statistics for business economics by anderson 2

Brief ContentsPreface xxv About the Authors xxix Chapter 1 Data and Statistics 1 Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations 26 Chapter 3 Descriptive Statistic

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z value For example, for

z = –.85, the cumulativeprobability is 1977

z

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give the area under thecurve to the left of the

z value For example, for

z = 1.25, the cumulative

probability is 8944

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STATISTICS FOR BUSINESS AND ECONOMICS 10e

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David R Anderson University of Cincinnati

Dennis J Sweeney University of Cincinnati

Thomas A Williams Rochester Institute of Technology

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VP/Editorial Director:

Jack W Calhoun

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Dedicated to

Marcia, Cherri, and Robbie

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Brief Contents

Preface xxv About the Authors xxix

Chapter 1 Data and Statistics 1

Chapter 2 Descriptive Statistics: Tabular and Graphical

Presentations 26

Chapter 3 Descriptive Statistics: Numerical Measures 81

Chapter 4 Introduction to Probability 141

Chapter 5 Discrete Probability Distributions 186

Chapter 6 Continuous Probability Distributions 225

Chapter 7 Sampling and Sampling Distributions 257

Chapter 8 Interval Estimation 299

Chapter 9 Hypothesis Tests 338

Chapter 10 Statistical Inference About Means and Proportions

with Two Populations 393

Chapter 11 Inferences About Population Variances 434

Chapter 12 Tests of Goodness of Fit and Independence 457

Chapter 13 Experimental Design and Analysis of Variance 490

Chapter 14 Simple Linear Regression 543

Chapter 15 Multiple Regression 624

Chapter 16 Regression Analysis: Model Building 693

Chapter 17 Index Numbers 744

Chapter 18 Forecasting 765

Chapter 19 Nonparametric Methods 812

Chapter 20 Statistical Methods for Quality Control 846

Chapter 21 Decision Analysis 879

Chapter 22 Sample Survey On CD

Appendix A References and Bibliography 916

Appendix B Tables 918

Appendix C Summation Notation 946

Appendix D Self-Test Solutions and Answers to Even-Numbered

Exercises 948

Appendix E Using Excel Functions 995

Appendix F Computing p-Values Using Minitab and Excel 1000

Index 1004

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Preface xxv About the Authors xxix

Chapter 1 Data and Statistics 1 Statistics in Practice: BusinessWeek 2 1.1 Applications in Business and Economics 3

Accounting 3 Finance 4 Marketing 4 Production 4 Economics 4

1.4 Descriptive Statistics 13 1.5 Statistical Inference 15 1.6 Computers and Statistical Analysis 17 Summary 17

Glossary 18 Supplementary Exercises 19

Chapter 2 Descriptive Statistics: Tabular and Graphical

Presentations 26 Statistics in Practice: Colgate-Palmolive Company 27 2.1 Summarizing Qualitative Data 28

Frequency Distribution 28 Relative Frequency and Percent Frequency Distributions 29 Bar Graphs and Pie Charts 29

2.2 Summarizing Quantitative Data 34

Frequency Distribution 34

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Relative Frequency and Percent Frequency Distributions 35 Dot Plot 36

Histogram 36 Cumulative Distributions 37 Ogive 39

2.3 Exploratory Data Analysis: The Stem-and-Leaf Display 43 2.4 Crosstabulations and Scatter Diagrams 48

Crosstabulation 48 Simpson’s Paradox 51 Scatter Diagram and Trendline 52

Summary 57 Glossary 59 Key Formulas 60 Supplementary Exercises 60 Case Problem 1: Pelican Stores 66 Case Problem 2: Motion Picture Industry 67 Appendix 2.1 Using Minitab for Tabular and Graphical Presentations 68 Appendix 2.2 Using Excel for Tabular and Graphical Presentations 70

Chapter 3 Descriptive Statistics: Numerical Measures 81 Statistics in Practice: Small Fry Design 82

3.1 Measures of Location 83

Mean 83 Median 84 Mode 85 Percentiles 86 Quartiles 87

3.2 Measures of Variability 91

Range 92 Interquartile Range 92 Variance 93

Standard Deviation 95 Coefficient of Variation 95

3.3 Measures of Distribution Shape, Relative Location, and Detecting Outliers 98

Distribution Shape 98

z-Scores 99

Chebyshev’s Theorem 100 Empirical Rule 101 Detecting Outliers 102

3.4 Exploratory Data Analysis 105

Five-Number Summary 105 Box Plot 106

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3.5 Measures of Association Between Two Variables 110

Covariance 110

Interpretation of the Covariance 112

Correlation Coefficient 114

Interpretation of the Correlation Coefficient 115

3.6 The Weighted Mean and Working with

Case Problem 1: Pelican Stores 132

Case Problem 2: Motion Picture Industry 133

Case Problem 3: Business Schools of Asia-Pacific 133

Appendix 3.1 Descriptive Statistics Using Minitab 135

Appendix 3.2 Descriptive Statistics Using Excel 137

Chapter 4 Introduction to Probability 141

Statistics in Practice: Rohm and Hass Company 142

4.1 Experiments, Counting Rules, and Assigning

Probabilities 143

Counting Rules, Combinations, and

Permutations 144

Assigning Probabilities 148

Probabilities for the KP&L Project 150

4.2 Events and Their Probabilities 153

4.3 Some Basic Relationships of Probability 157

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Chapter 5 Discrete Probability Distributions 186 Statistics in Practice: Citibank 187

