statistics 14th by mendenhall

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Introduction to Probability and Statistics

William Mendenhall, III

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Introduction to Probability and Statistics, Fourteenth Edition Mendenhall/Beaver/Beaver

Editor in Chief: Michelle Julet Publisher: Richard Stratton Senior Sponsoring Editor: Molly Taylor Assistant Editor: Shaylin Walsh Editorial Assistant: Alexander Gontar Associate Media Editor: Andrew Coppola Marketing Director: Mandee Eckersley Senior Marketing Manager: Barb Bartoszek Marketing Coordinator: Michael Ledesma Marketing Communications Manager:

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Every time you pick up a newspaper or a magazine, watch TV, or surf the Internet, youencounter statistics Every time you fill out a questionnaire, register at an online website,

or pass your grocery rewards card through an electronic scanner, your personal mation becomes part of a database containing your personal statistical information Youcannot avoid the fact that in this information age, data collection and analysis are anintegral part of our day-to-day activities In order to be an educated consumer and citi-zen, you need to understand how statistics are used and misused in our daily lives

infor-THE SECRET TO OUR SUCCESS

The first college course in introductory statistics that we ever took used Introduction to

Probability and Statistics by William Mendenhall Since that time, this text—currently

in the fourteenth edition—has helped several generations of students understand whatstatistics is all about and how it can be used as a tool in their particular area of applica-

tion The secret to the success of Introduction to Probability and Statistics is its ability

to blend the old with the new With each revision we try to build on the strong points

of previous editions, while always looking for new ways to motivate, encourage, andinterest students using new technological tools

HALLMARK FEATURES OF THE FOURTEENTH EDITION

The fourteenth edition retains the traditional outline for the coverage of descriptive andinferential statistics This revision maintains the straightforward presentation of thethirteenth edition In this spirit, we have continued to simplify and clarify the languageand to make the language and style more readable and “user friendly”—without sacri-ficing the statistical integrity of the presentation Great effort has been taken to explainnot only how to apply statistical procedures, but also to explain

• how to meaningfully describe real sets of data

• what the results of statistical tests mean in terms of their practical applications

• how to evaluate the validity of the assumptions behind statistical tests

• what to do when statistical assumptions have been violated

Preface

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In the tradition of all previous editions, the variety and number of real applications inthe exercise sets is a major strength of this edition We have revised the exercise sets toprovide new and interesting real-world situations and real data sets, many of which aredrawn from current periodicals and journals The fourteenth edition contains over 1300problems, many of which are new to this edition A set of classic exercises compiledfrom previous editions is available on the website (http://www.cengage com/statistics/mendenhall) Exercises are graduated in level of difficulty; some, involving only basictechniques, can be solved by almost all students, while others, involving practicalapplications and interpretation of results, will challenge students to use more sophisti-cated statistical reasoning and understanding

Organization and Coverage

We believe that Chapters 1 through 10—with the possible exception of Chapter 3—should be covered in the order presented The remaining chapters can be covered in anyorder The analysis of variance chapter precedes the regression chapter, so that theinstructor can present the analysis of variance as part of a regression analysis Thus, themost effective presentation would order these three chapters as well

Chapters 1–3 present descriptive data analysis for both one and two variables,

us-ing both MINITAB and Microsoft Excel®graphics Chapter 4 includes a full tion of probability and probability distributions Three optional sections—CountingRules, the Total Law of Probability, and Bayes’ Rule—are placed into the generalflow of text, and instructors will have the option of complete or partial coverage Thesections that present event relations, independence, conditional probability, and theMultiplication Rule have been rewritten in an attempt to clarify concepts that oftenare difficult for students to grasp As in the thirteenth edition, the chapters on analy-sis of variance and linear regression include both calculational formulas and computerprintouts in the basic text presentation These chapters can be used with equal ease

presenta-by instructors who wish to use the “hands-on” computational approach to linear gression and ANOVA and by those who choose to focus on the interpretation of com-puter-generated statistical printouts

re-One important feature in the hypothesis testing chapters involves the emphasis on

p-values and their use in judging statistical significance With the advent of

computer-generated p-values, these probabilities have become essential components in

report-ing the results of a statistical analysis As such, the observed value of the test statistic

and its p-value are presented together at the outset of our discussion of statistical

hy-pothesis testing as equivalent tools for decision-making Statistical significance is

de-fined in terms of preassigned values of a, and the p-value approach is presented as

an alternative to the critical value approach for testing a statistical hypothesis amples are presented using both the p-value and critical value approaches to hypoth-

Ex-esis testing Discussion of the practical interpretation of statistical results, along withthe difference between statistical significance and practical significance, is emphasized

in the practical examples in the text

Special Features of the Fourteenth Edition

• NEED TO KNOW .: A special feature of this edition are highlighted sections

sections provide information consisting of definitions, procedures or step-by-step

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hints on problem solving for specific questions such as “NEED TO KNOW… How

to Construct a Relative Frequency Histogram?” or “NEED TO KNOW… How toDecide Which Test to Use?”

• Applets: Easy access to the Internet has made it possible for students to visualizestatistical concepts using an interactive webtool called an applet Applets written

by Gary McClelland, author of Seeing StatisticsTM ,are found on the CourseMate

Website that accompanies the text Following each applet, appropriateexercises are available that provide visual reinforcement of the concepts pre-sented in the text Applets allow the user to perform a statistical experiment, tointeract with a statistical graph, to change its form, or to access an interactive

“statistical table.”

• Graphical and numerical data description includes both traditional and EDA

methods, using computer graphics generated by MINITAB 16 for Windows and

MS Excel

PREFACE ❍ v

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“black box.” Rather, we choose to use the computational shortcuts and interactive visualtools that modern technology provides to give us more time to emphasize statistical rea-soning as well as the understanding and interpretation of statistical results.

In this edition, students will be able to use computers for both standard statisticalanalyses and as a tool for reinforcing and visualizing statistical concepts Both MS Excel

and MINITAB 16 (consistent with earlier versions of MINITAB) are used exclusively

as the computer packages for statistical analysis However, we have chosen to isolatethe instructions for generating computer output into individual sections called Tech-nology Today at the end of each chapter Each discussion uses numerical examples toguide the student through the MS Excel commands and option necessary for the pro-cedures presented in that chapter, and then present the equivalent steps and commands

needed to produce the same or similar results using MINITAB We have included screen captures from both MS Excel and MINITAB 16, so that the student can actually work

through these sections as “mini-labs.”

If you do not need “hands-on” knowledge of MINITAB or MS Excel, or if you are

using another software package, you may choose to skip these sections and simplyuse the printouts as guides for the basic understanding of computer printouts

• All examples and exercises in the text contain printouts based on MINITAB 16 and consistent with earlier versions of MINITAB or MS Excel Printouts are pro-

vided for some exercises, while other exercises require the student to obtain lutions without using a computer

so-1.47 Presidential Vetoes Here is a list of the

44 presidents of the United States along with the number of regular vetoes used by each: 5 Washington 2 B Harrison 19

Source: The World Almanac and Book of Facts 2011

Use an appropriate graph to describe the number of vetoes cast by the 44 presidents Write a summary paragraph describing this set of data.

