Business statistics 8th edition 20101

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Library of Congress Cataloging-in-Publication Data

Business statistics : a decision-making approach / David F Groebner [et al.] — 8th ed.

David F Groebner

To Kathy, my wife and best friend; to our children, Jackie and Jason;

and to my parents, John and Ruth Shannon.

David F Groebneris Professor Emeritus of Production Management in theCollege of Business and Economics at Boise State University He has bachelor’s and mas-ter’s degrees in engineering and a Ph.D in business administration After working as anengineer, he has taught statistics and related subjects for 27 years In addition to writ-ing textbooks and academic papers, he has worked extensively with both small andlarge organizations, including Hewlett-Packard, Boise Cascade, Albertson’s, and Ore-Ida He has worked with numerous government agencies, including Boise Cityand the U.S Air Force.

Patrick W Shannon, Ph.D. is Dean and Professor of Supply Chain Operations

Management in the College of Business and Economics at Boise State University In addition to his

administrative responsibilities, he has taught graduate and undergraduate courses in business

statis-tics, quality management, and production and operations management In addition, Dr Shannon has

lectured and consulted in the statistical analysis and quality management areas for over 20 years

Among his consulting clients are Boise Cascade Corporation; Hewlett-Packard; PowerBar, Inc.;

Potlatch Corporation; Woodgrain Millwork, Inc.; J.R Simplot Company; Zilog Corporation;

and numerous other public- and private-sector organizations Professor Shannon has co-authored

several university-level textbooks and has published numerous articles in such journals as Business Horizons,

Interfaces, Journal of Simulation, Journal of Production and Inventory Control, Quality Progress, and

Journal of Marketing Research He obtained B.S and M.S degrees from the University of Montana and a

Ph.D in Statistics and Quantitative Methods from the University of Oregon

Phillip C Fryis a Professor in the College of Business and Economics at BoiseState University, where he has taught since 1988 Phil received his B.A and M.B.A

degrees from the University of Arkansas, and his M.S and Ph.D degrees fromLouisiana State University His teaching and research interests are in the areas ofbusiness statistics, production management, and quantitative business modeling Inaddition to his academic responsibilities, Phil has consulted with and provided training to small and large organizations, including Boise Cascade Corporation;

Hewlett-Packard Corporation; The J.R Simplot Company; United Water of Idaho;

Woodgrain Millwork, Inc.; Boise City; and Micron Electronics

Phil spends most of his free time with his wife, Susan, and his four children, Phillip Alexander,

Alejan-dra Johanna, and twins Courtney Rene and Candace Marie

Kent D Smithreceived a Ph.D in Applied Statistics from the University of California, Riverside

He holds a master of science degree in Statistics from the University of California, Riverside, and a

mas-ter of science degree in Systems Analysis from the Air Force Institute of Technology His bachelor of arts

degree in Mathematics was obtained from the University of Utah Dr Smith has served as a

Univer-sity Statistical Consultant at the UniverUniver-sity of California, Riverside, and at California

Polytech-nic State University, San Luis Obispo His private consulting has ranged from serving as an

expert witness in legal cases, survey sampling for corporations and private researchers,

med-ical and orthodontic research, and assisting graduate students with analysis required for

mas-ter and doctoral degrees in various disciplines

Dr Smith began teaching as a part-time lecturer at California State University, San Bernardino While

completing his doctoral dissertation, he served as a lecturer at University of California, Riverside Currently,

he is Professor Emeritus of Statistics at California Polytechnic State University, San Luis Obispo Though

tired, he still teaches part time at the university The subjects he teaches include upper-division courses in

re-gression, analysis of variance, linear models, and probability and mathematical statistics, as well as a full array

of service courses

v

Chapter 1 The Where, Why, and How of Data Collection 1

Chapter 2 Graphs, Charts, and Tables—Describing Your Data 31

Chapter 3 Describing Data Using Numerical Measures 85

Chapters 1–3 Special Review Section 139

Chapter 4 Using Probability and Probability Distributions 146

Chapter 5 Discrete Probability Distributions 191

Chapter 6 Introduction to Continuous Probability Distributions 233

Chapter 7 Introduction to Sampling Distributions 264

Chapter 8 Estimating Single Population Parameters 305

Chapter 9 Introduction to Hypothesis Testing 346

Chapter 10 Estimation and Hypothesis Testing for Two Population Parameters 397

Chapter 11 Hypothesis Tests and Estimation for Population Variances 448

Chapter 12 Analysis of Variance 475

Chapters 8–12 Special Review Section 530

Chapter 13 Goodness-of-Fit Tests and Contingency Analysis 547

Chapter 14 Introduction to Linear Regression and Correlation Analysis 579

Chapter 15 Multiple Regression Analysis and Model Building 633

Chapter 16 Analyzing and Forecasting Time-Series Data 709

Chapter 17 Introduction to Nonparametric Statistics 770

Chapter 18 Introduction to Quality and Statistical Process Control 804

APPENDIX B Binomial Distribution Table 838

APPENDIX C Poisson Probability Distribution Table 851

APPENDIX D Standard Normal Distribution Table 856

APPENDIX E Exponential Distribution Table 857

APPENDIX F Values of tfor Selected Probabilities 858

APPENDIX G Values of2for Selected Probabilities 859

APPENDIX H F-Distribution Table 860

APPENDIX I Critical Values of Hartley’s FmaxTest 866

APPENDIX J Distribution of the Studentized Range (q-values) 867

APPENDIX K Critical Values of rin the Runs Test 869

APPENDIX L Mann-WhitneyUTest Probabilities (n < 9) 870

APPENDIX M Mann-WhitneyUTest Critical Values (9  n  20) 872

APPENDIX N Critical Values of Tin the Wilcoxon Matched-Pairs Signed-Ranks Test (n 25) 874

APPENDIX O Critical Values dLand dU of the Durbin-Watson Statistic D 875

APPENDIX P Lower and Upper Critical Values Wof Wilcoxon Signed-Ranks Test 877

APPENDIX Q Control Chart Factors 878

vi

Preface xix

Chapter 1 The Where, Why, and How of Data Collection 1

What is Business Statistics? 2

Descriptive Statistics 2 Charts and Graphs 3 Inferential Procedures 5 Estimation 5

Hypothesis Testing 5

Procedures for Collecting Data 7

Data Collection 7 Written Questionnaires and Surveys 9 Direct Observation and Personal Interviews 11 Other Data Collection Methods 11 Data Collection Issues 12 Interviewer Bias 12 Nonresponse Bias 12 Selection Bias 12 Observer Bias 12 Measurement Error 13 Internal Validity 13 External Validity 13

Populations, Samples, and Sampling Techniques 14

Populations and Samples 14 Parameters and Statistics 15 Sampling Techniques 15 Statistical Sampling 16

Data Types and Data Measurement Levels 20

Quantitative and Qualitative Data 21 Time-Series Data and Cross-Sectional Data 21 Data Measurement Levels 21

Nominal Data 21 Ordinal Data 22 Interval Data 22 Ratio Data 22Visual Summary 26 • Key Terms 28 • Chapter Exercises 28

Video Case 1: Statistical Data Collection @ McDonald’s 29

References 29

Chapter 2 Graphs, Charts, and Tables—Describing Your Data 31

Frequency Distributions and Histograms 32

Frequency Distribution 33 Grouped Data Frequency Distributions 36 Steps for Grouping Data into Classes 39 Histograms 41

Issues with Excel 44 Relative Frequency Histograms and Ogives 45 Joint Frequency Distributions 47

Bar Charts, Pie Charts, and Stem and Leaf Diagrams 54

Bar Charts 54 Pie Charts 60 Stem and Leaf Diagrams 62

vii

Line Charts and Scatter Diagrams 66

Line Charts 66 Scatter Diagrams 70 Personal Computers 70Visual Summary 76 • Equations 77 • Key Terms 77 •Chapter Exercises 77

Video Case 2: Drive-Thru Service Times @ McDonald’s 80 Case 2.1: Server Downtime 81

Case 2.2: Yakima Apples, Inc 81 Case 2.3: Welco Lumber Company—Part A 83

References 84

Chapter 3 Describing Data Using Numerical Measures 85

Measures of Center and Location 85

Parameters and Statistics 86 Population Mean 86 Sample Mean 89 The Impact of Extreme Values on the Mean 90 Median 91

Skewed and Symmetric Distributions 92 Mode 93

Applying the Measures of Central Tendency 94 Issues with Excel 96

Other Measures of Location 97 Weighted Mean 97

Percentiles 98 Quartiles 99 Issues with Excel 100 Box and Whisker Plots 100 Data-Level Issues 102

Measures of Variation 107

Range 107 Interquartile Range 108 Population Variance and Standard Deviation 109 Sample Variance and Standard Deviation 112

Using the Mean and Standard Deviation Together 118

Coefficient of Variation 118 The Empirical Rule 120 Tchebysheff’s Theorem 121 Standardized Data Values 122Visual Summary 128 • Equations 129 • Key Terms 130 •Chapter Exercises 130

Video Case 3: Drive-Thru Service Times at McDonald’s 135 Case 3.1: WGI—Human Resources 135

Case 3.2: National Call Center 136 Case 3.3: Welco Lumber Company—Part B 137 Case 3.4: AJ’s Fitness Center 137

References 138

Chapters 1–3 Special Review Section 139

Chapters 1–3 139 Exercises 142 Review Case 1: State Department of Insurance 144 Term Project Assignments 144