5.4 Binomial Probability Distribution 200

A Binomial Experiment 201 Martin Clothing Store Problem 202 Using Tables of Binomial Probabilities 206 Expected Value and Variance for the Binomial Distribution 207

5.5 Poisson Probability Distribution 210

An Example Involving Time Intervals 211

An Example Involving Length or Distance Intervals 213

5.6 Hypergeometric Probability Distribution 214 Summary 217

Glossary 218 Key Formulas 219 Supplementary Exercises 220 Appendix 5.1 Discrete Probability Distributions with Minitab 222 Appendix 5.2 Discrete Probability Distributions with Excel 223

Chapter 6 Continuous Probability Distributions 225 Statistics in Practice: Procter & Gamble 226

6.1 Uniform Probability Distribution 227

Area as a Measure of Probability 228

6.2 Normal Probability Distribution 231

Normal Curve 231 Standard Normal Probability Distribution 233 Computing Probabilities for Any Normal Probability Distribution 238 Grear Tire Company Problem 239

6.3 Normal Approximation of Binomial Probabilities 243 6.4 Exponential Probability Distribution 246

Computing Probabilities for the Exponential Distribution 247 Relationship Between the Poisson and Exponential Distributions 248

Summary 250 Glossary 250 Key Formulas 251 Supplementary Exercises 251

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Case Problem: Specialty Toys 254

Appendix 6.1 Continuous Probability Distributions with Minitab 255

Appendix 6.2 Continuous Probability Distributions with Excel 256

Chapter 7 Sampling and Sampling Distributions 257

Statistics in Practice: MeadWestvaco Corporation 258

7.1 The Electronics Associates Sampling Problem 259

7.2 Simple Random Sampling 260

Sampling from a Finite Population 260

Sampling from an Infinite Population 261

Relationship Between the Sample Size and the Sampling

7.6 Sampling Distribution of p _ 280

7.7 Properties of Point Estimators 285

Unbiased 286

Efficiency 287

Consistency 287

7.8 Other Sampling Methods 288

Stratified Random Sampling 288

Appendix 7.1 The Expected Value and Standard Deviation of x _ 295

Appendix 7.2 Random Sampling with Minitab 296

Appendix 7.3 Random Sampling with Excel 297

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Chapter 8 Interval Estimation 299 Statistics in Practice: Food Lion 300 8.1 Population Mean: ␴ Known 301

Margin of Error and the Interval Estimate 301 Practical Advice 305

8.2 Population Mean: ␴ Unknown 307

Margin of Error and the Interval Estimate 308 Practical Advice 311

Using a Small Sample 311 Summary of Interval Estimation Procedures 313

8.3 Determining the Sample Size 316 8.4 Population Proportion 319

Determining the Sample Size 321

Summary 324 Glossary 325 Key Formulas 326 Supplementary Exercises 326 Case Problem 1: Young Professional Magazine 329 Case Problem 2: Gulf Real Estate Properties 330 Case Problem 3: Metropolitan Research, Inc 332 Appendix 8.1 Interval Estimation with Minitab 332 Appendix 8.2 Interval Estimation Using Excel 334

Chapter 9 Hypothesis Tests 338 Statistics in Practice: John Morrell & Company 339 9.1 Developing Null and Alternative Hypotheses 340

Testing Research Hypotheses 340 Testing the Validity of a Claim 340 Testing in Decision-Making Situations 341 Summary of Forms for Null and Alternative Hypotheses 341

9.2 Type I and Type II Errors 342 9.3 Population Mean: ␴ Known 345

One-Tailed Test 345 Two-Tailed Test 351 Summary and Practical Advice 354 Relationship Between Interval Estimation and Hypothesis Testing 355

9.4 Population Mean: ␴ Unknown 359

One-Tailed Test 360 Two-Tailed Test 361 Summary and Practical Advice 362

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9.5 Population Proportion 365

Summary 368

9.6 Hypothesis Testing and Decision Making 370

9.7 Calculating the Probability of Type II Errors 371

9.8 Determining the Sample Size for a Hypothesis Test About

Case Problem 1: Quality Associates, Inc 385

Case Problem 2: Unemployment Study 386

Appendix 9.1 Hypothesis Testing with Minitab 386

Appendix 9.2 Hypothesis Testing with Excel 388

Chapter 10 Statistical Inference About Means and Proportions

Statistics in Practice: U.S Food and Drug Administration 394

10.1 Inferences About the Difference Between Two Population Means:

Case Problem: Par, Inc 428

Appendix 10.1 Inferences About Two Populations Using Minitab 429

Appendix 10.2 Inferences About Two Populations Using Excel 431

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Chapter 11 Inferences About Population Variances 434 Statistics in Practice: U.S General Accounting Office 435 11.1 Inferences About a Population Variance 436

