Business statistics david f groebner

TATIS TIC

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A DECISION-MAKING APPROACH

A D

EC IS

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A P

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DAVID F.

GROEBNER

PATRICK W.

SHANNON

PHILLIP C.

FRYGROEBNER SHANNON

FRY

TENTH EDITION

TENTH EDITION

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Business statistics

A Decision-Making Approach

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Business statistics

A Decision-Making Approach

David F. Groebner Boise State University, Professor Emeritus of Production Management

Patrick W. Shannon Boise State University, Professor Emeritus of Supply Chain Management

Phillip C. Fry Boise State University, Professor of Supply Chain Management

t e n t h e d i t i o n

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Library of Congress Cataloging-in-Publication Data Names: Groebner, David F., author. | Shannon, Patrick W., author. | Fry, Phillip C., author. Title: Business statistics : a decision-making approach / David F. Groebner, Boise State University, Professor Emeritus of Production Management, Patrick W. Shannon, Boise State University, Professor Emeritus of Supply Chain Management, Phillip C. Fry, Boise State University, Professor of Supply Chain Management. Description: Tenth edition. | Boston : Pearson, 2016. | Revised edition of Business statistics, 2014. Identifiers: LCCN 2016016744 | ISBN 9780134496498 (hardcover) | ISBN 0134496493 (hardcover) Subjects: LCSH: Commercial statistics. | Statistical decision. Classification: LCC HF1017 .G73 2016 | DDC 519.5–dc23 LC record available at https://lccn.loc.gov/2016016744

ISBN-10: 0-13-449649-3 ISBN-13: 978-0-13-449649-8

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To Jane and my family, who survived the process one more time.

david f. groebner

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

patrick w. shannon

To my wonderful family: Susan, Alex, Allie, Candace, and Courtney.

phillip c. fry

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About the Authors

David F. Groebner, PhD, is Professor Emeritus of Production Management in the College of Business and Economics at Boise State University. He has bachelor’s and master’s degrees in engineering and a PhD in business administration. After working as an engineer, he has taught statistics and related subjects for 27 years. In addition to writing textbooks and academic papers, he has worked extensively with both small and large organizations, includ- ing Hewlett-Packard, Boise Cascade, Albertson’s, and Ore-Ida. He has also consulted for numerous government agencies, including Boise City and the U.S. Air Force.

Patrick W. Shannon, PhD, is Professor Emeritus of Supply Chain Operations Management in the College of Business and Economics at Boise State University. He has taught graduate and undergraduate courses in business statistics, quality management and lean operations and supply chain management. Dr. Shannon has lectured and consulted in the statistical analysis and lean/quality management areas for more than 30 years. Among his consulting clients are Boise Cascade Corporation, Hewlett-Packard, PowerBar, Inc., Pot- latch 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 BS and MS de- grees from the University of Montana and a PhD in statistics and quantitative methods from the University of Oregon.

Phillip C. Fry, PhD, is a professor of Supply Chain Management in the College of Business and Economics at Boise State University, where he has taught since 1988. Phil received his BA. and MBA degrees from the University of Arkansas and his MS and PhD degrees from Louisiana State University. His teaching and research interests are in the areas of business statistics, supply chain management, and quantitative business modeling. In ad- dition 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 Intermountain Gas Company.

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Brief Contents 1 the Where, Why, and how of data Collection 1 2 Graphs, Charts, and tables—describing Your data 28 3 describing data Using numerical Measures 73

1–3 Special Re vie w Section 122

4 introduction to Probability 128 5 discrete Probability distributions 172 6 introduction to Continuous Probability distributions 212 7 introduction to Sampling distributions 239 8 estimating Single Population Parameters 277 9 introduction to hypothesis testing 316 10 estimation and hypothesis testing for two Population Parameters 363 11 hypothesis tests and estimation for Population Variances 410 12 Analysis of Variance 434