Chapter 4 Introduction to Probability 146

The Basics of Probability 147

Important Probability Terms 147 Events and Sample Space 147 Using Tree Diagrams 148 Mutually Exclusive Events 150 Independent and Dependent Events 150 Methods of Assigning Probability 152 Classical Probability Assessment 152 Relative Frequency Assessment 153 Subjective Probability Assessment 155

The Rules of Probability 159

Measuring Probabilities 159 Possible Values and the Summation of Possible Values 159 Addition Rule for Individual Outcomes 160

Complement Rule 162 Addition Rule for Two Events 163 Addition Rule for Mutuallly Exclusive Events 167 Conditional Probability 167

Tree Diagrams 170 Conditional Probability for Independent Events 171 Multiplication Rule 172

Multiplication Rule for Two Events 172 Using a Tree Diagram 173 Multiplication Rule for Independent Events 174 Bayes’ Theorem 175

Visual Summary 185 • Equations 186 • Key Terms 186 •Chapter Exercises 186

Case 4.1: Great Air Commuter Service 189 Case 4.2: Let’s Make a Deal 190

References 190

Chapter 5 Discrete Probability Distributions 191

Introduction to Discrete Probability Distributions 192

Random Variables 192 Displaying Discrete Probability Distributions Graphically 192 Mean and Standard Deviation of Discrete Distributions 193 Calculating the Mean 193

Calculating the Standard Deviation 194

The Binomial Probability Distribution 199

The Binomial Distribution 199 Characteristics of the Binomial Distribution 199 Combinations 201

Binomial Formula 202 Using the Binomial Distribution Table 204 Mean and Standard Deviation of the Binomial Distribution 205 Additional Information about the Binomial Distribution 208

Other Discrete Probability Distributions 213

The Poisson Distribution 213 Characteristics of the Poisson Distribution 213 Poisson Probability Distribution Table 214 The Mean and Standard Deviation of the Poisson Distribution 217 The Hypergeometric Distribution 217

The Hypergeometric Distribution with More Than Two Possible Outcomes per Trial 222Visual Summary 226 • Equations 227 • Key Terms 227 •Chapter Exercises 227

Case 5.1: SaveMor Pharmacies 230 Case 5.2: Arrowmark Vending 231

Case 5.3: Boise Cascade Corporation 232

References 232

Chapter 6 Introduction to Continuous Probability

Distributions 233The Normal Probability Distribution 234

The Normal Distribution 234 The Standard Normal Distribution 235 Using the Standard Normal Table 237 Approximate Areas under the Normal Curve 245

Other Continuous Probability Distributions 249

Uniform Probability Distribution 249 The Exponential Probability Distribution 252Visual Summary 258 • Equations 259 • Key Terms 259

Chapter 7 Introduction to Sampling Distributions 264

Sampling Error: What It Is and Why It Happens 265

Calculating Sampling Error 265 The Role of Sample Size in Sampling Error 268 Sampling Distribution of the Mean 273 Simulating the Sampling Distribution for x– 274 Sampling from Normal Populations 277

The Central Limit Theorem 282

Sampling Distribution of a Proportion 289

Working with Proportions 289 Sampling Distribution of p 291Visual Summary 298 • Equations 299 • Key Terms 299

• Chapter Exercises 299

Case 7.1: Carpita Bottling Company 303 Case 7.2: Truck Safety Inspection 303

References 304

Chapter 8 Estimating Single Population Parameters 305

Point and Confidence Interval Estimates for a Population Mean 306

Point Estimates and Confidence Intervals 306 Confidence Interval Estimate for the Population Mean, Known 308

Confidence Interval Calculation 309 Impact of the Confidence Level on the Interval Estimate 311 Impact of the Sample Size on the Interval Estimate 314 Confidence Interval Estimates for the Population Mean, Unknown 314

Student’s t-Distribution 314 Estimation with Larger Sample Sizes 320

Determining the Required Sample Size for Estimating a Population Mean 324

Determining the Required Sample Size for Estimating ,  Known 325

Determining the Required Sample Size for Estimating ,  Unknown 326

Estimating a Population Proportion 330

Confidence Interval Estimate for a Population Proportion 331 Determining the Required Sample Size for Estimating a Population Proportion 333Visual Summary 339 • Equations 340 • Key Terms 340

• Chapter Exercises 340

Video Case 4: New Product Introductions @ McDonald’s 343 Case 8.1: Management Solutions, Inc 343

Case 8.2: Federal Aviation Administration 344 Case 8.3: Cell Phone Use 344

References 345

Chapter 9 Introduction to Hypothesis Testing 346

Hypothesis Tests for Means 347

Formulating the Hypotheses 347 Null and Alternative Hypotheses 347 Testing the Status Quo 347 Testing a Research Hypothesis 348 Testing a Claim about the Population 348 Types of Statistical Errors 350 Significance Level and Critical Value 351 Hypothesis Test for ,  Known 352

Calculating Critical Values 352 Decision Rules and Test Statistics 354

p-Value Approach 357 Types of Hypothesis Tests 358

p-Value for Two-Tailed Tests 359 Hypothesis Test for ,  Unknown 361

Hypothesis Tests for Proportions 368

Testing a Hypothesis about a Single Population Proportion 368

Type II Errors 376

Calculating Beta 376 Controlling Alpha and Beta 378 Power of the Test 382Visual Summary 387 • Equations 388 • Key Terms 389

Chapter 10 Estimation and Hypothesis Testing for

Two Population Parameters 397Estimation for Two Population Means Using Independent Samples 398

Estimating the Difference between Two Population Means when 1 and2 Are Known, Using Independent Samples 398

Estimating the Difference between Two Means when  1 and  2 Are Unknown, Using Independent Samples 400

What if the Population Variances Are Not Equal 404

Hypothesis Tests for Two Population Means Using Independent Samples 409

Testing for 1 –2 When1 and2 Are Known, Using Independent Samples 409

Usingp-Values 412 Testing 1 –2 When1 and2 Are Unknown, Using Independent Samples 412

What If the Population Variances are Not Equal? 419

Interval Estimation and Hypothesis Tests for Paired Samples 423

Why Use Paired Samples? 423 Hypothesis Testing for Paired Samples 427

Estimation and Hypothesis Tests for Two Population Proportions 432

Estimating the Difference between Two Population Proportions 432 Hypothesis Tests for the Difference between Two Population Proportions 433Visual Summary 440 • Equations 441 • Key Terms 442

• Chapter Exercises 442

Case 10.1: Motive Power Company—Part 1 445 Case 10.2: Hamilton Marketing Services 446 Case 10.3: Green Valley Assembly Company 446 Case 10.4: U-Need-It Rental Agency 447

References 447

Chapter 11 Hypothesis Tests and Estimation for Population

Variances 448Hypothesis Tests and Estimation for a Single Population Variance 449

Chi-Square Test for One Population Variance 449 Interval Estimation for a Population Variance 454

Hypothesis Tests for Two Population Variances 458

F-Test for Two Population Variances 458 AdditionalF-Test Considerations 467Visual Summary 470 • Equations 471 • Key Terms 471

• Chapter Exercises 471

Case 11.1: Motive Power Company—Part 2 474

References 474

Chapter 12 Analysis of Variance 475

One-Way Analysis of Variance 476

Introduction to One-Way ANOVA 476 Partitioning the Sum of Squares 477 The ANOVA Assumptions 478 Applying One-Way ANOVA 481 The Tukey-Kramer Procedure for Multiple Comparisons 488 Fixed Effects Versus Random Effects in Analysis of Variance 493

Randomized Complete Block Analysis of Variance 497

Randomized Complete Block ANOVA 497 Was Blocking Necessary? 500

Fisher’s Least Significant Difference Test 505

Two-Factor Analysis of Variance with Replication 509

Two-Factor ANOVA with Replications 510 Interaction Explained 512

A Caution about Interaction 517Visual Summary 521 • Equations 522 • Key Terms 522

References 529

Chapters 8–12 530 Using the Flow Diagrams 543 Exercises 544

Term Project Assignments 546 Business Statistics Capstone Project 546

Chapter 13 Goodness-of-Fit Tests and Contingency Analysis 547

Introduction to Goodness-of-Fit Tests 548

Chi-Square Goodness-of-Fit Test 548

Introduction to Contingency Analysis 562

2  2 Contingency Tables 562

rcContingency Tables 566 Chi-Square Test Limitations 569Visual Summary 573 • Equations 574 • Key Term 574

The Correlation Coefficient 580 Significance Test for the Correlation 582 Cause-and-Effect Interpretations 586

Simple Linear Regression Analysis 589

The Regression Model and Assumptions 590 Meaning of the Regression Coefficients 591 Least Squares Regression Properties 596 Significance Tests in Regression Analysis 599 The Coefficient of Determination,R2 600 Significance of the Slope Coefficient 604

Uses for Regression Analysis 612

Regression Analysis for Description 612 Regression Analysis for Prediction 615 Confidence Interval for the Average y, Given x 616 Prediction Interval for a Particular y, Given x 616

Common Problems Using Regression Analysis 618

Visual Summary 624 • Equations 625 • Key Terms 626

• Chapter Exercises 626

Case 14.1: A & A Industrial Products 630 Case 14.2: Sapphire Coffee—Part 1 630 Case 14.3: Alamar Industries 631 Case 14.4: Continental Trucking 631