Interval Estimation 436 Hypothesis Testing 440

11.2 Inferences About Two Populations Variances 445 Summary 452

Key Formulas 452 Supplementary Exercises 453 Case Problem: Air Force Training Program 454 Appendix 11.1 Population Variances with Minitab 455 Appendix 11.2 Population Variances with Excel 456

Chapter 12 Tests of Goodness of Fit and Independence 457 Statistics in Practice: United Way 458

12.1 Goodness of Fit Test: A Multinomial Population 459 12.2 Test of Independence 464

12.3 Goodness of Fit Test: Poisson and Normal Distributions 472

Poisson Distribution 472 Normal Distribution 476

Summary 481 Glossary 481 Key Formulas 481 Supplementary Exercises 482 Case Problem: A Bipartisan Agenda for Change 485 Appendix 12.1 Tests of Goodness of Fit and Independence Using Minitab 486 Appendix 12.2 Tests of Goodness of Fit and Independence Using Excel 487

Chapter 13 Experimental Design and Analysis of Variance 490 Statistics in Practice: Burke Marketing Services, Inc 491

13.1 An Introduction to Experimental Design and Analysis of Variance 492

Data Collection 493 Assumptions for Analysis of Variance 494 Analysis of Variance: A Conceptual Overview 494

13.2 Analysis of Variance and the Completely Randomized Design 497

Between-Treatments Estimate of Population Variance 498 Within-Treatments Estimate of Population Variance 499

Comparing the Variance Estimates: The F Test 500

ANOVA Table 502 Computer Results for the Analysis of Variance 503

Testing for the Equality of k Population Means: An Observational Study 504

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13.3 Multiple Comparison Procedures 508

Fisher’s LSD 508

Type I Error Rates 511

13.4 Randomized Block Design 514

Air Traffic Controller Stress Test 515

Case Problem 1: Wentworth Medical Center 536

Case Problem 2: Compensation for Sales Professionals 537

Appendix 13.1 Analysis of Variance with Minitab 538

Appendix 13.2 Analysis of Variance with Excel 539

Chapter 14 Simple Linear Regression 543

Statistics in Practice: Alliance Data Systems 544

14.1 Simple Linear Regression Model 545

Regression Model and Regression Equation 545

Estimated Regression Equation 546

14.2 Least Squares Method 548

Some Cautions About the Interpretation of Significance Tests 573

14.6 Using the Estimated Regression Equation for Estimation

and Prediction 577

Point Estimation 577

Interval Estimation 577

Confidence Interval for the Mean Value of y 578

Prediction Interval for an Individual Value of y 579

14.7 Computer Solution 583

14.8 Residual Analysis: Validating Model Assumptions 588

Residual Plot Against x 589

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Residual Plot Against yˆ 590

Standardized Residuals 590 Normal Probability Plot 593

14.9 Residual Analysis: Outliers and Influential Observations 597

Detecting Outliers 597 Detecting Influential Observations 599

Summary 604 Glossary 605 Key Formulas 606 Supplementary Exercises 608 Case Problem 1: Measuring Stock Market Risk 614 Case Problem 2: U.S Department of Transportation 615 Case Problem 3: Alumni Giving 616

Case Problem 4: Major League Baseball Team Values 616 Appendix 14.1 Calculus-Based Derivation of Least Squares Formulas 618 Appendix 14.2 A Test for Significance Using Correlation 619

Appendix 14.3 Regression Analysis with Minitab 620 Appendix 14.4 Regression Analysis with Excel 621

Chapter 15 Multiple Regression 624 Statistics in Practice: International Paper 625 15.1 Multiple Regression Model 626

Regression Model and Regression Equation 626 Estimated Multiple Regression Equation 626

15.2 Least Squares Method 627

An Example: Butler Trucking Company 628 Note on Interpretation of Coefficients 630

15.3 Multiple Coefficient of Determination 636 15.4 Model Assumptions 639

15.5 Testing for Significance 640

15.7 Qualitative Independent Variables 649

An Example: Johnson Filtration, Inc 649 Interpreting the Parameters 651

More Complex Qualitative Variables 653

15.8 Residual Analysis 658

Detecting Outliers 659 Studentized Deleted Residuals and Outliers 660

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Influential Observations 661

Using Cook’s Distance Measure to Identify Influential Observations 661

15.9 Logistic Regression 665

Logistic Regression Equation 666

Estimating the Logistic Regression Equation 667

Testing for Significance 669

Case Problem 1: Consumer Research, Inc 685

Case Problem 2: Predicting Student Proficiency Test Scores 686

Case Problem 3: Alumni Giving 687

Case Problem 4: Predicting Winning Percentage for the NFL 689

Appendix 15.1 Multiple Regression with Minitab 690

Appendix 15.2 Multiple Regression with Excel 690

Appendix 15.3 Logistic Regression with Minitab 691

Chapter 16 Regression Analysis: Model Building 693

Statistics in Practice: Monsanto Company 694

16.1 General Linear Model 695

Modeling Curvilinear Relationships 695

Interaction 699

Transformations Involving the Dependent Variable 701

Nonlinear Models That Are Intrinsically Linear 705

16.2 Determining When to Add or Delete Variables 710

General Case 712

Use of p-Values 713

16.3 Analysis of a Larger Problem 717

16.4 Variable Selection Procedures 720

Stepwise Regression 721

Forward Selection 722

Backward Elimination 723

Best-Subsets Regression 723

Making the Final Choice 724

16.5 Multiple Regression Approach to Experimental Design 727

16.6 Autocorrelation and the Durbin-Watson Test 731

Summary 736

Glossary 736

Key Formulas 736

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Supplementary Exercises 737 Case Problem 1: Analysis of PGA Tour Statistics 740 Case Problem 2: Fuel Economy for Cars 741