8–12 Special Re vie w Section 481

13 Goodness-of-Fit tests and Contingency Analysis 497 14 introduction to Linear Regression and Correlation Analysis 526 15 Multiple Regression Analysis and Model Building 573 16 Analyzing and Forecasting time-Series data 636 17 introduction to nonparametric Statistics 687 18 introducing Business Analytics 718 19 introduction to decision Analysis (Online) 20 introduction to Quality and Statistical Process Control (Online)

appendices A Random numbers table 744 B Cumulative Binomial distribution table 745 C Cumulative Poisson Probability distribution table 759 D Standard normal distribution table 764 E exponential distribution table 765 F Values of t for Selected Probabilities 766 G Values of x2 for Selected Probabilities 767 H F-distribution table 768 I distribution of the Studentized Range (q-values) 774 J Critical Values of r in the Runs test 776 K Mann–Whitney U-test Probabilities (n * 9) 777 L Mann–Whitney U-test Critical Values (9 " n " 20) 779 M Critical Values of T in the Wilcoxon Matched-Pairs Signed-Ranks test (n " 25) 781 N Critical Values dL and dU of the durbin-Watson Statistic D 782 O Lower and Upper Critical Values W of Wilcoxon Signed-Ranks test 784 P Control Chart Factors 785

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Preface xix

ChaPTer 1 the Where, Why, and how of data Collection 1 1.1 What Is Business Statistics? 2

Descriptive Statistics 3 Inferential Procedures 4

1.2 Procedures for Collecting Data 5 Primary Data Collection Methods 5 Other Data Collection Methods 10 Data Collection Issues 11

1.3 Populations, Samples, and Sampling Techniques 13 Populations and Samples 13 Sampling Techniques 14

1.4 Data Types and Data Measurement Levels 19 Quantitative and Qualitative Data 19 Time-Series Data and Cross-Sectional Data 20 Data Measurement Levels 20

1.5 a Brief Introduction to Data Mining 23 Data Mining—Finding the Important, Hidden Relationships in Data 23

Summary 25 • Key Terms 27 • Chapter exercises 27

ChaPTer 2 Graphs, Charts, and tables—describing Your data 28 2.1 Frequency Distributions and histograms 29

Frequency Distributions 29 Grouped Data Frequency Distributions 33 Histograms 38 Relative Frequency Histograms and Ogives 41 Joint Frequency Distributions 43

2.2 Bar Charts, Pie Charts, and Stem and Leaf Diagrams 50 Bar Charts 50 Pie Charts 53 Stem and Leaf Diagrams 54

2.3 Line Charts, Scatter Diagrams, and Pareto Charts 59 Line Charts 59 Scatter Diagrams 62 Pareto Charts 64

Summary 68 • equations 69 • Key Terms 69 • Chapter exercises 69

Case 2.1 Server Downtime 71

Case 2.2 hudson Valley apples, Inc. 72

Case 2.3 Pine river Lumber Company—Part 1 72

ChaPTer 3 describing data Using numerical Measures 73 3.1 Measures of Center and Location 74

Parameters and Statistics 74 Population Mean 74 Sample Mean 77 The Impact of Extreme Values on the Mean 78 Median 79

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Contents

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xii Contents

Skewed and Symmetric Distributions 80 Mode 81 Applying the Measures of Central Tendency 83 Other Measures of Location 84 Box and Whisker Plots 87 Developing a Box and Whisker Plot in Excel 2016 89 Data-Level Issues 89

3.2 Measures of Variation 95 Range 95 Interquartile Range 96 Population Variance and Standard Deviation 97 Sample Variance and Standard Deviation 100

3.3 Using the Mean and Standard Deviation Together 106 Coefficient of Variation 106 Tchebysheff’s Theorem 109 Standardized Data Values 109

Summary 114 • equations 115 • Key Terms 116 • Chapter exercises 116

Case 3.1: SDW—human resources 120

Case 3.2: National Call Center 120

Case 3.3: Pine river Lumber Company—Part 2 121

Case 3.4: aJ’s Fitness Center 121

ChaPTerS 1–3 SPeCiAL Re Vie W SeCtion 122 Chapters 1–3 122 Exercises 125 Review Case 1 State Department of Insurance 126 Term Project Assignments 127

ChaPTer 4 introduction to Probability 128 4.1 The Basics of Probability 129

Important Probability Terms 129 Methods of Assigning Probability 134

4.2 The rules of Probability 141 Measuring Probabilities 141 Conditional Probability 149 Multiplication Rule 153 Bayes’ Theorem 156

Summary 165 • equations 165 • Key Terms 166 • Chapter exercises 166

Case 4.1: Great air Commuter Service 169

Case 4.2: Pittsburg Lighting 170

ChaPTer 5 discrete Probability distributions 172 5.1 Introduction to Discrete Probability Distributions 173

Random Variables 173 Mean and Standard Deviation of Discrete Distributions 175

5.2 The Binomial Probability Distribution 180 The Binomial Distribution 181 Characteristics of the Binomial Distribution 181