References 632

Chapter 15 Multiple Regression Analysis and Model Building 633

Introduction to Multiple Regression Analysis 634

Basic Model-Building Concepts 636 Model Specification 636

Model Building 637 Model Diagnosis 637 Computing the Regression Equation 640 The Coefficient of Determination 642

Is the Model Significant? 643 Are the Individual Variables Significant? 645

Is the Standard Deviation of the Regression Model Too Large? 646

Is Multicollinearity a Problem? 647 Confidence Interval Estimation for Regression Coefficients 649

Using Qualitative Independent Variables 654

Possible Improvements to the First City Appraisal Model 657

Working with Nonlinear Relationships 661

The Partial-FTest 671

Stepwise Regression 678

Forward Selection 678 Backward Elimination 679 Standard Stepwise Regression 683 Best Subsets Regression 683

Determining the Aptness of the Model 689

Analysis of Residuals 689 Checking for Linearity 690

Do the Residuals Have Equal Variances at all Levels of Each xVariable? 692 Are the Residuals Independent? 693

Checking for Normally Distributed Error Terms 693 Corrective Actions 697

Visual Summary 700 • Equations 701 • Key Terms 701 • ChapterExercises 701

Case 15.1: Dynamic Scales, Inc 705 Case 15.2: Glaser Machine Works 706 Case 15.3: Hawlins Manufacturing 706 Case 15.4: Sapphire Coffee—Part 2 707 Case 15.5: Wendell Motors 707

References 708

Chapter 16 Analyzing and Forecasting Time-Series Data 709

Introduction to Forecasting, Time-Series Data, and Index Numbers 710

General Forecasting Issues 710 Components of a Time Series 711 Trend Component 711

Seasonal Component 712 Cyclical Component 713 Random Component 713 Introduction to Index Numbers 714 Aggregate Price Indexes 715 Weighted Aggregate Price Indexes 717 The Paasche Index 717

The Laspeyres Index 718 Commonly Used Index Numbers 719 Consumer Price Index 719

Producer Price Index 720 Stock Market Indexes 720 Using Index Numbers to Deflate a Time Series 721

Trend-Based Forecasting Techniques 724

Developing a Trend-Based Forecasting Model 724 Comparing the Forecast Values to the Actual Data 727 Autocorrelation 728

True Forecasts 732 Nonlinear Trend Forecasting 734 Some Words of Caution 738 Adjusting for Seasonality 738 Computing Seasonal Indexes 739 The Need to Normalize the Indexes 741 Deseasonalizing 742

Using Dummy Variables to Represent Seasonality 744

Forecasting Using Smoothing Methods 750

Exponential Smoothing 750 Single Exponential Smoothing 750 Double Exponential Smoothing 755Visual Summary 762 • Equations 763 • Key Terms 763 • ChapterExercises 764

Video Case 2: Restaurant Location and Re-imaging Decisions @ McDonald’s 766

Case 16.1: Park Falls Chamber of Commerce 767 Case 16.2: The St Louis Companies 768

Case 16.3: Wagner Machine Works 768

References 769

Chapter 17 Introduction to Nonparametric Statistics 770

The Wilcoxon Signed Rank Test for One Population Median 771

The Wilcoxon Signed Rank Test—Single Population 771

Nonparametric Tests for Two Population Medians 776

The Mann–Whitney U-Test 776 Mann–WhitneyU-Test—Large Samples 780 The Wilcoxon Matched-Pairs Signed Rank Test 782 Ties in the Data 784

Large-Sample Wilcoxon Test 784

Kruskal–Wallis One-Way Analysis of Variance 789

Limitations and Other Considerations 793Visual Summary 797 • Equations 798 • Chapter Exercises 799

Case 17.1: Bentford Electronics—Part 2 802

References 803

Chapter 18 Introduction to Quality and Statistical

Process Control 804Quality Management and Tools for Process Improvement 805

The Tools of Quality for Process Improvement 806 Process Flowcharts 807

Brainstorming 807 Fishbone Diagram 807 Histograms 807 Trend Charts 807 Scatter Plots 807 Statistical Process Control Charts 807

Introduction to Statistical Process Control Charts 808

The Existence of Variation 808 Sources of Variation 808 Types of Variation 809 The Predictability of Variation: Understanding the Normal Distribution 810 The Concept of Stability 810

Introducing Statistical Process Control Charts 810x–-Chart and R-Chart 811

Using the Control Charts 818

p-Charts 820 Using the p-Chart 823

c-Charts 824 Other Control Charts 827Visual Summary 831 • Equations 832 • Key Terms 833

• Chapter Exercises 833

Case 18.1: Izbar Precision Casters, Inc 834

References 835

Appendices 836

APPENDIX A Random Numbers Table 837

APPENDIX B Binomial Distribution Table 838

APPENDIX C Poisson Probability Distribution Table 851

APPENDIX D Standard Normal Distribution Table 856

APPENDIX E Exponential Distribution Table 857

APPENDIX F Values of tfor Selected Probabilities 858

APPENDIX G Values of 2 for Selected Probabilities 859

APPENDIX H F-Distribution Table 860

APPENDIX I Critical Values of Hartley’s FmaxTest 866

APPENDIX J Distribution of the Studentized Range (q-values) 867

APPENDIX K Critical Values of rin the Runs Test 869

APPENDIX L Mann-WhitneyUTest Probabilities (n< 9) 870

APPENDIX M Mann-WhitneyUTest Critical Values (9n20) 872

APPENDIX N Critical Values of Tin the Wilcoxon Matched-Pairs Signed-Ranks Test

(n25) 874

APPENDIX O Critical Values dLanddUof the Durbin-Watson Statistic D 875

APPENDIX P Lower and Upper Critical Values Wof Wilcoxon Signed-Ranks Test 877

APPENDIX Q Control Chart Factors 879

Answers to Selected Odd-Numbered Problems 879 Glossary 900

Index 906

In today’s workplace, students can have an immediate competitive edge over both new ates and experienced employees if they know how to apply statistical analysis skills to real-world decision-making problems.

gradu-Our intent in writing Business Statistics: A Decision-Making Approach is to provide an

in-troductory business statistics text for students who do not necessarily have an extensive ematics background but who need to understand how statistical tools and techniques are applied

math-in busmath-iness decision makmath-ing

This text differs from its competitors in three key ways:

1 Use of a direct approach and concepts and techniques consistently presented in a tematic and ordered way

sys-2 Presentation of the content at a level that makes it accessible to students of all levels ofmathematical maturity The text features clear, step-by-step explanations that make learn-ing business statistics straightforward

3 Engaging examples, drawn from our years of experience as authors, educators, and sultants, to show the relevance of the statistical techniques in realistic business decisionsituations

con-Regardless of how accessible or engaging a textbook is, we recognize that many students

do not read the chapters from front to back Instead, they use the text “backward.” That is, they

go to the assigned exercises and try them, and if they get stuck, they turn to the text to look forexamples to help them Thus, this text features clearly marked, step-by-step examples that stu-dents can follow Each detailed example is linked to a section exercise, which students can use

to build specific skills needed to work exercises in the section

Each chapter begins with a clear set of specific chapter outcomes The examples and tice exercises are designed to reinforce the objectives and lead students toward the desired out-comes The exercises are ordered from easy to more difficult and are divided into categories:Conceptual, Skill Development, Business Applications, and Database Exercises

prac-Another difference is the importance this text places on data and how data are obtained.Many business statistics texts assume that data have already been collected We have decided

to underscore a more modern theme: Data are the starting point We believe that effective cision making relies on a good understanding of the different types of data and the different datacollection options that exist To highlight our theme, we begin a discussion of data and collect-ing data in Chapter 1 before any discussion of data analysis is presented In Chapters 2 and 3,where the important descriptive statistical techniques are introduced, we tie these statisticaltechniques to the type and level of data for which they are best suited

de-Although we know that the role of the computer is important in applying business tics, it can be overdone at the beginning level to the point where instructors are required tospend too much time teaching the software and too little time teaching statistical concepts.This text features Excel and Minitab but limits the inclusion of software output to those areaswhere it is of particular advantage to beginning students

statis-New to This Edition

䊏 Textual examples: More than 50 new examples throughout the text provide

step-by-step details, enabling students to follow solution techniques easily Students can thenapply the methodology from each example to solve other problems These examples areprovided in addition to the vast array of business applications to give students a real-world, competitive edge Featured companies in these new examples include DoveShampoo and Soap, The Frito-Lay Company, Goodyear Tire Company, LockheedMartin Corporation, the National Federation of Independent Business, Oakland RaidersNFL Football, Southwest Airlines, and Whole Foods Grocery

䊏 Visual summaries: Each main heading is summarized using a flow diagram, which

reminds students of the intended outcomes and leads them to the chapter’s conclusion

xvii

䊏 MyStatLab: This proven book-specific online homework and assessment tool provides

a rich and flexible set of course materials, featuring free-response exercises that arealgorithmically generated for unlimited practice and mastery Students can also use avariety of online tools to independently improve their understanding and performance inthe course Instructors can use MyStatLab’s homework and test manager to select andassign their own online exercises and can import TestGen tests for added flexibility