1.48 Windy Cities Are some cities more windy than others? Does Chicago deserve to be

(1950) 121.3 122.3 121.3 122.0 123.0 121.4 123.2 122.1 125.0 122.1 (1960) 122.2 124.0 120.2 121.4 120.0 121.1 122.0 120.3 122.1 121.4 (1970) 123.2 123.1 121.4 119.2 † 124.0 122.0 121.3 122.1 121.1 122.2 (1980) 122.0 122.0 122.2 122.1 122.2 120.1 122.4 123.2 122.2 125.0 (1990) 122.0 123.0 123.0 122.2 123.3 121.1 121.0 122.4 122.2 123.2 (2000) 121.0 119.97 121.13 121.19 124.06 122.75 121.36 122.17 121.86 122.66 (2010) 124.4

†

Record time set by Secretariat in 1973.

Source: www.kentuckyderby.com

a Do you think there will be a trend in the winning

times over the years? Draw a line chart to verify your answer.

b Describe the distribution of winning times using an

appropriate graph Comment on the shape of the distribution and look for any unusual observations.

1.50 Gulf Oil Spill Cleanup On April 20,

2010, the United States experienced a major environmental disaster when a Deepwater Horizon drilling rig exploded in the Gulf of Mexico The number of personnel and equipment used in the Gulf oil spill cleanup, beginning May 2, 2010 (Day 13) through June 9, 2010 (Day 51) is given in the following table 13

Day 13 Day 26 Day 39 Day 51 Number of personnel (1000s) 3.0 17.5 20.0 24.0 Federal Gulf fishing areas closed 3% 8% 25% 32%

Dispersants used (1000 gallons) 156 500 870 1143 EX0147

EX0148

EX0150

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PREFACE ❍ vii

Any student who has Internet access can use the applets found on the CourseMateWebsite to visualize a variety of statistical concepts (access instructions for theCourseMate Website are listed on the Printed Access Card that is an optional bundle withthis text) In addition, some of the applets can be used instead of computer software toperform simple statistical analyses Exercises written specifically for use with these appletsalso appear on the CourseMate Website Students can use the applets at home or in acomputer lab They can use them as they read through the text material, once they havefinished reading the entire chapter, or as a tool for exam review Instructors can use theapplets as a tool in a lab setting, or use them for visual demonstrations during lectures

We believe that these applets will be a powerful tool that will increase student asm for, and understanding of, statistical concepts and procedures

enthusi-STUDY AIDS

The many and varied exercises in the text provide the best learning tool for studentsembarking on a first course in statistics The answers to all odd-numbered exercises are

given in the back of the text, and a detailed solution appears in the Student Solutions

Manual, which is available as a supplement for students Each application exercise has

Numerical Descriptive Measures in Excel

MS Excel provides most of the basic descriptive statistics presented in Chapter

a single command on the Data tab Other descriptive statistics can be calculate the Function command on the Formulas tab.

The following data are the front and rear leg rooms (in inches) for nine differenutility vehicles:14

Make & Model Front Leg Room Rear Leg Room Acura MDX 41.0 28.5 Buick Enclave 41.5 30.0 Chevy TrailBlazer 40.0 25.5 Chevy Tahoe Hybrid V8 CVT 41.0 27.5 GMC Terrain 1LT 4-cyl 43 0 31 0

E X A M P L E 2.15

Numerical Descriptive Measures in MINITAB

MINITAB provides most of the basic descriptive statistics presented in Chapter 2 using a

single command in the drop-down menus

The following data are the front and rear leg rooms (in inches) for nine different sportsutility vehicles:14

Make and Model Front Leg Room Rear Leg Room Acura MDX 41.0 28.5 Buick Enclave 41.5 30.0 Chevy TrailBlazer 40.0 25.5 Chevy Tahoe Hybrid V8 CVT 41.0 27.5 GMC Terrain 1LT 4-cyl 43.0 31.0 Honda CR-V 41.0 29.5

H ndai T cson 42 5 29 5

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a title, making it easier for students and instructors to immediately identify both thecontext of the problem and the area of application.

Students should be encouraged to use the “NEED TO KNOW .” sections as they

occur in the text The placement of these sections is intended to answer questions asthey would normally arise in discussions In addition, there are numerous hints called

“NEED A TIP?” that appear in the margins of the text The tips are short and concise.

viii ❍ PREFACE

Finally, sections called Key Concepts and Formulas appear in each chapter as a

review in outline form of the material covered in that chapter

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INSTRUCTOR RESOURCES

The Instructor’s Website (http://www.cengage.com/statistics/mendenhall), available to

adopters of the fourteenth edition, provides a variety of teaching aids, including

• All the material from the CourseMate website including exercises using theLarge Data Sets, which is accompanied by three large data sets that can beused throughout the course A file named “Fortune” contains the revenues (in

millions) for the Fortune 500 largest U.S industrial corporations in a recent

year; a file named “Batting” contains the batting averages for the Nationaland American baseball league batting champions from 1976 to 2010; and afile named “Blood Pressure” contains the age and diastolic and systolic bloodpressures for 965 men and 945 women compiled by the National Institutes ofHealth

• Classic exercises with data sets and solutions

• PowerPoint lecture slides

• Applets by Gary McClelland (the complete set of Java applets used for theMyApps exercises on the website)

• TI Calculator Tech Guide, which includes instructions for performing many

of the techniques in the text using the Tl-83/84/89 graphing calculators.Also available for instructors:

Aplia

Aplia is a web-based learning solution that increases student effort and ment It helps make statistics relevant and engaging to students by connectingreal-world examples to course concepts When combined with the textual

engage-material of Introduction to Probability and Statistics (IPS) 14,

• Students receive immediate, detailed explanations for every answer

• Math and graphing tutorials help students ovecome deficiencies in thesecrucial areas

• Grades are automatically recorded in the instructor’s Aplia gradebook

Solution Builder

This online instructor database offers complete worked-out solutions to allexercises in the text, allowing you to create customized, secure solutionsprintouts (in PDF format) matched exactly to the problems you assign in class.Sign up for access at www.cengage.com/solutionbuilder

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PowerLecture with ExamView®for Introduction to Probability and Statistics

contains the Instructor’s Solutions Manual, PowerPoint lectures, ExamViewComputerized Testing, Classic Exercises, and TI-83/84/89 calculator Tech Guidewhich includes instructions for performing many of the techniques in the text us-ing the Tl-83/84/89 graphing calculators

ACKNOWLEDGMENTS

The authors are grateful to Molly Taylor and the editorial staff of Cengage Learning fortheir patience, assistance, and cooperation in the preparation of this edition A specialthanks to Gary McClelland for the Java applets used in the text

Thanks are also due to fourteenth edition reviewers Ronald C Degges, Bob C.Denton, Dr Dorothy M French, Jungwon Mun, Kazuhiko Shinki, Florence P Shuand thirteenth edition reviewers Bob Denton, Timothy Husband, Rob LaBorde, CraigMcBride, Marc Sylvester, Kanapathi Thiru, and Vitaly Voloshin We wish to thankauthors and organizations for allowing us to reprint selected material; acknowledg-ments are made wherever such material appears in the text