5.3 Other Probability Distributions 193 The Poisson Distribution 193 The Hypergeometric Distribution 197

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Contents xiii

Summary 205 • equations 205 • Key Terms 206 • Chapter exercises 206

Case 5.1: SaveMor Pharmacies 209

Case 5.2: arrowmark Vending 210

Case 5.3: Boise Cascade Corporation 211

ChaPTer 6 introduction to Continuous Probability distributions 212 6.1 The Normal Distribution 213

The Normal Distribution 213 The Standard Normal Distribution 214 Using the Standard Normal Table 216

6.2 Other Continuous Probability Distributions 226 The Uniform Distribution 226 The Exponential Distribution 228

Summary 233 • equations 234 • Key Terms 234 • Chapter exercises 234

Case 6.1: State entitlement Programs 237

Case 6.2: Credit Data, Inc. 238

Case 6.3: National Oil Company—Part 1 238

ChaPTer 7 introduction to Sampling distributions 239 7.1 Sampling error: What It Is and Why It happens 240

Calculating Sampling Error 240

7.2 Sampling Distribution of the Mean 248 Simulating the Sampling Distribution for x 249 The Central Limit Theorem 255

7.3 Sampling Distribution of a Proportion 262 Working with Proportions 262 Sampling Distribution of p 264

Summary 271 • equations 272 • Key Terms 272 • Chapter exercises 272

Case 7.1: Carpita Bottling Company—Part 1 275

Case 7.2: Truck Safety Inspection 276

ChaPTer 8 estimating Single Population Parameters 277 8.1 Point and Confidence Interval estimates for a Population Mean 278

Point Estimates and Confidence Intervals 278 Confidence Interval Estimate for the Population Mean, S Known 279 Confidence Interval Estimates for the Population Mean, S Unknown 286 Student’s t-Distribution 286

8.2 Determining the required Sample Size for estimating a Population Mean 295 Determining the Required Sample Size for Estimating M, S Known 296 Determining the Required Sample Size for Estimating M, S Unknown 297

8.3 estimating a Population Proportion 301 Confidence Interval Estimate for a Population Proportion 302 Determining the Required Sample Size for Estimating a Population Proportion 304

Summary 310 • equations 311 • Key Terms 311 • Chapter exercises 311

Case 8.1: Management Solutions, Inc. 314

Case 8.2: Federal aviation administration 315

Case 8.3: Cell Phone Use 315

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xiv Contents

ChaPTer 9 introduction to hypothesis testing 316 9.1 hypothesis Tests for Means 317

Formulating the Hypotheses 317 Significance Level and Critical Value 321 Hypothesis Test for M, S Known 322 Types of Hypothesis Tests 328 p-Value for Two-Tailed Tests 329 Hypothesis Test for M, S Unknown 331

9.2 hypothesis Tests for a Proportion 338 Testing a Hypothesis about a Single Population Proportion 338

9.3 Type II errors 344 Calculating Beta 344 Controlling Alpha and Beta 346 Power of the Test 350

Summary 355 • equations 357 • Key Terms 357 • Chapter exercises 357

Case 9.1: Carpita Bottling Company—Part 2 361

Case 9.2: Wings of Fire 361

ChaPTer 10 estimation and hypothesis testing for two Population Parameters 363 10.1 estimation for Two Population Means Using Independent Samples 364

Estimating the Difference between Two Population Means When S1 and S2 Are Known, Using Independent Samples 364 Estimating the Difference between Two Population Means When S1 and S2 Are Unknown, Using Independent Samples 366

10.2 hypothesis Tests for Two Population Means Using Independent Samples 374 Testing for M1 − M2 When S1 and S2 Are Known, Using Independent Samples 374 Testing for M1 − M2 When S1 and S2 Are Unknown, Using Independent Samples 377

10.3 Interval estimation and hypothesis Tests for Paired Samples 386 Why Use Paired Samples? 387 Hypothesis Testing for Paired Samples 390

10.4 estimation and hypothesis Tests for Two Population Proportions 395 Estimating the Difference between Two Population Proportions 395 Hypothesis Tests for the Difference between Two Population Proportions 396