䊏 Quick prep links: At the beginning of each chapter, students are supplied with several

ways to get ready for the topics discussed in the chapter

䊏 Chapter outcomes: Identifying what is to be gained from completing the chapter helps

focus a student’s attention At the beginning of each chapter, every outcome is linked tothe corresponding main heading Throughout the text, the chapter outcomes are recalled

at main headings to remind students of the objectives

䊏 How to do it: Associated with the textual examples, lists are provided throughout each

chapter to summarize major techniques and reinforce fundamental concepts

䊏 Online chapter—Introduction to Decision Analysis: This chapter discusses the

ana-lytic methods used to deal with the wide variety of decision situations a student mightencounter

Key Pedagogical Features

䊏 Business applications: One of the strengths of the previous editions of this textbook

has been the emphasis on business applications and decision making This feature isexpanded even more in the eighth edition Many new applications are included, and allapplications are highlighted in the text with special icons, making them easier for stu-dents to locate as they use the text

䊏 Quick prep links: Each chapter begins with a list that provides several ways to get

ready for the topics discussed in the chapter

䊏 Chapter outcomes: At the beginning of each chapter, outcomes, which identify what is

to be gained from completing the chapter, are linked to the corresponding main ings Throughout the text, the chapter outcomes are recalled at the appropriate mainheadings to remind students of the objectives

head-䊏 Step-by-step approach: This edition provides continued and improved emphasis on

providing concise, step-by-step details to reinforce chapter material

• How to do it lists are provided throughout each chapter to summarize major

techniques and reinforce fundamental concepts

• Textual examples throughout the text provide step-by-step details, enabling

students to follow solution techniques easily Students can then apply the ology from each example to solve other problems These examples are provided inaddition to the vast array of business applications to give students a real-world,competitive edge

method-䊏 Real-world application: The chapters and cases feature real companies, actual

applica-tions, and rich data sets, allowing the authors to concentrate their efforts on addressinghow students apply this statistical knowledge to the decision-making process

• McDonald’s Corporation video cases —The authors’ relationship with McDonald’s

provides students with real-world statistical data and integrated video case series

• Chapter cases —Cases provided in nearly every chapter are designed to give

stu-dents the opportunity to apply statistical tools Each case challenges stustu-dents todefine a problem, determine the appropriate tool to use, apply it, and then write asummary report

䊏 Special review sections: For Chapters 1 to 3 and Chapters 8 to 12, special review

sec-tions provide a summary and review of the key issues and statistical techniques Highlyeffective flow diagrams help students sort out which statistical technique is appropriate

to use in a given problem or exercise These flow diagrams serve as a mini-decision port system that takes the emphasis off memorization and encourages students to seek a

sup-MyStatLab

higher level of understanding and learning Integrative questions and exercises askstudents to demonstrate their comprehension of the topics covered in these sections.

䊏 Problems and exercises: This edition includes an extensive revision of exercise sections,

featuring more than 250 new problems The exercise sets are broken down into threecategories for ease of use and assignment purposes:

1 Skill Development—These problems help students build and expand upon statistical

methods learned in the chapter

2 Business Applications—These problems involve realistic situations in which students

apply decision-making techniques

3 Computer Applications—In addition to the problems that may be worked out

man-ually, many problems have associated data files and can be solved using Excel,Minitab, or other statistical software

䊏 Virtual office hours: The authors appear in three- to five-minute video clips in which

they work examples taken directly from the book Now students can watch and listen tothe instructor walk through an example and obtain even greater clarity with respect tohow the example is worked and how the results are interpreted

䊏 Computer integration: The text seamlessly integrates computer applications with

textual examples and figures, always focusing on interpreting the output The goal is for students to be able to know which tools to use, how to apply the tools, and how toanalyze their results for making decisions

• Minitab 14 is featured, with associated instructions.

• Microsoft Excel 2007 integration instructs students in how to use the Excel 2007

user interface for statistical applications

• PHStat2 is a specially developed Excel add-in package that is compatible with the

Excel 2007 release It performs a number of statistical features not included withExcel The added functions and procedures are useful in the study and application ofbusiness statistics When installed, PHStat2 attaches itself to the Excel menu bar,providing users with a pull-down menu of topics that supplement the Data Analysisadd-in tools in Microsoft Excel

PHStat2 uses a set of simple and consistent dialog boxes that allow students tospecify values and options for almost 50 tools included in the software PHStat2produces Excel worksheets organized into areas for input data, intermediate calcula-tions, and the results of analyses Unlike with some competitors’ add-ins, most ofthese worksheets contain live formulas that allow students to engage immediately infurther “what-if” explorations of the data (Where applicable, these worksheetscontain special cell tints that distinguish the cells that contain user-modifiable inputvalues from the cells containing the results, making “what-if” analysis even easier.)Completing the package is an excellent online help system

• MyStatLab is a proven book-specific online homework and assessment tool that

provides a rich and flexible set of course materials, featuring free-response cises that are algorithmically generated for unlimited practice and mastery Stu-dents can also use a variety of online tools to independently improve their

exer-understanding and performance in the course Instructors can use MyStatLab’shomework and test manager to select and assign their own online exercises andimport TestGen tests for added flexibility

Student Resources

Student Solutions Manual

The Student Solutions Manual contains worked-out solutions to odd-numbered problems inthe text It displays the detailed process that students should use to work through the problems.The manual also provides interpretation of the answers and serves as a valuable learning toolfor students

MyStatLab

Part of the MyMathLab® and MathXL® product family, MyStatLab™ is a text-specific,

eas-ily customizable online course that integrates interactive multimedia instruction with textbookcontent MyStatLab gives you the tools you need to deliver all or a portion of your course online, whether your students are in a lab setting or working from home

䊏 Interactive tutorial exercises: A comprehensive set of exercises—correlated to your

textbook at the objective level—are algorithmically generated for unlimited practice andmastery Most exercises are free-response exercises and provide guided solutions, sam-ple problems, and learning aids for extra help at point-of-use

䊏 Personalized study plan: When a student completes a test or quiz in MyStatLab, the

program generates a personalized study plan for that student, indicating which topicshave been mastered and linking students directly to tutorial exercises for topics theyneed to study and retest

䊏 Multimedia learning aids: Students can use online learning aids, such as video

lec-tures, animations, and a complete multimedia textbook, to help independently improvetheir understanding and performance

䊏 Statistics tools: MyStatLab includes built-in tools for statistics, including statistical

software called StatCrunch Students also have access to statistics animations and plets that illustrate key ideas for the course For those who use technology in theircourse, technology manual PDFs are included

ap-䊏 StatCrunch: This powerful online tool provides an interactive environment for doing

statistics You can use StatCrunch for both numerical and graphical data analysis, takingadvantage of interactive graphics to help you see the connection between objects se-lected in a graph and the underlying data In MyStatLab, the data sets from your text-book are preloaded into StatCrunch StatCrunch is also available as a tool from theonline homework and practice exercises in MyStatLab and in MathXL for Statistics.Also available is Statcrunch.com, Web-based software that allows students to performcomplex statistical analysis in a simple manner

䊏 Pearson Tutor Center (www.pearsontutorservices.com): Access to the Pearson Tutor Center is automatically included with MyStatLab The Tutor Center is staffed by quali-

fied mathematics instructors who provide textbook-specific tutoring for students viatoll-free phone, fax, e-mail, and interactive Web sessions

MyStatLab is powered by CourseCompass™, Pearson Education’s online teaching and ing environment, and by MathXL®, an online homework, tutorial, and assessment system Formore information about MyStatLab, visit www.mystatlab.com

learn-Student Videos

Student videos—located at MyStatLab only—feature McDonald’s video cases and the virtualoffice hours videos

Student Companion Web Site

The Companion Web Site, www.pearsonhighered.com/groebner, contains valuable online sources for both students and professors, including:

re-䊏 Online chapter—Introduction to Decision Analysis: This chapter discusses the analytic

methods used to deal with the wide variety of decision situations a student might encounter

䊏 Data files: The text provides an extensive number of data files for examples, cases, and

exercises These files are also located at MyStatLab

䊏 Excel and Minitab tutorials: Customized PowerPoint tutorials for both Minitab and

Excel use data sets from text examples Separate tutorials for Excel 2003 and Excel

2007 are provided Students who need additional instruction in Excel or Minitab can cess the menu-driven tutorial, which shows exactly the steps needed to replicate allcomputer examples in the text These tutorials are also located at MyStatLab

ac-䊏 Excel simulations: Several interactive simulations illustrate key statistical topics and

allow students to do “what-if” scenarios These simulations are also located at MyStatLab

MyStatLab

䊏 PHStat: PHStat is a collection of statistical tools that enhance the capabilities of Excel

and assist students in learning the concepts of statistics; published by Pearson tion This tool is also located at MyStatLab

Educa-䊏 Online study guide: This guide contains practice or homework quizzes consisting of

multiple-choice, true/false, and essay questions that effectively review textual material

It is located on the Companion Web site only

Instructor Resources

䊏 Instructor Resource Center: The Instructor Resource Center contains the electronic

files for the complete Instructor’s Solutions Manual, the Test Item File, and LecturePowerPoint presentations (www.pearsonhighered.com/groebner)

䊏 Register, Redeem, Login: At www.pearsonhighered.com/irc, instructors can access a

variety of print, media, and presentation resources that are available with this text indownloadable, digital format For most texts, resources are also available for coursemanagement platforms such as Blackboard, WebCT, and Course Compass

䊏 It gets better: Once you register, you will not have additional forms to fill out or multiple

usernames and passwords to remember to access new titles and/or editions As a registeredfaculty member, you can log in directly to download resource files and receive immediateaccess and instructions for installing course management content to your campus server