Robert J Beaver Barbara M Beaver

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INTRODUCTION 1

DESCRIBING DATA WITH GRAPHS 7

DESCRIBING DATA WITH NUMERICAL MEASURES 50

DESCRIBING BIVARIATE DATA 94

PROBABILITY AND PROBABILITY DISTRIBUTIONS 123

SEVERAL USEFUL DISCRETE DISTRIBUTIONS 175

THE NORMAL PROBABILITY DISTRIBUTION 209

SAMPLING DISTRIBUTIONS 242

LARGE-SAMPLE ESTIMATION 281

LARGE-SAMPLE TESTS OF HYPOTHESES 324

INFERENCE FROM SMALL SAMPLES 364

THE ANALYSIS OF VARIANCE 425

LINEAR REGRESSION AND CORRELATION 482

MULTIPLE REGRESSION ANALYSIS 530

ANALYSIS OF CATEGORICAL DATA 574

Brief Contents

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Introduction: What is Statistics? 1

The Population and the Sample 3Descriptive and Inferential Statistics 4Achieving the Objective of Inferential Statistics: The Necessary Steps 4Keys for Successful Learning 5

DESCRIBING DATA WITH GRAPHS 7

1.1 Variables and Data 81.2 Types of Variables 91.3 Graphs for Categorical Data 11Exercises 14

1.4 Graphs for Quantitative Data 17Pie Charts and Bar Charts 17Line Charts 19

Dotplots 20Stem and Leaf Plots 20Interpreting Graphs with a Critical Eye 221.5 Relative Frequency Histograms 24Exercises 28

Chapter Review 33 Technology Today 33 Supplementary Exercises 42 CASE STUDY: How Is Your Blood Pressure? 49

DESCRIBING DATA WITH NUMERICAL MEASURES 50

2.1 Describing a Set of Data with Numerical Measures 512.2 Measures of Center 51

Exercises 552.3 Measures of Variability 57Exercises 62

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Contents

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2.4 On the Practical Significance of the Standard Deviation 63

2.5 A Check on the Calculation of s 67Exercises 69

2.6 Measures of Relative Standing 722.7 The Five-Number Summary and the Box Plot 77Exercises 80

Chapter Review 83 Technology Today 84 Supplementary Exercises 87 CASE STUDY: The Boys of Summer 93

DESCRIBING BIVARIATE DATA 94

3.1 Bivariate Data 953.2 Graphs for Categorical Variables 95Exercises 98

3.3 Scatterplots for Two Quantitative Variables 993.4 Numerical Measures for Quantitative Bivariate Data 101Exercises 107

Chapter Review 109 Technology Today 109 Supplementary Exercises 114

CASE STUDY: Are Your Dishes Really Clean? 121

PROBABILITY AND PROBABILITY DISTRIBUTIONS 123

4.1 The Role of Probability in Statistics 1244.2 Events and the Sample Space 1244.3 Calculating Probabilities Using Simple Events 127Exercises 130

4.4 Useful Counting Rules (Optional) 133Exercises 137

4.5 Event Relations and Probability Rules 139Calculating Probabilities for Unions and Complements 1414.6 Independence, Conditional Probability, and

the Multiplication Rule 144Exercises 149

4.7 Bayes’ Rule (Optional) 152Exercises 156

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CONTENTS ❍ xiii

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4.8 Discrete Random Variables and Their Probability Distributions 158Random Variables 158

Probability Distributions 158The Mean and Standard Deviation for a Discrete Random Variable 160Exercises 163

Chapter Review 166 Technology Today 167 Supplementary Exercises 169 CASE STUDY: Probability and Decision Making in the Congo 174

SEVERAL USEFUL DISCRETE DISTRIBUTIONS 175

5.1 Introduction 1765.2 The Binomial Probability Distribution 176Exercises 185

5.3 The Poisson Probability Distribution 188Exercises 193

5.4 The Hypergeometric Probability Distribution 194Exercises 196

Chapter Review 197 Technology Today 198 Supplementary Exercises 202 CASE STUDY: A Mystery: Cancers Near a Reactor 208

THE NORMAL PROBABILITY DISTRIBUTION 209

6.1 Probability Distributions for Continuous Random Variables 2106.2 The Normal Probability Distribution 213

6.3 Tabulated Areas of the Normal Probability Distribution 214The Standard Normal Random Variable 214

Calculating Probabilities for a General Normal Random Variable 218Exercises 221

6.4 The Normal Approximation to the Binomial Probability Distribution (Optional) 224

Exercises 229

Chapter Review 231 Technology Today 232 Supplementary Exercises 236 CASE STUDY: “Are You Going to Curve the Grades?” 241

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CONTENTS ❍ xv

SAMPLING DISTRIBUTIONS 242

7.1 Introduction 2437.2 Sampling Plans and Experimental Designs 243Exercises 246

7.3 Statistics and Sampling Distributions 2487.4 The Central Limit Theorem 251

7.5 The Sampling Distribution of the Sample Mean 254Standard Error 255

Exercises 2587.6 The Sampling Distribution of the Sample Proportion 260Exercises 264

7.7 A Sampling Application: Statistical Process Control (Optional) 266

A Control Chart for the Process Mean: The x Chart 267

A Control Chart for the Proportion Defective: The p Chart 269Exercises 271

Chapter Review 272 Technology Today 273 Supplementary Exercises 276 CASE STUDY: Sampling the Roulette at Monte Carlo 279

LARGE-SAMPLE ESTIMATION 281

8.1 Where We’ve Been 2828.2 Where We’re Going—Statistical Inference 2828.3 Types of Estimators 283

8.4 Point Estimation 284Exercises 289

8.5 Interval Estimation 291Constructing a Confidence Interval 292Large-Sample Confidence Interval for a Population Mean m 294Interpreting the Confidence Interval 295

Large-Sample Confidence Interval for a Population Proportion p 297Exercises 299

8.6 Estimating the Difference between Two Population Means 301Exercises 304

8.7 Estimating the Difference between Two Binomial Proportions 307Exercises 309

8.8 One-Sided Confidence Bounds 311

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8.9 Choosing the Sample Size 312Exercises 316

Chapter Review 318 Supplementary Exercises 318 CASE STUDY: How Reliable Is That Poll?