Summary 402 • equations 403 • Key Terms 404 • Chapter exercises 404

Case 10.1: Larabee engineering—Part 1 407

Case 10.2: hamilton Marketing Services 407

Case 10.3: Green Valley assembly Company 408

Case 10.4: U-Need-It rental agency 408

ChaPTer 11 hypothesis tests and estimation for Population Variances 410 11.1 hypothesis Tests and estimation for a Single Population Variance 411

Chi-Square Test for One Population Variance 411 Interval Estimation for a Population Variance 416

11.2 hypothesis Tests for Two Population Variances 420 F-Test for Two Population Variances 420

Summary 430 • equations 430 • Key Term 430 • Chapter exercises 430

Case 11.1: Larabee engineering—Part 2 432

ChaPTer 12 Analysis of Variance 434 12.1 One-Way analysis of Variance 435

Introduction to One-Way ANOVA 435 Partitioning the Sum of Squares 436 The ANOVA Assumptions 437

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Applying One-Way ANOVA 439 The Tukey-Kramer Procedure for Multiple Comparisons 446 Fixed Effects Versus Random Effects in Analysis of Variance 449

12.2 randomized Complete Block analysis of Variance 453 Randomized Complete Block ANOVA 454 Fisher’s Least Significant Difference Test 460

12.3 Two-Factor analysis of Variance with replication 464 Two-Factor ANOVA with Replications 464 A Caution about Interaction 470

Summary 474 • equations 475 • Key Terms 475 • Chapter exercises 475

Case 12.1: agency for New americans 478

Case 12.2: McLaughlin Salmon Works 479

Case 12.3: NW Pulp and Paper 479

Case 12.4: Quinn restoration 479

Business Statistics Capstone Project 480

ChaPTerS 8–12 SPeCiAL Re Vie W SeCtion 481 Chapters 8–12 481

Using the Flow Diagrams 493

exercises 494

ChaPTer 13 Goodness-of-Fit tests and Contingency Analysis 497 13.1 Introduction to Goodness-of-Fit Tests 498

Chi-Square Goodness-of-Fit Test 498

13.2 Introduction to Contingency analysis 510 2 : 2 Contingency Tables 511 r : c Contingency Tables 515 Chi-Square Test Limitations 517

Summary 521 • equations 521 • Key Term 521 • Chapter exercises 522

Case 13.1: National Oil Company—Part 2 524

Case 13.2: Bentford electronics—Part 1 524

ChaPTer 14 introduction to Linear Regression and Correlation Analysis 526 14.1 Scatter Plots and Correlation 527

The Correlation Coefficient 527

14.2 Simple Linear regression analysis 536 The Regression Model Assumptions 536 Meaning of the Regression Coefficients 537 Least Squares Regression Properties 542 Significance Tests in Regression Analysis 544

14.3 Uses for regression analysis 554 Regression Analysis for Description 554 Regression Analysis for Prediction 556 Common Problems Using Regression Analysis 558

Summary 565 • equations 566 • Key Terms 567 • Chapter exercises 567

Case 14.1: a & a Industrial Products 570

Case 14.2: Sapphire Coffee—Part 1 571

Case 14.3: alamar Industries 571

Case 14.4: Continental Trucking 572

ChaPTer 15 Multiple Regression Analysis and Model Building 573 15.1 Introduction to Multiple regression analysis 574

Basic Model-Building Concepts 576

Contents xv

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15.2 Using Qualitative Independent Variables 590 15.3 Working with Nonlinear relationships 597

Analyzing Interaction Effects 601 Partial F-Test 604

15.4 Stepwise regression 611 Forward Selection 611 Backward Elimination 611 Standard Stepwise Regression 613 Best Subsets Regression 614

15.5 Determining the aptness of the Model 618 Analysis of Residuals 619 Corrective Actions 624

Summary 628 • equations 629 • Key Terms 630 • Chapter exercises 630

Case 15.1: Dynamic Weighing, Inc. 632

Case 15.2: Glaser Machine Works 634

Case 15.3: hawlins Manufacturing 634

Case 15.4: Sapphire Coffee—Part 2 635

Case 15.5: Wendell Motors 635

ChaPTer 16 Analyzing and Forecasting time-Series data 636 16.1 Introduction to Forecasting and Time-Series Data 637

General Forecasting Issues 637 Components of a Time Series 638 Introduction to Index Numbers 641 Using Index Numbers to Deflate a Time Series 642

16.2 Trend-Based Forecasting Techniques 644 Developing a Trend-Based Forecasting Model 644 Comparing the Forecast Values to the Actual Data 646 Nonlinear Trend Forecasting 653 Adjusting for Seasonality 657