䊏 Need help? Our dedicated technical support team is ready to assist instructors with

questions about the media supplements that accompany this text Visit http://247.prenhall.com/ for answers to frequently asked questions and toll-free user supportphone numbers The supplements are available to adopting instructors Detailed

descriptions are provided on the Instructor Resource Center

Instructor’s Solutions Manual

The Instructor’s Solutions Manual contains worked-out solutions to all the problems and cases

in the text

Lecture PowerPoint Presentations

A PowerPoint presentation, created by Angela Mitchell of Wilmington College of Ohio, is able for each chapter The PowerPoint slides provide instructors with individual lecture outlines toaccompany the text The slides include many of the figures and tables from the text Instructors canuse these lecture notes as is or can easily modify the notes to reflect specific presentation needs

avail-Test Item File

The Test Item File, by Tariq Mughal of The University of Utah, contains a variety of true/false,multiple-choice, and short-answer questions for each chapter

TestGen

The computerized TestGen package allows instructors to customize, save, and generate room tests The test program permits instructors to edit, add, or delete questions from the testbank; edit existing graphics and create new graphics; analyze test results; and organize a data-base of test and student results This software allows for extensive flexibility and ease of use

class-It provides many options for organizing and displaying tests, along with search and sortfeatures The software and the test banks can be downloaded from the Instructor ResourceCenter, at www.pearsonhighered.com/groebner

MyStatLab

䊏 MathXL® for Statistics: This powerful online homework, tutorial, and assessment

sys-tem accompanies Pearson Education textbooks in statistics With MathXL for Statistics,instructors can create, edit, and assign online homework and tests, using algorithmically

MyStatLab

generated exercises correlated at the objective level to the textbook They can also createand assign their own online exercises and import TestGen tests for added flexibility Allstudent work is tracked in MathXL’s online gradebook Students can take chapter tests

in MathXL and receive personalized study plans based on their test results The studyplan diagnoses weaknesses and links students directly to tutorial exercises for the objec-tives they need to study and retest Students can also access supplemental animationsand video clips directly from selected exercises MathXL for Statistics is available toqualified adopters For more information, visit www.mathxl.com or contact your salesrepresentative

䊏 MyStatLab™: Part of the MyMathLab® and MathXL® product family, MyStatLab™

is a text-specific, easily customizable online course that integrates interactive dia instruction with textbook content MyStatLab gives you the tools you need to deliverall or a portion of your course online, whether your students are in a lab setting or work-ing from home

multime-䊏 Assessment Manager: An easy-to-use assessment manager lets instructors create online

homework, quizzes, and tests that are automatically graded and correlated directly to thetextbook Assignments can be created using a mix of questions from the MyStatLab exercise bank, instructor-created custom exercises, and/or TestGen test items

䊏 Gradebook: Designed specifically for mathematics and statistics, the MyStatLab

gradebook automatically tracks students’ results and gives you control over how to culate final grades You can also add offline (paper-and-pencil) grades to the gradebook

cal-䊏 Math Exercise Builder: You can use the MathXL Exercise Builder to create static and

algorithmic exercises for your online assignments A library of sample exercises vides an easy starting point for creating questions, and you can also create questionsfrom scratch

pro-Acknowledgments

Publishing this eighth edition of Business Statistics: A Decision-Making Approach has been a

team effort involving the contributions of many people At the risk of overlooking someone, weexpress our sincere appreciation to the many key contributors Throughout the two years wehave worked on this revision, many of our colleagues from colleges and universities around thecountry have taken time from their busy schedules to provide valuable input and suggestionsfor improvement We would like to thank the following people:

Donald I Bosshardt, Canisius College Sara T DeLoughy, Western Connecticut State University Nicholas R Farnum, California State University—Fullerton Kent E Foster, Winthrop University

John Gum, University of South Florida—St Petersburg Jeffery Guyse, California State Polytechnic University, Pomona Chaiho Kim, Santa Clara University

David Knopp, Chattanooga State Technical Community College Linda Leighton, Fordham University

Sally A Lesik, Central Connecticut State University Merrill W Liechty, Drexel University

Robert M Lynch, University of Northern Colorado—Monfort College of Business Jennifer Martin, York College of Pennsylvania

Constance McLaren, Indiana State University Mahour Mellat-Parast, University of North Carolina—Pembroke Carl E Miller, Northern Kentucky University

Tariq Mughal, David Eccles, School of Business, University of Utah Tom Naugler, Johns Hopkins University

Kenneth Paetsch, Cleveland State University

Ed Pappanastos, Troy University

Michael D Polomsky, Cleveland State University

Peter Royce, University of New Hampshire

Rose Sebastianelli, University of Scranton

Bulent Uyar, University of Northern Iowa

Tom Wheeler, Georgia Southwestern State University

We also wish to thank Professor Angela Mitchell, who designed and developed thePowerPoint slides that accompany this text Thanks also to David Stephen for his expert work

in developing the PHStat add-ins for Excel that accompany the text

Thanks, too, to Annie Puciloski, who checked the solutions to every exercise This is avery time-consuming but extremely important role, and we greatly appreciate her efforts In ad-dition, we wish to thank Tariq Mughal of The University of Utah for developing the test man-ual This, too, requires a huge commitment of time and effort, and we appreciate Dr Mughal’scontributions to the package of materials that accompany the text Howard Flomberg at theMetropolitan State College of Denver contributed his skills and creative abilities to develop theExcel and Minitab tutorials that are so useful to students, and we thank him for all his contri-butions Thanks, too, to Bob Donnelly of Goldey-Beacom College for his development of theOnline Study Guide

Finally, we wish to give our utmost thanks and appreciation to the Prentice Hall ing team that has assisted us in every way possible to make this eighth edition a reality BlairBrown was responsible for the text design Allison Longley oversaw all the media productsthat accompany this text Clara Bartunek, in her role as production project manager, guided thedevelopment of the book from its initial design all the way through to final printing Mary KateMurray, assistant editor, served as our day-to-day contact and expertly facilitated the project

publish-in every way imagpublish-inable And fpublish-inally, we wish to give the highest thanks possible to Chuck ovec, the senior acquisitions editor for decision sciences, who has provided valuable guidance,motivation, and leadership from beginning to end on this project It has been a great pleasure

Syn-to work with Chuck and his team at Prentice Hall

—David F Groebner

—Patrick W Shannon

—Phillip C Fry

—Kent D Smith

The Where, Why, and How

of Data Collection

such as Fortune or Business Week, and take

note of the graphs, charts, and tables that are

used in the articles and advertisements

written survey or respond to a telephonesurvey

Minitab and familiarize yourself with thesoftware

1.1 What Is Business Statistics?

Outcome 1.Know the key data collection methods

Why you need to know

Although you may not realize it yet, by taking this business statistics course you will be learning about some of the

most useful business procedures available for decision makers In today’s workplace, you can have an immediate

competitive edge over other new employees, and even those with more experience, by applying statistical analysis

skills to real-world decision making The purpose of this text is to assist in your learning process and to complement

your instructor’s efforts in conveying how to apply a variety of important statistical procedures Each chapter

intro-duces one or more statistical procedure and technique that, regardless of your major, will be useful in your career

Wal-Mart, the world’s largest retail chain, collects and manages massive amounts of data related to the

operation of its stores throughout the world Its highly sophisticated database systems contain sales data, detailed

customer data, employee satisfaction data, and much more Ford Motor Company maintains databases with

infor-mation on production, quality, customer satisfaction, safety records, and much more Governmental agencies

amass extensive data on such things as unemployment, interest rates,

incomes, and education However, access to data is not limited to large

compa-nies The relatively low cost of computer hard drives with 100-gigabyte or

larger capacities makes it possible for small firms, and even individuals, to

store vast amounts of data on desktop computers But without some way to

transform the data into useful information, the data any of these companies

have gathered are of little value

Transforming data into information is where business statistics comes

in—the statistical procedures introduced in this text are those that are used

to help transform data into information This text focuses on the practical

application of statistics; we do not develop the theory you would find in a

Outcome 2.Know the difference between a population and asample

Outcome 3.Understand the similarities and differencesbetween different sampling methods

1 Outcome 4.Understand how to categorize data by type andlevel of measurement

mathematical statistics course Will you need to use math in this course? Yes, but mainly the concepts covered inyour college algebra course.

Statistics does have its own terminology You will need to learn various terms that have special statistical meaning.You will also learn certain dos and don’ts related to statistics But most importantly you will learn specific methods toeffectively convert data into information Don’t try to memorize the concepts; rather, go to the next level of learningcalledunderstanding Once you understand the underlying concepts, you will be able to think statistically

Because data are the starting point for any statistical analysis, Chapter 1 is devoted to discussing variousaspects of data, from how to collect data to the different types of data that you will be analyzing You need to gain anunderstanding of the where, why, and how of data and data collection because the remaining chapters deal with thetechniques for transforming data into useful information

Every day, your local newspaper contains stories that report descriptors such as stock prices,crime rates, and government-agency budgets Such descriptors can be found in many places

However, they are just a small part of the discipline called business statistics, which provides

a wide variety of methods to assist in data analysis and decision making Business is oneimportant area of application for these methods

Descriptive Statistics

The procedures and techniques that comprise business statistics include those specially

designed to describe data, such as charts, graphs, and numerical measures Also included are inferential procedures that help decision makers draw inferences from a set of data Inferen-

tial procedures include estimation and hypothesis testing A brief discussion of these niques follows The examples illustrate data that have been entered into the Microsoft Exceland Minitab software packages

tech-BUSINESS APPLICATION DESCRIBING DATA INDEPENDENT TEXTBOOK PUBLISHING, INC The college textbook publishing indus-

try has witnessed a great amount of consolidation in recent years Large companies have acquiredsmaller companies An exception to this consolidation is Independent Text Publishing, Inc Thecompany currently publishes 15 texts in the business and social sciences areas Figure 1.1

Excel 2007 Instructions:

1 Open File: Independent

Textbook.xls

Business Statistics

A collection of procedures and techniques that

are used to convert data into meaningful

information in a business environment.