CBS News: How and Where America Eats 322

LARGE-SAMPLE TESTS OF HYPOTHESES 324

9.1 Testing Hypotheses about Population Parameters 3259.2 A Statistical Test of Hypothesis 325

9.3 A Large-Sample Test about a Population Mean 328The Essentials of the Test 329

Calculating the p-Value 332Two Types of Errors 335The Power of a Statistical Test 336Exercises 339

9.4 A Large-Sample Test of Hypothesis for the Difference between Two Population Means 341

Hypothesis Testing and Confidence Intervals 343Exercises 344

9.5 A Large-Sample Test of Hypothesis for a Binomial Proportion 347Statistical Significance and Practical Importance 349

Exercises 3509.6 A Large-Sample Test of Hypothesis for the Difference between Two Binomial Proportions 351

Exercises 3549.7 Some Comments on Testing Hypotheses 356

Chapter Review 357 Supplementary Exercises 358 CASE STUDY: An Aspirin a Day ? 362

INFERENCE FROM SMALL SAMPLES 364

10.1 Introduction 365

10.2 Student’s t Distribution 365

Assumptions behind Student’s t Distribution 36810.3 Small-Sample Inferences Concerning a Population Mean 369Exercises 373

10.4 Small-Sample Inferences for the Difference between Two Population Means: Independent Random Samples 376Exercises 382

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CONTENTS ❍ xvii

10.5 Small-Sample Inferences for the Difference between Two Means: A Paired-Difference Test 386

Exercises 39110.6 Inferences Concerning a Population Variance 394Exercises 400

10.7 Comparing Two Population Variances 401Exercises 407

10.8 Revisiting the Small-Sample Assumptions 409

Chapter Review 410 Technology Today 410 Supplementary Exercises 416 CASE STUDY: School Accountability Study—

How Is Your School Doing? 424

THE ANALYSIS OF VARIANCE 425

11.1 The Design of an Experiment 42611.2 What Is an Analysis of Variance? 42711.3 The Assumptions for an Analysis of Variance 42711.4 The Completely Randomized Design: A One-Way Classification 42811.5 The Analysis of Variance for a Completely Randomized Design 429Partitioning the Total Variation in an Experiment 429

Testing the Equality of the Treatment Means 432Estimating Differences in the Treatment Means 434Exercises 437

11.6 Ranking Population Means 440Exercises 443

11.7 The Randomized Block Design: A Two-Way Classification 44411.8 The Analysis of Variance for a Randomized Block Design 445Partitioning the Total Variation in the Experiment 445

Testing the Equality of the Treatment and Block Means 448Identifying Differences in the Treatment and Block Means 450Some Cautionary Comments on Blocking 451

Exercises 452

11.9 The a b Factorial Experiment: A Two-Way Classification 456 11.10 The Analysis of Variance for an a b Factorial Experiment 458

Exercises 46211.11 Revisiting the Analysis of Variance Assumptions 466Residual Plots 467

11.12 A Brief Summary 469

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Chapter Review 469 Technology Today 470 Supplementary Exercises 475 CASE STUDY: How to Save Money on Groceries! 481

LINEAR REGRESSION AND CORRELATION 482

12.1 Introduction 48312.2 A Simple Linear Probabilistic Model 48312.3 The Method of Least Squares 48612.4 An Analysis of Variance for Linear Regression 488Exercises 491

12.5 Testing the Usefulness of the Linear Regression Model 494Inferences Concerning b, the Slope of the Line of Means 495

The Analysis of Variance F-Test 498Measuring the Strength of the Relationship:

The Coefficient of Determination 498Interpreting the Results of a Significant Regression 499Exercises 500

12.6 Diagnostic Tools for Checking the Regression Assumptions 503Dependent Error Terms 503

Residual Plots 503Exercises 50412.7 Estimation and Prediction Using the Fitted Line 507Exercises 511

12.8 Correlation Analysis 513Exercises 517

Chapter Review 519 Technology Today 520 Supplementary Exercises 523 CASE STUDY: Is Your Car “Made in the U.S.A.”? 528

MULTIPLE REGRESSION ANALYSIS 530

13.1 Introduction 53113.2 The Multiple Regression Model 53113.3 A Multiple Regression Analysis 532The Method of Least Squares 533The Analysis of Variance for Multiple Regression 534Testing the Usefulness of the Regression Model 535Interpreting the Results of a Significant Regression 536

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CONTENTS ❍ xix

Checking the Regression Assumptions 538Using the Regression Model for Estimation and Prediction 53813.4 A Polynomial Regression Model 539

Exercises 54213.5 Using Quantitative and Qualitative Predictor Variables

in a Regression Model 546Exercises 552

13.6 Testing Sets of Regression Coefficients 55513.7 Interpreting Residual Plots 558

13.8 Stepwise Regression Analysis 55913.9 Misinterpreting a Regression Analysis 560Causality 560

Multicollinearity 56013.10 Steps to Follow When Building a Multiple Regression Model 562

Chapter Review 562 Technology Today 563 Supplementary Exercises 565 CASE STUDY: “Made in the U.S.A.”—Another Look 572

ANALYSIS OF CATEGORICAL DATA 574

14.1 A Description of the Experiment 57514.2 Pearson’s Chi-Square Statistic 57614.3 Testing Specified Cell Probabilities: The Goodness-of-Fit Test 577Exercises 579

14.4 Contingency Tables: A Two-Way Classification 581The Chi-Square Test of Independence 582

Exercises 58614.5 Comparing Several Multinomial Populations: A Two-Way Classification with Fixed Row or Column Totals 588Exercises 591

14.6 The Equivalence of Statistical Tests 59214.7 Other Applications of the Chi-Square Test 593

Chapter Review 594 Technology Today 595 Supplementary Exercises 598 CASE STUDY: Who is the Primary Breadwinner in Your Family? 604

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NONPARAMETRIC STATISTICS 606

15.1 Introduction 60715.2 The Wilcoxon Rank Sum Test: Independent Random Samples 607Normal Approximation for the Wilcoxon Rank Sum Test 611

Exercises 61415.3 The Sign Test for a Paired Experiment 616Normal Approximation for the Sign Test 617Exercises 619

15.4 A Comparison of Statistical Tests 62015.5 The Wilcoxon Signed-Rank Test for a Paired Experiment 621Normal Approximation for the Wilcoxon Signed-Rank Test 624Exercises 625

15.6 The Kruskal–Wallis H-Test for Completely Randomized Designs 627Exercises 631

15.7 The Friedman F r-Test for Randomized Block Designs 633Exercises 636

15.8 Rank Correlation Coefficient 637Exercises 641

15.9 Summary 643

Chapter Review 644 Technology Today 645 Supplementary Exercises 648 CASE STUDY: How’s Your Cholesterol Level? 653

APPENDIX I 655

Table 1 Cumulative Binomial Probabilities 656Table 2 Cumulative Poisson Probabilities 662Table 3 Areas under the Normal Curve 664Table 4 Critical Values of t 667

Table 5 Critical Values of Chi-Square 668Table 6 Percentage Points of the F Distribution 670Table 7 Critical Values of T for the Wilcoxon Rank

Sum Test, n1 n2 678Table 8 Critical Values of T for the Wilcoxon Signed-Rank

Test, n 5(1)50 680Table 9 Critical Values of Spearman’s Rank Correlation Coefficient

for a One-Tailed Test 681

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CONTENTS ❍ xxi

Table 10 Random Numbers 682

Table 11 Percentage Points of the Studentized Range, q.05(k, df ) 684

DATA SOURCES 688 ANSWERS TO SELECTED EXERCISES 700 INDEX 714

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What is statistics? Have you ever met a statistician?

Do you know what a statistician does? Perhaps you are

thinking of the person who sits in the broadcast booth

at the Rose Bowl, recording the number of pass

comple-tions, yards rushing, or interceptions thrown on New

Year’s Day Or perhaps the mere mention of the word

statistics sends a shiver of fear through you You may

think you know nothing about statistics; however, it is

almost inevitable that you encounter statistics in one

form or another every time you pick up a daily

newspa-per Here are some examples concerning the California

2010 elections:

• Rowdy crowd jeers Whitman GOP candidate criticizes

unions; earlier stop draws friendlier audience.