Case Problem 3: Predicting Graduation Rates for Colleges and Universities 741

Appendix 16.1: Variable Selection Procedures with Minitab 742

Chapter 17 Index Numbers 744 Statistics in Practice: U.S Department of Labor, Bureau of Labor Statistics 745

17.1 Price Relatives 746 17.2 Aggregate Price Indexes 746 17.3 Computing an Aggregate Price Index from Price Relatives 750 17.4 Some Important Price Indexes 752

Consumer Price Index 752 Producer Price Index 752 Dow Jones Averages 753

17.5 Deflating a Series by Price Indexes 754 17.6 Price Indexes: Other Considerations 758

Selection of Items 758 Selection of a Base Period 758 Quality Changes 758

17.7 Quantity Indexes 759 Summary 761

Glossary 761 Key Formulas 761 Supplementary Exercises 762

Chapter 18 Forecasting 765 Statistics in Practice: Nevada Occupational Health Clinic 766 18.1 Components of a Time Series 767

Trend Component 767 Cyclical Component 769 Seasonal Component 770 Irregular Component 770

18.2 Smoothing Methods 770

Moving Averages 770 Weighted Moving Averages 772 Exponential Smoothing 774

18.3 Trend Projection 780

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18.4 Trend and Seasonal Components 786

Multiplicative Model 786

Calculating the Seasonal Indexes 787

Deseasonalizing the Time Series 791

Using the Deseasonalized Time Series to Identify Trend 791

Case Problem 1: Forecasting Food and Beverage Sales 806

Case Problem 2: Forecasting Lost Sales 807

Appendix 18.1 Forecasting with Minitab 808

Appendix 18.2 Forecasting with Excel 810

Chapter 19 Nonparametric Methods 812

Statistics in Practice: West Shell Realtors 813

19.1 Sign Test 815

Small-Sample Case 815

Large-Sample Case 817

Hypothesis Test About a Median 818

19.2 Wilcoxin Signed-Rank Test 820

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Chapter 20 Statistical Methods for Quality Control 846 Statistics in Practice: Dow Chemical Company 847

20.1 Philosophies and Frameworks 848

Malcolm Baldrige National Quality Award 848 ISO 9000 849

x

_ Chart: Process Mean and Standard Deviation Unknown 855

Summary 874 Glossary 874 Key Formulas 875 Supplementary Exercises 876 Appendix 20.1 Control Charts with Minitab 878

Chapter 21 Decision Analysis 879 Statistics in Practice: Ohio Edison Company 880 21.1 Problem Formulation 881

Payoff Tables 882 Decision Trees 882

21.2 Decision Making with Probabilities 883

Expected Value Approach 883 Expected Value of Perfect Information 885

21.3 Decision Analysis with Sample Information 891

Decision Tree 892 Decision Strategy 893 Expected Value of Sample Information 896

21.4 Computing Branch Probabilities Using Bayes’ Theorem 902 Summary 906

Glossary 907 Key Formulas 908 Case Problem: Lawsuit Defense Strategy 908 Appendix 21.1 Solving the PDC Problem with TreePlan 909

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Chapter 22 Sample Survey On CD

Statistics in Practice: Duke Energy 22-2

22.1 Terminology Used in Sample Surveys 22-2

22.2 Types of Surveys and Sampling Methods 22-3

Determining the Sample Size 22-9

22.5 Stratified Simple Random Sampling 22-12

Appendix: Self-Test Solutions and Answers to Even-Numbered Exercises 22-37

Appendix A References and Bibliography 916

Appendix B Tables 918

Appendix C Summation Notation 946

Appendix D Self-Test Solutions and Answers to Even-Numbered

Exercises 948

Appendix E Using Excel Functions 995

Appendix F Computing p-Values Using Minitab and Excel 1000 Index 1004

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The purpose of STATISTICS FOR BUSINESS AND ECONOMICS is to give students,

pri-marily those in the fields of business administration and economics, a conceptual duction to the field of statistics and its many applications The text is applications orientedand written with the needs of the nonmathematician in mind; the mathematical prerequisite

intro-is knowledge of algebra

Applications of data analysis and statistical methodology are an integral part of the nization and presentation of the text material The discussion and development of each tech-nique is presented in an application setting, with the statistical results providing insights todecisions and solutions to problems

orga-Although the book is applications oriented, we have taken care to provide sound ological development and to use notation that is generally accepted for the topic being covered.Hence, students will find that this text provides good preparation for the study of more ad-vanced statistical material A bibliography to guide further study is included as an appendix.The text introduces the student to the software packages of Minitab and Microsoft®Excel and emphasizes the role of computer software in the application of statistical analysis.Minitab is illustrated as it is one of the leading statistical software packages for botheducation and statistical practice Excel is not a statistical software package, but the wideavailability and use of Excel makes it important for students to understand the statisticalcapabilities of this package Minitab and Excel procedures are provided in appendixes so thatinstructors have the flexibility of using as much computer emphasis as desired for the course

method-Changes in the Tenth Edition

We appreciate the acceptance and positive response to the previous editions of STATISTICS FOR BUSINESS AND ECONOMICS Accordingly, in making modifications for this new

edition, we have maintained the presentation style and readability of those editions Thesignificant changes in the new edition are summarized here