16.3 Forecasting Using Smoothing Methods 667 Exponential Smoothing 667 Forecasting with Excel 2016 674

Summary 681 • equations 682 • Key Terms 682 • Chapter exercises 682

Case 16.1: Park Falls Chamber of Commerce 685

Case 16.2: The St. Louis Companies 686

Case 16.3: Wagner Machine Works 686

ChaPTer 17 introduction to nonparametric Statistics 687 17.1 The Wilcoxon Signed rank Test for One Population Median 688

The Wilcoxon Signed Rank Test—Single Population 688

17.2 Nonparametric Tests for Two Population Medians 693 The Mann–Whitney U-Test 693 Mann–Whitney U-Test—Large Samples 696

17.3 Kruskal–Wallis One-Way analysis of Variance 705 Limitations and Other Considerations 709

Summary 712 • equations 713 • Chapter exercises 714

Case 17.1: Bentford electronics—Part 2 717

ChaPTer 18 introducing Business Analytics 718 18.1 What Is Business analytics? 719

Descriptive Analytics 720 Predictive Analytics 723

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18.2 Data Visualization Using Microsoft Power BI Desktop 725 Using Microsoft Power BI Desktop 729

Summary 741 • Key Terms 741

Case 18.1: New York City Taxi Trips 741

ChaPTer 19 introduction to decision Analysis 19.1 Decision-Making environments and Decision Criteria

Certainty Uncertainty Decision Criteria Nonprobabilistic Decision Criteria Probabilistic Decision Criteria

19.2 Cost of Uncertainty 19.3 Decision-Tree analysis Case 19.1: rockstone International

Case 19.2: hadden Materials and Supplies, Inc.

ChaPTer 20 introduction to Quality and Statistical Process Control 20.1 Introduction to Statistical Process Control Charts

The Existence of Variation Introducing Statistical Process Control Charts x-Chart and R-Chart

Case 20.1: Izbar Precision Controls, Inc.

(Online)

(Online)

Contents xvii

Appendices 743 A Random Numbers Table 744 B Cumulative Binomial Distribution Table 745 C Cumulative Poisson Probability Distribution Table 759 D Standard Normal Distribution Table 764 E Exponential Distribution Table 765 F Values of t for Selected Probabilities 766 G Values of x2 for Selected Probabilities 767 H F-Distribution Table 768 I Distribution of the Studentized Range (q-values) 774 J Critical Values of r in the Runs Test 776 K Mann–Whitney U-Test Probabilities (n * 9) 777 L Mann–Whitney U-Test Critical Values (9 " n " 20) 779 M Critical Values of T in the Wilcoxon Matched-Pairs Signed-Ranks Test (n " 25) 781 N Critical Values dL and du of the Durbin-Watson Statistic D 782 O Lower and Upper Critical Values W of Wilcoxon Signed-Ranks

Test 784

P Control Chart Factors 785

Answers to Selected Odd-Numbered Problems 787

References 815

Glossary 819

Index 825

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xix

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

Our intent in writing Business Statistics: A Decision- Making Approach is to provide an introductory business statis- tics text for students who do not necessarily have an extensive mathematics background but who need to understand how sta- tistical tools and techniques are applied in business decision making.

This text differs from its competitors in three key ways:

1. Use of a direct approach with concepts and techniques consistently presented in a systematic and ordered way.

2. Presentation of the content at a level that makes it acces- sible to students of all levels of mathematical maturity. The text features clear, step-by-step explanations that make learning business statistics straightforward.

3. Engaging examples, drawn from our years of experience as authors, educators, and consultants, to show the rel- evance of the statistical techniques in realistic business decision situations.

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 for examples to help them. Thus, this text features clearly marked, step-by-step examples that students 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 out- comes. The examples and practice exercises are designed to reinforce the objectives and lead students toward the desired outcomes. The exercises are ordered from easy to more difficult and are divided into categories: Conceptual, Skill Development, Business Applications, and Computer Software Exercises.

This text places on data and how data are obtained. Many business statistics texts assume that data have already been col- lected. We have decided to underscore a more modern theme: Data are the starting point. We believe that effective decision making relies on a good understanding of the different types of data and the different data collection options that exist. To highlight our theme, we begin a discussion of data and data collection methods in Chapter 1 before any discussion of data analysis is presented. In Chapters 2 and 3, where the important