GLENDALE— Whitman, a billionaire, has spent $142

million from her personal fortune in the race so far

A Field Poll released Thursday showed her trailing Jerry Brown 49 percent to 39 percent among likely voters 1

• Fiorina calls herself similar to Feinstein, who supports

Boxer.

MENLO PARK—Republican Carly Fiorina said Friday she

would be a like-minded colleague of Democratic Sen.

Dianne Feinstein if she unseats Barbara Boxer next week, drawing sharp responses from both Democratic senators.

Fiorina, the former CEO of Hewlett-Packard Co., disputed a Field Poll released Friday showing Boxer leading her among likely voters, 49 percent to 41percent.2

• Race for attorney general tight Field Poll: Nearly a

quarter of those surveyed are undecided Newsom holds a slim lead over Maldonado for lieutenant governor.

1

Introduction

What is Statistics?

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SACRAMENTO—Tuesday’s election for attorney general is a tossup, with Democrat

Kamala Harris and Republican Steve Cooley virtually tied as Harris gains ground in voter-rich Los Angeles County and among women according to the latest Field Poll.

Today’s poll shows Cooley with 39 percent and Harris with 38 percent among likely voters Almost a quarter of likely voters remain undecided.

Newsom, the mayor of San Francisco, leads Maldonado, who was appointed lieutenant governor this year, 42 percent to 37 percent A fifth of voters are undecided.

Today’s poll was conducted for The Press-Enterprise and other California media

subscribers It was conducted October 14 through October 26 and included 1092 voters It has

a margin of error of plus or minus 3.2 percent.3

—The Press-Enterprise, Riverside, CA

2 ❍ INTRODUCTION TRAIN YOUR BRAIN FOR STATISTICS

Articles similar to these are commonplace in our newspapers and magazines, and in theperiod just prior to a presidential or congressional election, a new poll is reportedalmost every day The language of these articles are very familiar to us; however, theyleave the inquisitive reader with some unanswered questions How were the people inthe poll selected? Will these people give the same response tomorrow? Will they givethe same response on election day? Will they even vote? Are these people representa-tive of all those who will vote on election day? It is the job of a statistician to ask thesequestions and to find answers for them in the language of the poll

Most Believe “Cover-Up” of JFK Assassination Facts

A majority of the public believes the assassination of President John F Kennedy was part of a larger conspiracy, not the act of one individual In addition, most Americans think there was a cover-up of facts about the 1963 shooting Almost 50 years after JFK’s assassination, a FOX news poll shows many Americans disagree with the government’s conclusions about the killing.

The Warren Commission found that Lee Harvey Oswald acted alone when he shot Kennedy,

but 66 percent of the public today think the assassination was “part of a larger conspiracy” while only 25 percent think it was the “act of one individual.”

“For older Americans, the Kennedy assassination was a traumatic experience that began a loss of confidence in government,” commented Opinion Dynamics President John Gorman.

“Younger people have grown up with movies and documentaries that have pretty much pushed the ‘conspiracy’ line Therefore, it isn’t surprising there is a fairly solid national consensus that

we still don’t know the truth.”

(The poll asked): “Do you think that we know all the facts about the assassination of dent John F Kennedy or do you think there was a cover-up?”

Presi-We Know All the Facts (%) There Was a Cover-Up (Not Sure)

Hot News: 98.6 Not Normal

After believing for more than a century that 98.6 was the normal body temperature for humans, researchers now say normal is not normal anymore.

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For some people at some hours of the day, 99.9 degrees could be fine And readings as low

as 96 turn out to be highly human.

The 98.6 standard was derived by a German doctor in 1868 Some physicians have always been suspicious of the good doctor’s research His claim: 1 million readings—in an epoch without computers.

So Mackowiak & Co took temperature readings from 148 healthy people over a three-day period and found that the mean temperature was 98.2 degrees Only 8 percent of the readings were 98.6.

—The Press-Enterprise5What questions come to your mind when you read this article? How did the researcherselect the 148 people, and how can we be sure that the results based on these 148 peopleare accurate when applied to the general population? How did the researcher arrive atthe normal “high” and “low” temperatures given in the article? How did the Germandoctor record 1 million temperatures in 1868? Again, we encounter a statistical prob-lem with an application to everyday life

Statistics is a branch of mathematics that has applications in almost every facet ofour daily life It is a new and unfamiliar language for most people, however, and, likeany new language, statistics can seem overwhelming at first glance But once the lan-guage of statistics is learned and understood, it provides a powerful tool for dataanalysis in many different fields of application

THE POPULATION AND THE SAMPLE

In the language of statistics, one of the most basic concepts is sampling In most tistical problems, a specified number of measurements or data—a sample—is drawn from a much larger body of measurements, called the population.

sta-For the body-temperature experiment, the sample is the set of body-temperaturemeasurements for the 148 healthy people chosen by the experimenter We hope thatthe sample is representative of a much larger body of measurements—the population—the body temperatures of all healthy people in the world!

Which is of primary interest, the sample or the population? In most cases, we areinterested primarily in the population, but the population may be difficult or impossible

to enumerate Imagine trying to record the body temperature of every healthy person onearth or the presidential preference of every registered voter in the United States!

Instead, we try to describe or predict the behavior of the population on the basis of information obtained from a representative sample from that population.

The words sample and population have two meanings for most people For example,

you read in the newspapers that a Gallup poll conducted in the United States was based

on a sample of 1823 people Presumably, each person interviewed is asked a particularquestion, and that person’s response represents a single measurement in the sample Isthe sample the set of 1823 people, or is it the 1823 responses that they give?

Population

Sample

THE POPULATION AND THE SAMPLE ❍ 3

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In statistics, we distinguish between the set of objects on which the measurementsare taken and the measurements themselves To experimenters, the objects on which

measurements are taken are called experimental units The sample survey statistician calls them elements of the sample.

DESCRIPTIVE AND INFERENTIAL STATISTICS

When first presented with a set of measurements—whether a sample or a population—you need to find a way to organize and summarize it The branch of statistics that

presents techniques for describing sets of measurements is called descriptive tics You have seen descriptive statistics in many forms: bar charts, pie charts, and

statis-line charts presented by a political candidate; numerical tables in the newspaper; orthe average rainfall amounts reported by the local television weather forecaster.Computer-generated graphics and numerical summaries are commonplace in oureveryday communication

Definition Descriptive statistics consists of procedures used to summarize and

describe the important characteristics of a set of measurements

If the set of measurements is the entire population, you need only to draw sions based on the descriptive statistics However, it might be too expensive or too timeconsuming to enumerate the entire population Perhaps enumerating the populationwould destroy it, as in the case of “time to failure” testing For these or other reasons,you may have only a sample from the population By looking at the sample, you want

conclu-to answer questions about the population as a whole The branch of statistics that deals

with this problem is called inferential statistics.