Content Revisions

The following list summarizes selected content revisions for the new edition

• p-Values In the previous edition, we emphasized the use of p-values as the preferred

approach to hypothesis testing We continue this approach in the new edition

How-ever, we have eased the introduction to p-values by simplifying the conceptual nition for the student We now say, “A p-value is a probability that provides a measure

defi-of the evidence against the null hypothesis provided by the sample The smaller the

p-value, the more evidence there is against H0.” After this conceptual definition, we

provide operational definitions that make it clear how the p-value is computed for a

lower tail test, an upper tail test, and a two-tail test Based on our experience, we havefound that separating the conceptual definition from the operational definitions ishelpful to the student trying to digest difficult new material

• Minitab and Excel Procedures for Computing p-values New to this edition is an

appendix showing how Minitab and Excel can be used to compute p-values ated with z, t,2, and F test statistics Students who use hand calculations to com-

associ-pute the value of test statistics will be shown how statistical tables can be used to

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provide a range for the p-value Appendix F provides a means for these students to

compute the exact p-value using Minitab or Excel This appendix will be helpful for

the coverage of hypothesis testing in Chapters 9 through 16

• Cumulative Standard Normal Distribution Table It may be a surprise to many

of our users, but in the new edition we use the cumulative standard normal tion table We are making this change because of what we believe is the growingtrend for more and more students and practitioners alike to use statistics in an envi-ronment that emphasizes modern computer software Historically, a table was used

distribu-by everyone because a table was the only source of information about the normaldistribution However, many of today’s students are ready and willing to learn aboutthe use of computer software in statistics Students will find that virtually everycomputer software package uses the cumulative standard normal distribution Thus,

it is becoming more and more important for introductory statistical texts to use anormal probability table that is consistent with what the student will see when work-ing with statistical software It is no longer desirable to use one form of the standardnormal distribution table in the text and then use a different type of standard normaldistribution calculation when using a software package Those who are using the cu-mulative normal distribution table for the first time will find that, in general, it easesthe normal probability calculations In particular, a cumulative normal probability

table makes it easier to compute p-values for hypothesis testing.

• Experimental Design and Analysis of Variance Chapter 13 has been shortened

and now begins with an introduction to experimental design concepts The pletely randomized design, the randomized block design, and factorial experimentsare covered Analysis of variance is presented as the primary technique for analyz-ing these designs We also show that the analysis of variance procedure can be usedfor observational studies

com-• Other Content Revisions The following additional content revisions appear in the

new edition

• New examples of times series data are provided in Chapter 1

• The Excel appendix to Chapter 2 now provides more complete instructions onhow to develop a frequency distribution and a histogram for quantitative data

• Revised guidelines on the sample size necessary to use the t distribution now provide a consistency for the use of the t distribution in Chapters 8, 9, and 10.

• Chapter 17 has been updated with current index numbers

• The Solutions Manual now shows the exercise solution steps using the tive normal distribution and more details in the explanations about how to

cumula-compute p-values for hypothesis testing.

New Examples and Exercises Based on Real Data

We have added approximately 200 new examples and exercises based on real data and cent reference sources of statistical information Using data pulled from sources also used

re-by the Wall Street Journal, USA Today, Fortune, Barron’s, and a variety of other sources,

we have drawn actual studies to develop explanations and to create exercises that strate many uses of statistics in business and economics We believe that the use of real datahelps generate more student interest in the material and enables the student to learn aboutboth the statistical methodology and its application The tenth edition of the text containsapproximately 350 examples and exercises based on real data

demon-New Case Problems

We have added six new case problems to this edition, bringing the total number of caseproblems in the text to thirty-one The new case problems appear in the chapters on

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descriptive statistics, interval estimation, and regression These case problems providestudents with the opportunity to analyze somewhat larger data sets and prepare managerialreports based on the results of the analysis.