FIGURE 1.1 |

Excel 2007 Spreadsheet

of Independent Textbook

Publishing, Inc

Number of Books

Under 50,000 50,000  100,000 100,000  150,000 150,000  200,000

Number of Copies Sold

Independent Textbook Publishing, Inc Distribution of Copies Sold

012345678

FIGURE 1.2 |

Histogram Showing the

Copies Sold Distribution

0 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000

Total Copies Sold

Total Copies Sold by Market Class

SocialSciences

Business

FIGURE 1.3 |

Bar Chart Showing Copies

Sold by Sales Category

shows an Excel spreadsheet containing data for each of these 15 textbooks Each column in thespreadsheet corresponds to a different factor for which data were collected Each row corre-sponds to a different textbook Many statistical procedures might help the owners describe

these textbook data, including charts, graphs, and numerical measures.

one shown in Figure 1.2, called a histogram This graph displays the shape and spread of the distribution of number of copies sold The bar chart shown in Figure 1.3 shows the total num-

ber of textbooks sold broken down by the two markets, business and social sciences

Bar charts and histograms are only two of the techniques that could be used to cally analyze the data for the textbook publisher In Chapter 2 you will learn more about theseand other techniques

graphi-BUSINESS APPLICATION DESCRIBING DATA CROWN INVESTMENTS During the 1990s and early 2000s, many major changes occurred

in the financial services industry Numerous banks merged Money flowed into the stock ket at rates far surpassing anything the U.S economy had previously witnessed The interna-tional financial world fluctuated greatly All these developments have spurred the need formore financial analysts who can critically evaluate and explain financial data to customers

mar-At Crown Investments, a senior analyst is preparing to present data to upper management

on the 100 fastest growing companies on the Hong Kong Stock Exchange Figure 1.4 shows aMinitab worksheet containing a subset of the data The columns correspond to the different

* –99.00 indicates missing data

FIGURE 1.4 |

Crown Investment Example

items of interest (growth percentage, sales, and so on) The data for each company are in a gle row The data file is called “Fast100.”

sin-In addition to preparing appropriate graphs, the analyst will compute important cal measures One of the most basic and most useful measures in business statistics is one

numeri-with which you are already familiar: the arithmetic mean or average.

Average

The sum of all the values divided by the number of values In equation form:

(1.1)

where:

N Number of data values

x i  ith data value

Average  

x N i

As we will discuss in greater depth in Chapter 3, the average, or mean, is a measure

of the center of the data In this case, the analyst may use the average profit as an indicator—firms with above-average profits are rated higher than firms with below-average profits

The graphical and numerical measures illustrated here are only some of the manydescriptive procedures that will be introduced in Chapters 2 and 3 The key to remember isthat the purpose of any descriptive procedure is to describe data Your task will be to select theprocedure that best accomplishes this As Figure 1.5 reminds you, the role of statistics is toconvert data into meaningful information

Average$ ,3 193 600 000, , $ , , , or $

100 31 936 000 331 936. million dollars

Arithmetic Mean or Average

The sum of all values divided by the number of

variables.

Information Data DescriptiveInferential

they use statistical inference procedures to come up with this information.

There are two primary categories of statistical inference procedures: estimation and hypothesis testing These procedures are closely related but serve very different

purposes

set but it is impractical to work with all the data, decision makers can use techniques to mate what the larger data set looks like The estimates are formed by looking closely at a sub-set of the larger data set

esti-BUSINESS APPLICATION STATISTICAL INFERENCE

TV RATINGS The television networks cannot know for sure how many people watched

last year’s Super Bowl They cannot possibly ask everyone what he or she saw that day ontelevision Instead, the networks rely on organizations such as Nielsen Media Research tosupply program ratings For example, Nielsen (www.nielsenmedia.com) surveys peoplefrom only a small number of homes across the country asking what shows they watched,and then uses the data from the survey to estimate the number of viewers per show for theentire population

Advertisers and television networks enter into contracts in which price per ad is based on

a certain minimum viewership If Nielsen Media Research estimate an audience smaller thanthis minimum, then a network must refund some money to its advertisers

In Chapter 8 we will discuss the estimating techniques that companies such as Nielsen use

might hear that “Goodyear tires will last at least 60,000 miles” or that “more doctorsrecommend Bayer Aspirin than any other brand.” Other claims might include statementslike “General Electric lightbulbs last longer than any other brand” or “customers preferMcDonald’s over Burger King.” Are these just idle boasts, or are they based on actualdata? Probably some of both! However, consumer research organizations such as Con-

sumers Union, publisher of Consumer Reports, regularly test these types of claims For example, in the hamburger case, Consumer Reports might select a sample of customers

who would be asked to blind taste test Burger King’s and McDonald’s hamburgers, underthe hypothesis that there is no difference in customer preferences between the two restau-rants If the sample data show a substantial difference in preferences, then the hypothesis

of no difference would be rejected If only a slight difference in preferences was detected,

then Consumer Reports could not reject the hypothesis Chapters 9 and 10 introduce basic

hypothesis-testing techniques that are used to test claims about products and servicesusing information taken from samples

Statistical Inference Procedures

Procedures that allow a decision maker to reach

a conclusion about a set of data based on a

subset of that data.

Skill Development

1-1 For the following situation indicate whether the

statistical application is primarily descriptive or

inferential

“The manager of Anna’s Fabric Shop has collected data

for 10 years on the number of each type of dress fabric

that has been sold at the store She is interested in

making a presentation that will illustrate these data

effectively.”

1-2 Consider the following graph that appeared in a

company annual report What type of graph is this?

Explain

Business Applications1-10 Describe how statistics could be used by a business to

determine if the dishwasher parts it produces lastlonger than a competitor’s brand

1-11 Locate a business periodical such as Fortune or Forbes

or a business newspaper such as The Wall Street

Journal Find three examples of the use of a graph to

display data For each graph

a Give the name, date, and page number of theperiodical in which the graph appeared

b Describe the main point made by the graph

c Analyze the effectiveness of the graphs

1-12 The human resources manager of an automotive supply

store has collected the following data showing thenumber of employees in each of five categories by thenumber of days missed due to illness or injury duringthe past year

FOOD STORE SALES

Canned Goods Department

Cereal and Dry Goods

Other

$0

Missed Days 0–2 days 3–5 days 6–8 days 8–10 days

1-3 Review Figures 1.2 and 1.3 and discuss any

differences you see between the histogram and

the bar chart

1-4 Think of yourself as working for an advertising firm.

Provide an example of how hypothesis testing can be

used to evaluate a product claim

1-5 Define what is meant by hypothesis testing Provide

an example in which you personally have tested a

hypothesis (even if you didn’t use formal statistical

techniques to do so.)

1-6 In what situations might a decision maker need to use

statistical inference procedures?

1-7 Explain under what circumstances you would use

hypothesis testing as opposed to an estimation

procedure

1-8 Discuss any advantages a graph showing a whole set

of data has over a single measure, such as an average

1-9 Discuss any advantages a single measure, such as

an average, has over a table showing a whole set

of data

Construct the appropriate chart for these data Be sure

to use labels and to add a title to your chart

1-13 Suppose Fortune would like to determine the average

age and income of its subscribers How could statistics

be of use in determining these values?

1-14 Locate an example from a business periodical or

newspaper in which estimation has been used

a What specifically was estimated?

b What conclusion was reached using theestimation?

c Describe how the data were extracted and how theywere used to produce the estimation

d Keeping in mind the goal of the estimation, discusswhether you believe that the estimation wassuccessful and why

e Describe what inferences were drawn as a result ofthe estimation

1-15 Locate one of the online job Web sites and pick

several job listings For each job type, discuss one ormore situations where statistical analyses would beused Base your answer on research (Internet,business periodicals, personal interviews, etc.).Indicate whether the situations you are describinginvolve descriptive statistics or inferential statistics or

a combination of both

1-16 Suppose Super-Value, a major retail food company,

is thinking of introducing a new product line into amarket area It is important to know the agecharacteristics of the people in the market area

a If the executives wish to calculate a number that

would characterize the “center” of the age data,

what statistical technique would you suggest?

Explain your answer

b The executives need to know the percentage

of people in the market area that are senior

citizens Name the basic category of statisticalprocedure they would use to determine thisinformation

c Describe a hypothesis which the executives mightwish to test concerning the percentage of seniorcitizens in the market area

A plan for performing an experiment in which

the variable of interest is defined One or more

factors are identified to be manipulated,

changed, or observed so that the impact (or

influence) on the variable of interest can be

measured or observed.