Definition Inferential statistics consists of procedures used to make inferences

about population characteristics from information contained in a sample drawn fromthis population

The objective of inferential statistics is to make inferences (that is, draw conclusions,

make predictions, make decisions) about the characteristics of a population from mation contained in a sample

infor-ACHIEVING THE OBJECTIVE

OF INFERENTIAL STATISTICS:

THE NECESSARY STEPS

How can you make inferences about a population using information contained in asample? The task becomes simpler if you organize the problem into a series of logicalsteps

1 Specify the questions to be answered and identify the population of interest.

In the California election poll, the objective is to determine who will get themost votes on election day Hence, the population of interest is the set of allvotes in the California election When you select a sample, it is important that

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the sample be representative of this population, not the population of voter

preferences on October 30 or on some other day prior to the election

2 Decide how to select the sample This is called the design of the experiment or

the sampling procedure Is the sample representative of the population of

inter-est? For example, if a sample of registered voters is selected from the city ofSan Francisco, will this sample be representative of all voters in California?Will it be the same as a sample of “likely voters”—those who are likely toactually vote in the election? Is the sample large enough to answer the ques-tions posed in step 1 without wasting time and money on additional informa-tion? A good sampling design will answer the questions posed with minimalcost to the experimenter

3 Select the sample and analyze the sample information No matter how much

information the sample contains, you must use an appropriate method of sis to extract it Many of these methods, which depend on the sampling proce-dure in step 2, are explained in the text

analy-4 Use the information from step 3 to make an inference about the tion Many different procedures can be used to make this inference, and some

popula-are better than others For example, 10 different methods might be available toestimate human response to an experimental drug, but one procedure might bemore accurate than others You should use the best inference-making procedureavailable (many of these are explained in the text)

5 Determine the reliability of the inference Since you are using only a fraction

of the population in drawing the conclusions described in step 4, you might bewrong! How can this be? If an agency conducts a statistical survey for you andestimates that your company’s product will gain 34% of the market this year,how much confidence can you place in this estimate? Is this estimate accurate

to within 1, 5, or 20 percentage points? Is it reliable enough to be used in ting production goals? Every statistical inference should include a measure ofreliability that tells you how much confidence you have in the inference

set-Now that you have learned a few basic terms and concepts, we again pose the tion asked at the beginning of this discussion: Do you know what a statistician does?The statistician’s job is to implement all of the preceding steps

ques-KEYS FOR SUCCESSFUL LEARNING

As you begin to study statistics, you wiil find that there are many new terms and cepts to be mastered Since statistics is an applied branch of mathematics, many ofthese basic concepts are mathematical—developed and based on results from calculus

con-or higher mathematics However, you do not have to be able to derive results in con-order

to apply them in a logical way In this text, we use numerical examples and sense arguments to explain statistical concepts, rather than more complicated mathe-matical arguments

common-In recent years, computers have become readily available to many students andprovide them with an invaluable tool In the study of statistics, even the beginning stu-dent can use packaged programs to perform statistical analyses with a high degree ofspeed and accuracy Some of the more common statistical packages available at com-

puter facilities are MINITABTM, SAS (Statistical Analysis System), and SPSS

KEYS FOR SUCCESSFUL LEARNING ❍ 5

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(Statistical Package for the Social Sciences); personal computers will support packages

such as MINITAB, MS Excel, and others There are even online statistical programs and

interactive “applets” on the Internet

These programs, called statistical software, differ in the types of analyses able, the options within the programs, and the forms of printed results (called output).

avail-However, they are all similar In this book, we use both MINITAB and Microsoft Excel as

statistical tools Understanding the basic output of these packages will help you pret the output from other software systems

inter-At the end of most chapters, you will find a section called “Technology Today.” These sections present numerical examples to guide you through the MINITAB and MS Excel commands and options that are used for the procedures in that chapter If you are using MINITAB or MS Excel in a lab or home setting, you may want to work through this

section at your own computer so that you become familiar with the hands-on methods

in computer analysis If you do not need hands-on knowledge of MINITAB or MS Excel,

you may choose to skip this section and simply use the computer printouts for analysis

as they appear in the text

Another learning tool called statistical applets can be found on the CourseMate Web

site Also found on this Web site are explanatory sections called “Using the Applets,”which will help you understand how the applets can be used to visualize many of the chapter concepts An accompanying section called “Applet APPs” provides someexercises (with solutions) that can be solved using the statistical applets Whenever there

is an applet available for a particular concept or application, you will find an icon in the left margin of the text, together with the name of the appropriate applet

Most important, using statistics successfully requires common sense and logicalthinking For example, if we want to find the average height of all students at a particu-lar university, would we select our entire sample from the members of the basketballteam? In the body-temperature example, the logical thinker would question an 1868average based on 1 million measurements—when computers had not yet been invented

As you learn new statistical terms, concepts, and techniques, remember to viewevery problem with a critical eye and be sure that the rule of common sense applies.Throughout the text, we will remind you of the pitfalls and dangers in the use or mis-

use of statistics Benjamin Disraeli once said that there are three kinds of lies: lies,

damn lies, and statistics! Our purpose is to dispel this claim—to show you how to make

statistics work for you and not lie for you!

As you continue through the book, refer back to this introduction periodically Eachchapter will increase your knowledge of statistics and should, in some way, help youachieve one of the steps described here Each of these steps is essential in attaining theoverall objective of inferential statistics: to make inferences about a population usinginformation contained in a sample drawn from that population

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How Is Your Blood Pressure?

Is your blood pressure normal, or is it too high

or too low? The case study at the end of thischapter examines a large set of blood pressuredata You will use graphs to describe these dataand compare your blood pressure with that ofothers of your same age and gender

1

GENERAL OBJECTIVES

Many sets of measurements are samples selected from

larger populations Other sets constitute the entire

popula-tion, as in a national census In this chapter, you will learn

what a variable is, how to classify variables into several types,

and how measurements or data are generated You will then

learn how to use graphs to describe data sets.

CHAPTER INDEX

● Data distributions and their shapes (1.1, 1.4)

● Dotplots (1.4)

● Pie charts, bar charts, line charts (1.3, 1.4)

● Qualitative and quantitative variables—discrete and

continuous (1.2)

● Relative frequency histograms (1.5)

● Stem and leaf plots (1.4)

● Univariate and bivariate data (1.1)

● Variables, experimental units, samples and populations,

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A set of five students is selected from all undergraduates at a large university, and surements are entered into a spreadsheet as shown in Figure 1.1 Identify the variouselements involved in generating this set of measurements.

mea-Solution There are several variables in this example The experimental unit on

which the variables are measured is a particular undergraduate student on the campus,identified in column A Five variables are measured for each student: grade point aver-age (GPA), gender, year in college, major, and current number of units enrolled Each

of these characteristics varies from student to student If we consider the GPAs of allstudents at this university to be the population of interest, the five GPAs in column B

represent a sample from this population If the GPA of each undergraduate student at the university had been measured, we would have generated the entire population of

measurements for this variable

E X A M P L E

VARIABLES AND DATA

In Chapters 1 and 2, we will present some basic techniques in descriptive statistics— the branch of statistics concerned with describing sets of measurements, both samples and populations Once you have collected a set of measurements, how can you display

this set in a clear, understandable, and readable form? First, you must be able to definewhat is meant by measurements or “data” and to categorize the types of data that youare likely to encounter in real life We begin by introducing some definitions

Definition A variable is a characteristic that changes or varies over time and/or

for different individuals or objects under consideration

For example, body temperature is a variable that changes over time within a singleindividual; it also varies from person to person Religious affiliation, ethnic origin, income, height, age, and number of offspring are all variables—characteristics thatvary depending on the individual chosen

In the Introduction, we defined an experimental unit or an element of the sample as

the object on which a measurement is taken Equivalently, we could define an mental unit as the object on which a variable is measured When a variable is actually

experi-measured on a set of experimental units, a set of measurements or data result.