Features and Pedagogy

Authors Anderson, Sweeney, and Williams have continued many of the features that peared in previous editions Important ones for students are noted here

Methods Exercises and Applications Exercises

The end-of-section exercises are split into two parts, Methods and Applications The ods exercises require students to use the formulas and make the necessary computations.The Applications exercises require students to use the chapter material in real-world situa-tions Thus, students first focus on the computational “nuts and bolts” and then move on tothe subtleties of statistical application and interpretation

Meth-Self-Test Exercises

Certain exercises are identified as self-test exercises Completely worked-out solutions forthose exercises are provided in Appendix D at the back of the book Students can attemptthe self-test exercises and immediately check the solution to evaluate their understanding

of the concepts presented in the chapter

Margin Annotations and Notes and Comments

Margin annotations that highlight key points and provide additional insights for the student are

a key feature of this text These annotations, which appear in the margins, are designed to vide emphasis and enhance understanding of the terms and concepts being presented in the text

pro-At the end of many sections, we provide Notes and Comments designed to give the dent additional insights about the statistical methodology and its application Notes andComments include warnings about or limitations of the methodology, recommendations forapplication, brief descriptions of additional technical considerations, and other matters

stu-Data Files Accompany the Text

Over 200 data files are available on the CD-ROM that is packaged with the text The datasets are available in both Minitab and Excel formats Data set logos are used in the text toidentify the data sets that are available on the CD Data sets for all case problems as well

as data sets for larger exercises are included

Get Choice and Flexibility

with ThomsonNOW™

You envisioned it, we developed it Designed by instructors and students for instructors and

students, ThomsonNOW for ASW’s Statistics for Business and Economics is the most

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reliable, flexible, and easy-to-use online suite of services and resources With efficient andimmediate paths to success, ThomsonNOW delivers the results you expect.

• Personalized learning plans For every chapter, personalized learning plans allow

stu-dents to focus on what they still need to learn and to select the activities that best matchtheir learning styles (such as the relevant EasyStat tutorials, animations, step-by-stepproblem demonstrations, and text pages)

• More study options Students can choose how they read the textbook—via

inte-grated digital eBook or by reading the print version

Ancillary Learning Materials for Students

• A Student CD is packaged free with each new text It provides over 200 data files,

and they are available in both Minitab and Excel formats Data sets for all case lems, as well as data sets for larger exercises, are included The Student CD alsocontains the file for Chapter 22, Sample Survey, and the software and manual forthe educational version of TreePlan™ TreePlan is a Microsoft®Excel add-in thatallows users to build decision trees in Excel

prob-• EasyStat: Digital Tutor for Minitab Release 14 and EasyStat Digital Tutor for Microsoft ® Excel, Version 2 These focused online tutorials will make it easier for

students to learn how to use one of these well-known software products to performstatistical analysis In each digital video, one of the textbook authors demonstrateshow the software can be used to perform a particular statistical procedure The EasyStat for Excel tutorials are included in the ThomsonNOW packagedescribed earlier Students may purchase an online subscription for the Minitab or

the Excel version of EasyStat Digital Tutor at easystat.swlearning.com.

• Another student ancillary is the Microsoft ® Excel Companion for Business Statistics, 3e (ISBN: 0-324-22253-9) by David Eldredge of Murray State Univer-

sity This manual provides step-by-step instructions for using Excel to solve many

of the problems included in introductory business statistics Directions for the latestversion of Excel are included

Acknowledgments

A special thanks goes to our associates from business and industry that supplied the tics in Practice features We recognize them individually by a credit line in each of thearticles Finally, we are also indebted to our senior acquisitions editor Charles McCormick, Jr.,our senior developmental editor Alice Denny, our content project manager, Amy Hackett, oursenior marketing manager Larry Qualls, and others at Thomson South-Western for their ed-itorial counsel and support during the preparation of this text

Statis-David R Anderson Dennis J Sweeney Thomas A Williams

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About the Authors

David R Anderson. David R Anderson is Professor of Quantitative Analysis in the lege of Business Administration at the University of Cincinnati Born in Grand Forks, NorthDakota, he earned his B.S., M.S., and Ph.D degrees from Purdue University ProfessorAnderson has served as Head of the Department of Quantitative Analysis and OperationsManagement and as Associate Dean of the College of Business Administration In addition,

Col-he was tCol-he coordinator of tCol-he College’s first Executive Program

At the University of Cincinnati, Professor Anderson has taught introductory statisticsfor business students as well as graduate-level courses in regression analysis, multivariateanalysis, and management science He has also taught statistical courses at the Department

of Labor in Washington, D.C He has been honored with nominations and awards forexcellence in teaching and excellence in service to student organizations

Professor Anderson has coauthored ten textbooks in the areas of statistics, managementscience, linear programming, and production and operations management He is an activeconsultant in the field of sampling and statistical methods

Dennis J Sweeney. Dennis J Sweeney is Professor of Quantitative Analysis and Founder

of the Center for Productivity Improvement at the University of Cincinnati Born in DesMoines, Iowa, he earned a B.S.B.A degree from Drake University and his M.B.A andD.B.A degrees from Indiana University, where he was an NDEA Fellow During 1978–79,Professor Sweeney worked in the management science group at Procter & Gamble; during1981–82, he was a visiting professor at Duke University Professor Sweeney served as Head

of the Department of Quantitative Analysis and as Associate Dean of the College ofBusiness Administration at the University of Cincinnati

Professor Sweeney has published more than thirty articles and monographs in the area

of management science and statistics The National Science Foundation, IBM, Procter &Gamble, Federated Department Stores, Kroger, and Cincinnati Gas & Electric have funded

his research, which has been published in Management Science, Operations Research, Mathematical Programming, Decision Sciences, and other journals.