We have defined business statistics as a set of procedures that are used to transform data intoinformation Before you learn how to use statistical procedures, it is important that youbecome familiar with different types of data collection methods

Data Collection Methods

There are many methods and procedures available for collecting data The following are sidered some of the most useful and frequently used data collection methods:

con-● Experiments

● Telephone surveys

● Written questionnaires and surveys

● Direct observation and personal interviews

BUSINESS APPLICATION EXPERIMENTS FOOD PROCESSING A company often must conduct a specific experiment or set of

experiments to get the data managers need to make informed decisions For example, the

J R Simplot Company in Idaho is a primary supplier of french fries to companies such

as McDonald’s At its Caldwell, Idaho, factory, Simplot has a tech center that, amongother things, houses a mini french fry plant used to conduct experiments on its potato manu-facturing process McDonald’s has strict standards on the quality of the french fries it buys.One important attribute is the color of the fries after cooking They should be uniformly

“golden brown”—not too light or too dark

French fries are made from potatoes that are peeled, sliced into strips, blanched, partiallycooked, and then freeze-dried—not a simple process Because potatoes differ in many ways(such as sugar content and moisture), blanching time, cooking temperature, and other factorsvary from batch to batch

Simplot tech-center employees start their experiments by grouping the raw potatoes

into batches with similar characteristics They run some of the potatoes through the line

with blanch time and temperature settings set at specific levels defined by an experimental design After measuring one or more output variables for that run, employees change the

settings and run another batch, again measuring the output variables

Figure 1.6 shows a typical data collection form The output variable (for example, centage of fries without dark spots) for each combination of potato category, blanch time, andtemperature is recorded in the appropriate cell in the table Chapter 12 introduces the funda-mental concepts related to experimental design and analysis

per-BUSINESS APPLICATION TELEPHONE SURVEYS PUBLIC ISSUES One common method of obtaining data about people and their opinions is

the telephone survey Chances are that you have been on the receiving end of one “Hello Myname is Mary Jane and I represent the XYZ organization I am conducting a survey on .”Political groups use telephone surveys to poll people about candidates and issues

Telephone surveys are a relatively inexpensive and efficient data collection procedure Ofcourse, some people will refuse to respond to a survey, others are not home when the callscome, and some people do not have home phones—only have a cell phone—or cannot bereached by phone for one reason or another Figure 1.7 shows the major steps in conducting atelephone survey This example survey was run by a Seattle television station to determinepublic support for using tax dollars to build a new football stadium for the National FootballLeague’s Seattle Seahawks The survey was aimed at property tax payers only.

Potato Category

Blanch Temperature Blanch Time

100110120

10 minutes

100110120

15 minutes

100110120

20 minutes

100110120

PretesttheSurvey

Define thePopulation

of Interest

Select SampleandMake Calls

DevelopSurveyQuestions

Define theIssue

Do taxpayers favor a special bond to build a new football stadium for the Seahawks? If so, should the Seahawks’ owners share the cost?

Population is all residential property tax payers in King County, Washington The survey will be conducted among this group only

Limit the number of questions to keep survey short

Ask important questions first Provide specific response options when possible

Establish eligibility “Do you own a residence in King County?”

Add demographic questions at the end: age, income, etc

Introduction should explain purpose of survey and who is conducting it—stress that answers are anonymous

Try the survey out on a small group from the population Check for length, clarity, and ease of conducting Have we forgotten anything?Make changes if needed

Get phone numbers from a computer-generated or “current” list

Develop “callback” rule for no answers Callers should be trained to ask questions fairly Do not lead the respondent Record responses

on data sheet

Sample size is dependent on how confident we want to be of our results, how precise we want the results to be, and how much opinions differ among the population members Chapter 7 will show how sample sizes are computed Various sampling methods are available These are reviewed later in Chapter 1

FIGURE 1.7 |

Major Steps for a Telephone

Survey

Because most people will not stay on the line very long, the phone survey must be

short—usually one to three minutes The questions are generally what are called closed-end questions For example, a closed-end question might be “To which political party do you

belong? Republican? Democrat? Or other?”

The survey instrument should have a short statement at the beginning explaining the pose of the survey and reassuring the respondent that his or her responses will remain confi-dential The initial section of the survey should contain questions relating to the central issue

pur-of the survey The last part pur-of the survey should contain demographic questions (such as

gender, income level, education level) that will allow you to break down the responses andlook deeper into the survey results

A survey budget must be considered For example, if you have $3,000 to spend on callsand each call costs $10 to make, you obviously are limited to making 300 calls However,keep in mind that 300 calls may not result in 300 usable responses

The phone survey should be conducted in a short time period Typically, the prime callingtime for a voter survey is between 7:00 P.M and 9:00 P.M However, some people are not home inthe evening and will be excluded from the survey unless there is a plan for conducting callbacks

opin-ions and factual data from people is a written questionnaire In some instances, the naires are mailed to the respondent In others, they are administered directly to the potentialrespondents Written questionnaires are generally the least expensive means of collecting sur-vey data If they are mailed, the major costs include postage to and from the respondents,questionnaire development and printing costs, and data analysis Figure 1.8 shows the majorsteps in conducting a written survey Note how written surveys are similar to telephone sur-veys; however, written surveys can be slightly more involved and, therefore, take more time tocomplete than those used for a telephone survey However, you must be careful to construct aquestionnaire that can be easily completed without requiring too much time

question-Closed-End Questions

Questions that require the respondent to select

from a short list of defined choices.

Demographic Questions

Questions relating to the respondents’

characteristics, backgrounds, and attributes.

DetermineSample Size andSampling Method

PretesttheSurvey

Define thePopulation

of Interest

Select SampleandSend Surveys

Design theSurveyInstrument

Define theIssue

Clearly state the purpose of the survey Define the objectives What

do you want to learn from the survey? Make sure there is agreement before you proceed

Define the overall group of people to be potentially included in the survey and obtain a list of names and addresses of those individuals

in this group

Limit the number of questions to keep the survey short

Ask important questions first Provide specific response options when possible

Add demographic questions at the end: age, income, etc

Introduction should explain purpose of survey and who is conducting it—stress that answers are anonymous

Layout of the survey must be clear and attractive Provide location for responses

Try the survey out on a small group from the population Check for length, clarity, and ease of conducting Have we forgotten anything?Make changes if needed

Mail survey to a subset of the larger group

Include a cover letter explaining the purpose of the survey

Include return envelope for returning the survey

Sample size is dependent on how confident we want to be of our results, how precise we want the results to be, and how much opinions differ among the population members Chapter 7 will show how sample sizes are computed Various sampling methods are available These are reviewed later in Chapter 1

FIGURE 1.8 |

Written Survey Steps

A written survey can contain both closed-end and open-end questions.

Open-end questions provide the respondent with greater flexibility in answering a question;however, the responses can be difficult to analyze Note that telephone surveys can use open-endquestions, too However, the caller may have to transcribe a potentially long response and there

is risk that the interviewees’ comments may be misinterpreted

Written surveys also should be formatted to make it easy for the respondent to provideaccurate and reliable data This means that proper space must be provided for the responses,and the directions must be clear about how the survey is to be completed A written surveyneeds to be pleasing to the eye How it looks will affect the response rate, so it must lookprofessional

You also must decide whether to manually enter or scan the data gathered from your ten survey The survey design will be affected by the approach you take If you are adminis-tering a large number of surveys, scanning is preferred It cuts down on data entry errors andspeeds up the data gathering process However, you may be limited in the form of responsesthat are possible if you use scanning

writ-If the survey is administered directly to the desired respondents, you can expect a highresponse rate For example, you probably have been on the receiving end of a written surveymany times in your college career, when you were asked to fill out a course evaluation form atthe end of the term Most students will complete the form On the other hand, if a survey isadministered through the mail, you can expect a low response rate—typically 5% to 20%.Therefore, if you want 200 responses, you should mail out 1,000 to 4,000 questionnaires.Overall, written surveys can be a low-cost, effective means of collecting data if you canovercome the problems of low response Be careful to pretest the survey and spend extra time

on the format and look of the survey instrument

Developing a good written questionnaire or telephone survey instrument is a major lenge Among the potential problems are the following:

chal-● Leading questionsExample: “Do you agree with most other reasonably minded people that the cityshould spend more money on neighborhood parks?”

Issue: In this case, the phrase “Do you agree” may suggest that you should agree.Also, by suggesting that “most reasonably minded people” already agree, therespondent might be compelled to agree so that he or she can also be consid-ered “reasonably minded.”

Improvement: “In your opinion, should the city increase spending on hood parks?”

neighbor-Example: “To what extent would you support paying a small increase in your property taxes if it would allow poor and disadvantaged children to have food and shelter?”

Issue: The question is ripe with emotional feeling and may imply that if you don’tsupport additional taxes, you don’t care about poor children

Improvement: “Should property taxes be increased to provide additional fundingfor social services?”

● Poorly worded questionsExample: “How much money do you make at your current job?”

Issue: The responses are likely to be inconsistent When answering, does therespondent state the answer as an hourly figure or as a weekly or monthlytotal? Also, many people refuse to answer questions regarding their income.Improvement: “Which of the following categories best reflects your weeklyincome from your current job?

Open-End Questions

Questions that allow respondents the freedom to

respond with any value, words, or statements of

their own choosing.

Improvement: “After trying the new product, please rate its taste on a 1 to 10 scalewith 1 being best Also rate the product’s freshness using the same 1 to 10scale.