Definition An experimental unit is the individual or object on which a variable is measured A single measurement or data value results when a variable is actually

measured on an experimental unit

If a measurement is generated for every experimental unit in the entire collection, the

resulting data set constitutes the population of interest Any smaller subset of ments is a sample.

measure-Definition A population is the set of all measurements of interest to the

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The second variable measured on the students is gender, in column C This variable

is somewhat different from GPA, since it can take only one of two values—male (M)

or female (F) The population, if it could be enumerated, would consist of a set of Msand Fs, one for each student at the university Similarly, the third and fourth variables,year and major, generate nonnumerical data Year has four categories (Fr, So, Jr, Sr),and major has one category for each undergraduate major on campus The last variable,current number of units enrolled, is numerically valued, generating a set of numbersrather than a set of qualities or characteristics

Although we have discussed each variable individually, remember that we havemeasured each of these five variables on a single experimental unit: the student There-fore, in this example, a “measurement” really consists of five observations, one foreach of the five measured variables For example, the measurement taken on student 2produces this observation:

Variables can be classified into one of two types: qualitative or quantitative.

Definition Qualitative variables measure a quality or characteristic on each experimental unit Quantitative variables measure a numerical quantity or amount on

each experimental unit

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Qualitative variables produce data that can be categorized according to similarities

or differences in kind; hence, they are often called categorical data The variables

gen-der, year, and major in Example 1.1 are qualitative variables that produce categoricaldata Here are some other examples:

• Political affiliation: Republican, Democrat, Independent

• Taste ranking: excellent, good, fair, poor

• Color of an M&M’S®candy: brown, yellow, red, orange, green, blue

Quantitative variables, often represented by the letter x, produce numerical data,

such as those listed here:

• x Prime interest rate

• x Number of passengers on a flight from Los Angeles to New York City

• x Weight of a package ready to be shipped

• x Volume of orange juice in a glass

Notice that there is a difference in the types of numerical values that these quantitativevariables can assume The number of passengers, for example, can take on only the

values x 0, 1, 2, , whereas the weight of a package can take on any value greater

than zero, or 0 x To describe this difference, we define two types of quantitative

variables: discrete and continuous.

Definition A discrete variable can assume only a finite or countable number of values A continuous variable can assume the infinitely many values corresponding to

the points on a line interval

The name discrete relates to the discrete gaps between the possible values that the

variable can assume Variables such as number of family members, number of newcar sales, and number of defective tires returned for replacement are all examples ofdiscrete variables On the other hand, variables such as height, weight, time, distance,

and volume are continuous because they can assume values at any point along a line

interval For any two values you pick, a third value can always be found betweenthem!

Identify each of the following variables as qualitative or quantitative:

1 The most frequent use of your microwave oven (reheating, defrosting, ing, other)

warm-2 The number of consumers who refuse to answer a telephone survey

3 The door chosen by a mouse in a maze experiment (A, B, or C)

4 The winning time for a horse running in the Kentucky Derby

5 The number of children in a fifth-grade class who are reading at or above gradelevel

Solution Variables 1 and 3 are both qualitative because only a quality or

char-acteristic is measured for each individual The categories for these two variables

are shown in parentheses The other three variables are quantitative Variables 2 and 5 are discrete variables that can take on any of the values x 0, 1, 2, , with a

Discrete variables often

involve the “number of”

items in a set.

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maximum value depending on the number of consumers called or the number of dren in the class, respectively Variable 4, the winning time for a Kentucky Derby

chil-horse, is the only continuous variable in the list The winning time, if it could be

mea-sured with sufficient accuracy, could be 121 seconds, 121.5 seconds, 121.25 seconds,

or any values between any two times we have listed

Why should you be concerned about different kinds of variables (shown in Figure 1.2) and the data that they generate? The reason is that different types of datarequire you to use different methods for description, so that the data can be presentedclearly and understandably to your audience!

GRAPHS FOR CATEGORICAL DATA

After the data have been collected, they can be consolidated and summarized to showthe following information:

• What values of the variable have been measured

• How often each value has occurred

For this purpose, you can construct a statistical table that can be used to display the

data graphically as a data distribution The type of graph you choose depends on the

type of variable you have measured

When the variable of interest is qualitative or categorical, the statistical table is a list

of the categories being considered along with a measure of how often each valueoccurred You can measure “how often” in three different ways:

• The frequency, or number of measurements in each category

• The relative frequency, or proportion of measurements in each category

• The percentage of measurements in each category

If you let n be the total number of measurements in the set, you can find the relative

fre-quency and percentage using these relationships:

Relative frequency Frequ

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You will find that the sum of the frequencies is always n, the sum of the relative

fre-quencies is 1, and the sum of the percentages is 100%

When the variable is qualitative, the categories should be chosen so that

• a measurement will belong to one and only one category

• each measurement has a category to which it can be assigned

For example, if you categorize meat products according to the type of meat used, youmight use these categories: beef, chicken, seafood, pork, turkey, other To categorizeranks of college faculty, you might use these categories: professor, associate professor,assistant professor, instructor, lecturer, other The “other” category is included in bothcases to allow for the possibility that a measurement cannot be assigned to one of theearlier categories

Once the measurements have been categorized and summarized in a statistical table,

you can use either a pie chart or a bar chart to display the distribution of the data A

pie chart is the familiar circular graph that shows how the measurements are distributed among the categories A bar chart shows the same distribution of measurements

among the categories, with the height of the bar measuring how often a particularcategory was observed

In a survey concerning public education, 400 school administrators were asked torate the quality of education in the United States Their responses are summarized inTable 1.1 Construct a pie chart and a bar chart for this set of data

Solution To construct a pie chart, assign one sector of a circle to each category.The angle of each sector should be proportional to the proportion of measurements

(or relative frequency) in that category Since a circle contains 360°, you can use this

equation to find the angle:

Angle Relative frequency 360°

E X A M P L E

12 ❍ CHAPTER 1 DESCRIBING DATA WITH GRAPHS

Three steps to a data

Proportions add to 1.

Percents add to 100.

Sector angles add to 360°.

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The visual impact of these two graphs is somewhat different The pie chart is used todisplay the relationship of the parts to the whole; the bar chart is used to emphasize theactual quantity or frequency for each category Since the categories in this example areordered “grades” (A, B, C, D), we would not want to rearrange the bars in the chart to

change its shape In a pie chart, the order of presentation is irrelevant.