Professor Sweeney has coauthored ten textbooks in the areas of statistics, managementscience, linear programming, and production and operations management

Thomas A Williams. Thomas A Williams is Professor of Management Science in theCollege of Business at Rochester Institute of Technology Born in Elmira, New York, heearned his B.S degree at Clarkson University He did his graduate work at RensselaerPolytechnic Institute, where he received his M.S and Ph.D degrees

Before joining the College of Business at RIT, Professor Williams served for sevenyears as a faculty member in the College of Business Administration at the University ofCincinnati, where he developed the undergraduate program in Information Systems andthen served as its coordinator At RIT he was the first chairman of the Decision SciencesDepartment He teaches courses in management science and statistics, as well as graduatecourses in regression and decision analysis

Professor Williams is the coauthor of eleven textbooks in the areas of managementscience, statistics, production and operations management, and mathematics He has been

a consultant for numerous Fortune 500 companies and has worked on projects ranging from

the use of data analysis to the development of large-scale regression models

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Data and Statistics

1.3 DATA SOURCESExisting SourcesStatistical StudiesData Acquisition Errors

1.4 DESCRIPTIVE STATISTICS

1.5 STATISTICAL INFERENCE

1.6 COMPUTERS ANDSTATISTICAL ANALYSIS

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With a global circulation of more than 1 million,

Busi-nessWeek is the most widely read business magazine in

the world More than 200 dedicated reporters and editors

in 26 bureaus worldwide deliver a variety of articles of

interest to the business and economic community Along

with feature articles on current topics, the magazine

contains regular sections on International Business,

Eco-nomic Analysis, Information Processing, and Science &

Technology Information in the feature articles and the

regular sections helps readers stay abreast of current

de-velopments and assess the impact of those dede-velopments

on business and economic conditions

Most issues of BusinessWeek provide an in-depth

report on a topic of current interest Often, the in-depth

reports contain statistical facts and summaries that help

the reader understand the business and economic

infor-mation For example, the December 6, 2004, issue

in-cluded a special report on the pricing of goods made in

China; the January 3, 2005, issue provided information

about where to invest in 2005; and the April 4, 2005,

issue provided an overview of the BusinessWeek 50, a

diverse group of top-performing companies In addition,

the weekly BusinessWeek Investor provides statistics

about the state of the economy, including production

indexes, stock prices, mutual funds, and interest rates

BusinessWeek also uses statistics and statistical

in-formation in managing its own business For example,

an annual survey of subscribers helps the company learn

about subscriber demographics, reading habits, likely

purchases, lifestyles, and so on BusinessWeek managers

use statistical summaries from the survey to provide

better services to subscribers and advertisers One recentNorth American subscriber survey indicated that 90% of

BusinessWeek subscribers use a personal computer at home and that 64% of BusinessWeek subscribers are

involved with computer purchases at work Such

statis-tics alert BusinessWeek managers to subscriber interest

in articles about new developments in computers Theresults of the survey are also made available to potentialadvertisers The high percentage of subscribers usingpersonal computers at home and the high percentage ofsubscribers involved with computer purchases at workwould be an incentive for a computer manufacturer to

consider advertising in BusinessWeek.

In this chapter, we discuss the types of data availablefor statistical analysis and describe how the data are ob-tained We introduce descriptive statistics and statisticalinference as ways of converting data into meaningfuland easily interpreted statistical information

BusinessWeek uses statistical facts and summaries

BUSINESSWEEK*

NEW YORK, NEW YORK

*The authors are indebted to Charlene Trentham, Research Manager at

BusinessWeek, for providing this Statistics in Practice.

Frequently, we see the following types of statements in newspapers and magazines:

• The National Association of Realtors reported that the median selling price for a

house in the United States was $215,000 (The Wall Street Journal, January 16,

2006)

• The average cost of a 30-second television commercial during the 2006 Super Bowl

game was $2.5 million (USA Today, January 27, 2006).

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1.1 Applications in Business and Economics 3

• A Jupiter Media survey found 31% of adult males watch television 10 or more hours

a week For adult women it was 26% (The Wall Street Journal, January 26, 2004).

• General Motors, a leader in automotive cash rebates, provided an average cash

incentive of $4300 per vehicle (USA Today, January 27, 2006).

• More than 40% of Marriott International managers work their way up through the

ranks (Fortune, January 20, 2003).

• The New York Yankees have the highest payroll in major league baseball In 2005, the

team payroll was $208,306,817, with a median of $5,833,334 per player (USA Today

Salary Database, February 2006)

• The Dow Jones Industrial Average closed at 11,577 (Barron’s, May 6, 2006).