The way a question is worded can influence the responses Consider an example thatoccurred in September 2008 during the financial crisis that resulted from the sub-prime mort-gage crisis and bursting of the real estate bubble Three surveys were conducted on the samebasic issue The following questions were asked:

“Do you approve or disapprove of the steps the Federal Reserve and Treasury Departmenthave taken to try to deal with the current situation involving the stock market and majorfinancial institutions?” (ABC News/Washington Post) 44% Approve – 42% Disapprove –14% Unsure

“Do you think the government should use taxpayers’ dollars to rescue ailing privatefinancial firms whose collapse could have adverse effects on the economy and market,

or is it not the government’s responsibility to bail out private companies with taxpayerdollars?” (LA Times/Bloomberg) 31% Use Tax Payers’ Dollars – 55% Not Government’sResponsibility – 14% Unsure

“As you may know, the government is potentially investing billions to try and keepfinancial institutions and markets secure Do you think this is the right thing or the wrongthing for the government to be doing?” (Pew Research Center) 57% Right Thing – 30%Wrong Thing – 13% Unsure

Note the responses to each of these questions The way the question is worded can affectthe responses

that is often used to collect data As implied by the name, this technique requires that theprocess from which the data are being collected is physically observed and the data recordedbased on what takes place in the process

Possibly the most basic way to gather data on human behavior is to watch people If youare trying to decide whether a new method of displaying your product at the supermarket will

be more pleasing to customers, change a few displays and watch customers’ reactions If, as amember of a state’s transportation department, you want to determine how well motorists arecomplying with the state’s seat belt laws, place observers at key spots throughout the state tomonitor people’s seat belt habits A movie producer, seeking information on whether a newmovie will be a success, holds a preview showing and observes the reactions and comments ofthe movie patrons as they exit the screening The major constraints when collecting observa-tions are the time and money required to carry out the observations For observations to beeffective, trained observers must be used, which increases the cost Personal observation isalso time-consuming Finally, personal perception is subjective There is no guarantee thatdifferent observers will see a situation in the same way, much less report it the same way

Personal interviews are often used to gather data from people Interviews can be either

structured or unstructured, depending on the objectives, and they can utilize either

open-end or closed-open-end questions

Regardless of the procedure used for data collection, care must be taken that the data lected are accurate and reliable and that they are the right data for the purpose at hand

col-Other Data Collection Methods

Data collection methods that take advantage of new technologies are becoming more lent all the time For example, many people believe that Wal-Mart is the best company in theworld at collecting and using data about the buying habits of its customers Most of the dataare collected automatically as checkout clerks scan the UPC bar codes on the productscustomers purchase Not only are Wal-Mart’s inventory records automatically updated, butinformation about the buying habits of customers is recorded The data help managers orga-nize their stores to increase sales For instance, Wal-Mart apparently decided to locate beerand disposable diapers close together when it discovered that many male customers also pur-chase beer when they are sent to the store for diapers

preva-Structured Interview

Interviews in which the questions are scripted.

Unstructured Interview

Interviews that begin with one or more broadly

stated questions, with further questions being

based on the responses.

Bar code scanning is used in many different data collection applications In a DRAM(dynamic random-access memory) wafer fabrication plant, batches of silicon wafers have barcodes As the batches travel through the plant’s workstations, their progress and quality aretracked through the data that are automatically obtained by scanning.

Every time you use your credit card, data are automatically collected by the retailer andthe bank Computer information systems are developed to store the data and to provide deci-sion makers with procedures to access the data

In many instances your data collection method will require you to use physical

measure-ment For example, the Andersen Window Company has quality analysts physically measure

the width and height of its windows to assure that they meet customer specifications, and astate Department of Weights and Measures will physically test meat and produce scales todetermine that customers are being properly charged for their purchases

Data Collection Issues

There are several data collection issues of which you need to be aware When you need data tomake a decision, we suggest that you first see if appropriate data have already been collected,because it is usually faster and less expensive to use existing data than to collect data yourself.However, before you rely on data that were collected by someone else for another purpose, youneed to check out the source to make sure that the data were collected and recorded properly

Such organizations as Value Line and Fortune have built their reputations on providing

quality data Although data errors are occasionally encountered, they are few and far between.You really need to be concerned with data that come from sources with which you are notfamiliar This is an issue for many sources on the World Wide Web Any organization, or anyindividual, can post data to the Web Just because the data are there doesn’t mean they areaccurate Be careful

these is the potential for bias in the data collection There are many types of bias For

exam-ple, in a personal interview, the interviewer can interject bias (either accidentally or on pose) by the way she asks the questions, by the tone of her voice, or by the way she looks atthe subject being interviewed We recently allowed ourselves to be interviewed at a tradeshow The interviewer began by telling us that he would only get credit for the interview if weanswered all of the questions Next, he asked us to indicate our satisfaction with a particulardisplay He wasn’t satisfied with our less-than-enthusiastic rating and kept asking us if wereally meant what we said He even asked us if we would consider upgrading our rating! Howreliable do you think these data will be?

collec-tion process is called nonresponse bias We stated earlier that mail surveys suffer from a

high percentage of unreturned surveys Phone calls don’t always get through, or people refuse toanswer Subjects of personal interviews may refuse to be interviewed There is a potential prob-lem with nonresponse Those who respond may provide data that are quite different from thedata that would be supplied by those who choose not to respond If you aren’t careful, theresponses may be heavily weighted by people who feel strongly one way or another on an issue

collec-tion This is referred to as selection bias A study on the virtues of increasing the student athletic

fee at your university might not be best served by collecting data from students attending a ball game Sometimes, the problem is more subtle If we do a telephone survey during theevening hours, we will miss all of the people who work nights Do they share the same views,income, education levels, and so on as people who work days? If not, the data are biased.Written and phone surveys and personal interviews can also yield flawed data if the inter-

foot-viewees lie in response to questions For example, people commonly give inaccurate data

about such sensitive matters as income Sometimes, the data errors are not due to lies Therespondents may not know or have accurate information to provide the correct answer

People tend to view the same event or item differently This is referred to as observer bias.

Bias

An effect which alters a statistical result by

systematically distorting it; different from a

random error which may distort on any one

occasion but balances out on the average.

One area in which this can easily occur is in safety check programs in companies An tant part of behavioral-based safety programs is the safety observation Trained data collectorsperiodically conduct a safety observation on a worker to determine what, if any, unsafe actsmight be taking place We have seen situations in which two observers will conduct an obser-vation on the same worker at the same time, yet record different safety data This is especiallytrue in areas in which judgment is required on the part of the observer, such as the distance aworker is from an exposed gear mechanism People judge distance differently.

manufac-turer The company was having a quality problem with one of its saws A study was developed

to measure the width of boards that had been cut by the saw Two people were trained to usedigital calipers and record the data This caliper is a U-shaped tool that measures distance (ininches) to three decimal places The caliper was placed around the board and squeezed tightlyagainst the sides The width was indicated on the display Each person measured 500 boardsduring an 8-hour day When the data were analyzed, it looked like the widths were comingfrom two different saws; one set showed considerably narrower widths than the other Uponinvestigation, we learned that the person with the narrower width measurements was pressing

on the calipers much more firmly The soft wood reacted to the pressure and gave narrowerreadings Fortunately, we had separated the data from the two data collectors Had they beenmerged, the measurement error might have gone undetected

that proper controls have been put in place For instance, suppose a drug company such as Pfizer

is conducting tests on a drug that it hopes will reduce cholesterol One group of test participants

is given the new drug while a second group (a control group) is given a placebo Suppose thatafter several months, the group using the drug saw significant cholesterol reduction For the

results to have internal validity, the drug company would have had to make sure the two groups

were controlled for the many other factors that might affect cholesterol, such as smoking, diet,weight, gender, race, and exercise habits Issues of internal validity are generally addressed byrandomly assigning subjects to the test and control groups However, if the extraneous factorsare not controlled, there could be no assurance that the drug was the factor influencing reducedcholesterol For data to have internal validity, the extraneous factors must be controlled

con-cerned that the results can be generalized beyond the test environment For example, if the lesterol drug test had been performed in Europe, would the same basic results occur for people

cho-in North America, South America, or elsewhere? For that matter, the drug company would also

be interested in knowing whether the results could be replicated if other subjects are used in asimilar experiment If the results of an experiment can be replicated for groups different from the

original population, then there is evidence the results of the experiment have external validity.

An extensive discussion of how to measure the magnitude of bias and how to reduce biasand other data collection problems is beyond the scope of this text However, you should beaware that data may be biased or otherwise flawed Always pose questions about the potentialfor bias and determine what steps have been taken to reduce its effect

Internal Validity

A characteristic of an experiment in which data

are collected in such a way as to eliminate the

effects of variables within the experimental

environment that are not of interest to the

researcher.

External Validity

A characteristic of an experiment whose results

can be generalized beyond the test environment

so that the outcomes can be replicated when

the experiment is repeated.

MyStatLab

Skill Development

1-17 If a pet store wishes to determine the level of customer

satisfaction with its services, would it be appropriate to

conduct an experiment? Explain

1-18 Define what is meant by a leading question Provide

an example

1-19 Briefly explain what is meant by an experiment and an

experimental design

1-20 Refer to the three questions discussed in this

section involving the financial crises of 2008 and

2009 and possible government intervention Notethat the questions elicited different responses