1.3 GRAPHS FOR CATEGORICAL DATA ❍ 13

Rating Frequency Relative Frequency Percent Angle

A 35 35/400 09 9% 09 360 32.4º

B 260 260/400 65 65% 234.0º

C 93 93/400 23 23% 82.8º

D 12 12/400 03 3% 10.8º Total 400 1.00 100% 360º

D

B 65.0%

C 23.3%

A snack size bag of peanut M&M’S candies contains 21 candies with the colors listed in

Table 1.3 The variable “color” is qualitative, so Table 1.4 lists the six categories along

with a tally of the number of candies of each color The last three columns of Table 1.4show how often each category occurred Since the categories are colors and have no par-

ticular order, you could construct bar charts with many different shapes just by reordering

the bars To emphasize that brown is the most frequent color, followed by blue, green, andorange, we order the bars from largest to smallest and create the bar chart in Figure 1.5 A

bar chart in which the bars are ordered from largest to smallest is called a Pareto chart.

E X A M P L E 1.4

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UNDERSTANDING THE CONCEPTS

1.1 Experimental Units Identify the experimental

units on which the following variables are measured:

a Gender of a student

b Number of errors on a midterm exam

c Age of a cancer patient

d Number of flowers on an azalea plant

e Color of a car entering a parking lot

1.2 Qualitative or Quantitative? Identify eachvariable as quantitative or qualitative:

a Amount of time it takes to assemble a simple

puzzle

b Number of students in a first-grade classroom

c Rating of a newly elected politician (excellent,

good, fair, poor)

d State in which a person lives

Brown Green Brown Blue Red Red Green Brown Yellow Orange Green Blue Brown Blue Blue Brown Orange Blue Brown Orange Yellow

Category Tally Frequency Relative Frequency Percent

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1.3 Discrete or Continuous? Identify the following

quantitative variables as discrete or continuous:

a Population in a particular area of the United States

b Weight of newspapers recovered for recycling on a

single day

c Time to complete a sociology exam

d Number of consumers in a poll of 1000 who consider

nutritional labeling on food products to be important

1.4 Discrete or Continuous? Identify each

quanti-tative variable as discrete or continuous

a Number of boating accidents along a 50-mile stretch

of the Colorado River

b Time required to complete a questionnaire

c Cost of a head of lettuce

d Number of brothers and sisters you have

e Yield in kilograms of wheat from a 1-hectare plot in

a wheat field

1.5 Parking on Campus Six vehicles are selected

from the vehicles that are issued campus parking

per-mits, and the following data are recorded:

One-way Commute Age of Distance Vehicle Vehicle Type Make Carpool? (miles) (years)

6 Car Chevrolet No 5.4 9

a What are the experimental units?

b What are the variables being measured? What types

of variables are they?

c Is this univariate, bivariate, or multivariate data?

1.6 Past U.S Presidents A data set consists of the

ages at death for each of the 38 past presidents of the

United States now deceased

a Is this set of measurements a population or a sample?

b What is the variable being measured?

c Is the variable in part b quantitative or qualitative?

1.7 Voter Attitudes You are a candidate for your

state legislature, and you want to survey voter attitudes

regarding your chances of winning Identify the

popu-lation that is of interest to you and from which you

would like to select your sample How is this

popula-tion dependent on time?

1.8 Cancer Survival Times A medical researcherwants to estimate the survival time of a patient after theonset of a particular type of cancer and after a

particular regimen of radiotherapy

a What is the variable of interest to the medical

researcher?

b Is the variable in part a qualitative, quantitative

discrete, or quantitative continuous?

c Identify the population of interest to the medical

researcher

d Describe how the researcher could select a sample

from the population

e What problems might arise in sampling from this

population?

1.9 New Teaching Methods An educationalresearcher wants to evaluate the effectiveness of a newmethod for teaching reading to deaf students Achieve-ment at the end of a period of teaching is measured by

a student’s score on a reading test

a What is the variable to be measured? What type of

variable is it?

b What is the experimental unit?

c Identify the population of interest to the

experimenter

BASIC TECHNIQUES

1.10 Fifty people are grouped into four categories—

A, B, C, and D—and the number of people who fallinto each category is shown in the table:

a What is the experimental unit?

b What is the variable being measured? Is it

qualitative or quantitative?

c Construct a pie chart to describe the data.

d Construct a bar chart to describe the data.

e Does the shape of the bar chart in part d change

depending on the order of presentation of the fourcategories? Is the order of presentation important?

f What proportion of the people are in category B, C,

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1.11 Jeans A manufacturer of jeans has plants in

California, Arizona, and Texas A group of 25 pairs of

jeans is randomly selected from the computerized

database, and the state in which each is produced is

a What is the experimental unit?

b What is the variable being measured? Is it

qualitative or quantitative?

c Construct a pie chart to describe the data.

d Construct a bar chart to describe the data.

e What proportion of the jeans are made in Texas?

f What state produced the most jeans in the group?

g If you want to find out whether the three plants

produced equal numbers of jeans, or whether one

produced more jeans than the others, how can you

use the charts from parts c and d to help you? What

conclusions can you draw from these data?

APPLICATIONS

1.12 Election 2012 During the spring of 2010, the

news media were already conducting opinion polls that

tracked the fortunes of the major candidates hoping to

become the president of the United States One such

poll conducted by CNN/Opinion Research Corporation

Poll showed the following results:1

“If Barack Obama were the Democratic Party’s candidate and

[see below] were the Republican Party’s candidate, who would

you be more likely to vote for: Obama, the Democrat, or [see

below], the Republican?” If unsure: “As of today, who do you

lean more toward?”

Barack Mitt Neither 4/9–11/10 Obama (D) Romney (R) (vol.)

Mike Barack Huckabee Neither 4/9–11/10 Obama (D) (R) (vol.)

The results were based on a sample taken April 9–11,

2010, of 907 registered voters nationwide

a If the pollsters were planning to use these results to

predict the outcome of the 2012 presidentialelection, describe the population of interest to them

b Describe the actual population from which the

sample was drawn

c Some pollsters prefer to select a sample of “likely”

voters What is the difference between “registeredvoters” and “likely voters”? Why is this important?

d Is the sample selected by the pollsters representative

of the population described in part a? Explain

1.13 Want to Be President? Would you want to bethe president of the United States? Although manyteenagers think that they could grow up to be the presi-dent, most don’t want the job In an opinion poll con-

ducted by ABC News, nearly 80% of the teens were not

interested in the job.2When asked “What’s the mainreason you would not want to be president?” they gavethese responses:

Other career plans/no interest 40%

Too much pressure 20%

Too much work 15%

Wouldn’t be good at it 14%

Too much arguing 5%

a Are all of the reasons accounted for in this table?

Add another category if necessary

b Would you use a pie chart or a bar chart to

graphically describe the data? Why?

c Draw the chart you chose in part b.

d If you were the person conducting the opinion poll,

what other types of questions might you want toinvestigate?

1.14 Facebook Fanatics The social

network-ing site called Facebook has grown quickly since its inception in 2004 In fact, Facebook’s United States

user base grew from 42 million users to 103 million usersbetween 2009 and 2010 The table below shows the age

distribution of Facebook users (in thousands) as it

changed from January 2009 to January 2010.3

Age As of 1/04/2009 As of 1/04/2010 13–17 5675 10,680 18–24 17,192 26,076 25–34 11,255 25,580 35–54 6989 29,918

Unknown 23 1068 Total 42,089 103,086

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