The numerical facts in the preceding statements ($215,000; $2.5 million; 31%; 26%;

$4300; 40%; $5,833,334; and 11,577) are called statistics In this usage, the term statistics

refers to numerical facts such as averages, medians, percents, and index numbers that help

us understand a variety of business and economic conditions However, as you will see, thefield, or subject, of statistics involves much more than numerical facts In a broader sense,

statisticsis defined as the art and science of collecting, analyzing, presenting, and preting data Particularly in business and economics, the information provided by collect-ing, analyzing, presenting, and interpreting data gives managers and decision makers abetter understanding of the business and economic environment and thus enables them tomake more informed and better decisions In this text, we emphasize the use of statisticsfor business and economic decision making

inter-Chapter 1 begins with some illustrations of the applications of statistics in business and

economics In Section 1.2 we define the term data and introduce the concept of a data set This section also introduces key terms such as variables and observations, discusses the

difference between quantitative and qualitative data, and illustrates the uses of sectional and time series data Section 1.3 discusses how data can be obtained from exist-ing sources or through survey and experimental studies designed to obtain new data Theimportant role that the Internet now plays in obtaining data is also highlighted The uses ofdata in developing descriptive statistics and in making statistical inferences are described

cross-in Sections 1.4 and 1.5

1.1 Applications in Business and Economics

In today’s global business and economic environment, anyone can access vast amounts ofstatistical information The most successful managers and decision makers understand theinformation and know how to use it effectively In this section, we provide examples thatillustrate some of the uses of statistics in business and economics

Accounting

Public accounting firms use statistical sampling procedures when conducting audits fortheir clients For instance, suppose an accounting firm wants to determine whether theamount of accounts receivable shown on a client’s balance sheet fairly represents the ac-tual amount of accounts receivable Usually the large number of individual accounts re-ceivable makes reviewing and validating every account too time-consuming and expensive

As common practice in such situations, the audit staff selects a subset of the accountscalled a sample After reviewing the accuracy of the sampled accounts, the auditors draw aconclusion as to whether the accounts receivable amount shown on the client’s balancesheet is acceptable

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Financial analysts use a variety of statistical information to guide their investment mendations In the case of stocks, the analysts review a variety of financial data includingprice/earnings ratios and dividend yields By comparing the information for an individualstock with information about the stock market averages, a financial analyst can begin todraw a conclusion as to whether an individual stock is over- or underpriced For example,

recom-Barron’s (September 12, 2005) reported that the average price/earnings ratio for the 30 stocks

in the Dow Jones Industrial Average was 16.5 JPMorgan showed a price/earnings ratio of11.8 In this case, the statistical information on price/earnings ratios indicated a lower price

in comparison to earnings for JPMorgan than the average for the Dow Jones stocks fore, a financial analyst might conclude that JPMorgan was underpriced This and otherinformation about JPMorgan would help the analyst make a buy, sell, or hold recommen-dation for the stock

There-Marketing

Electronic scanners at retail checkout counters collect data for a variety of marketing search applications For example, data suppliers such as ACNielsen and Information Re-sources, Inc., purchase point-of-sale scanner data from grocery stores, process the data, andthen sell statistical summaries of the data to manufacturers Manufacturers spend hundreds

re-of thousands re-of dollars per product category to obtain this type re-of scanner data turers also purchase data and statistical summaries on promotional activities such as spe-cial pricing and the use of in-store displays Brand managers can review the scannerstatistics and the promotional activity statistics to gain a better understanding of the rela-tionship between promotional activities and sales Such analyses often prove helpful inestablishing future marketing strategies for the various products

Manufac-Production

Today’s emphasis on quality makes quality control an important application of statistics

in production A variety of statistical quality control charts are used to monitor the

out-put of a production process In particular, an x-bar chart can be used to monitor the average

output Suppose, for example, that a machine fills containers with 12 ounces of a soft drink.Periodically, a production worker selects a sample of containers and computes the average

number of ounces in the sample This average, or x-bar value, is plotted on an x-bar chart A

plotted value above the chart’s upper control limit indicates overfilling, and a plotted valuebelow the chart’s lower control limit indicates underfilling The process is termed “in con-

trol” and allowed to continue as long as the plotted x-bar values fall between the chart’s upper and lower control limits Properly interpreted, an x-bar chart can help determine when

adjustments are necessary to correct a production process

Economics

Economists frequently provide forecasts about the future of the economy or some aspect of

it They use a variety of statistical information in making such forecasts For instance, inforecasting inflation rates, economists use statistical information on such indicators as the Producer Price Index, the unemployment rate, and manufacturing capacity utilization.Often these statistical indicators are entered into computerized forecasting models thatpredict inflation rates

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1.2 Data 5

Applications of statistics such as those described in this section are an integral part ofthis text Such examples provide an overview of the breadth of statistical applications Tosupplement these examples, practitioners in the fields of business and economics providedchapter-opening Statistics in Practice articles that introduce the material covered in eachchapter The Statistics in Practice applications show the importance of statistics in a widevariety of business and economic situations

Dataare the facts and figures collected, analyzed, and summarized for presentation and terpretation All the data collected in a particular study are referred to as the data setfor thestudy Table 1.1 shows a data set containing information for 25 companies that are part ofthe S&P 500 The S&P 500 is made up of 500 companies selected by Standard & Poor’s.These companies account for 76% of the market capitalization of all U.S stocks S&P 500stocks are closely followed by investors and Wall Street analysts

in-Earnings

Source: BusinessWeek (April 4, 2005).

TABLE 1.1 DATA SET FOR 25 S&P 500 COMPANIES

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