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Essentials of Business Statistics 4th Edition Chapter 3

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Contents vii

Brief Contents

Preface xxi

About the Authors xxix

Chapter 1 Data and Statistics 1

Chapter 2 Descriptive Statistics: Tabular and Graphical

Presentations 31

Chapter 3 Descriptive Statistics: Numerical Measures 86

Chapter 4 Introduction to Probability 148

Chapter 5 Discrete Probability Distributions 193

Chapter 6 Continuous Probability Distributions 232

Chapter 7 Sampling and Sampling Distributions 265

Chapter 8 Interval Estimation 304

Chapter 9 Hypothesis Tests 344

Chapter 10 Comparisons Involving Means, Experimental Design,

and Analysis of Variance 392

Chapter 11 Comparisons Involving Proportions and a Test

of Independence 448

Chapter 12 Simple Linear Regression 483

Chapter 13 Multiple Regression 552

Appendix A References and Bibliography 602

Appendix B Tables 604

Appendix C Summation Notation 631

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

Exercises 633

Appendix E Using Excel Functions 665

Appendix F Computing p-Values Using Minitab and Excel 670

Index 674

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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Contents

Preface xxi

About the Authors xxix

Chapter 1 Data and Statistics 1

Statistics in Practice: Businessweek 2

1.1 Applications in Business and Economics 3

Accounting 3

Finance 4

Marketing 4

Production 4

Economics 4

1.2 Data 5

Elements, Variables, and Observations 5

Scales of Measurement 6

Categorical and Quantitative Data 7

Cross-Sectional and Time Series Data 7

1.3 Data Sources 10

Existing Sources 10

Statistical Studies 11

Data Acquisition Errors 13

1.4 Descriptive Statistics 13

1.5 Statistical Inference 15

1.6 Computers and Statistical Analysis 17

1.7 Data Mining 17

1.8 Ethical Guidelines for Statistical Practice 18

Summary 20

Glossary 20

Supplementary Exercises 21

Appendix An Introduction to StatTools 28

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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

x Contents

Chapter 2 Descriptive Statistics: Tabular and Graphical

Presentations 31

Statistics in Practice: Colgate-Palmolive Company 32

2.1 Summarizing Categorical Data 33

Frequency Distribution 33

Relative Frequency and Percent Frequency Distributions 34

Bar Charts and Pie Charts 34

2.2 Summarizing Quantitative Data 39

Frequency Distribution 39

Relative Frequency and Percent Frequency Distributions 41

Dot Plot 41

Histogram 42

Cumulative Distributions 44

Ogive 44

2.3 Exploratory Data Analysis: The Stem-and-Leaf Display 49

2.4 Crosstabulations and Scatter Diagrams 54

Crosstabulation 54

Simpson's Paradox 57

Scatter Diagram and Trendline 58

Summary 64

Glossary 65

Key Formulas 66

Supplementary Exercises 66

Case Problem 1: Pelican Stores 72

Case Problem 2: Motion Picture Industry 73

Appendix 2.1 Tabular and Graphical Presentations Using Minitab 74

Appendix 2.2 Tabular and Graphical Presentations Using Excel 76

Appendix 2.3 Tabular and Graphical Presentations Using StatTools 85

Chapter 3 Descriptive Statistics: Numerical Measures 86

Statistics in Practice: Small Fry Design 87

3.1 Measures of Location 88

Mean 88

Median 89

Mode 90

Percentiles 91

Quartiles 92

3.2 Measures of Variability 96

Range 97

Interquartile Range 97

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Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Contents xi

Variance 98

Standard Deviation 100

Coefficient of Variation 100

3.3 Measures of Distribution Shape, Relative Location, and Detection of

Outliers 103

Distribution Shape 103

z-Scores 104

Chebyshev's Theorem 105

Empirical Rule 106

Detection of Outliers 107

3.4 Exploratory Data Analysis 110

Five-Number Summary 110

Box Plot 111

3.5 Measures of Association Between Two Variables 116

Covariance 116

Interpretation of the Covariance 118

Correlation Coefficient 120

Interpretation of the Correlation Coefficient 121

3.6 The Weighted Mean and Working with Grouped Data 125

Weighted Mean 125

Grouped Data 126

Summary 131

Glossary 131

Key Formulas 133

Supplementary Exercises 134

Case Problem 1: Pelican Stores 138

Case Problem 2: Motion Picture Industry 140

Case Problem 3: Heavenly Chocolates Website Transactions 140

Appendix 3.1 Descriptive Statistics Using Minitab 141

Appendix 3.2 Descriptive Statistics Using Excel 143

Appendix 3.3 Descriptive Statistics Using StatTools 146

Chapter 4 Introduction to Probability 148

Statistics in Practice: Oceanwide Seafood 149

4.1 Experiments, Counting Rules, and Assigning Probabilities 150

Counting Rules, Combinations, and Permutations 151

Assigning Probabilities 155

Probabilities for the KP&L Project 157

4.2 Events and Their Probabilities 160

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xii Contents

4.3 Some Basic Relationships of Probability 164

Complement of an Event 164

Addition Law 165

4.4 Conditional Probability 171

Independent Events 174

Multiplication Law 174

4.5 Bayes' Theorem 178

Tabular Approach 182

Summary 184

Glossary 184

Key Formulas 185

Supplementary Exercises 186

Case Problem: Hamilton County Judges 190

Chapter 5 Discrete Probability Distributions 193

Statistics in Practice: Citibank 194

5.1 Random Variables 194

Discrete Random Variables 195

Continuous Random Variables 196

5.2 Discrete Probability Distributions 197

5.3 Expected Value and Variance 202

Expected Value 202

Variance 203

5.4 Binomial Probability Distribution 207

A Binomial Experiment 208

Martin Clothing Store Problem 209

Using Tables of Binomial Probabilities 213

Expected Value and Variance for the Binomial Distribution 214

5.5 Poisson Probability Distribution 218

An Example Involving Time Intervals 218

An Example Involving Length or Distance Intervals 220

5.6 Hypergeometric Probability Distribution 221

Summary 225

Glossary 226

Key Formulas 226

Supplementary Exercises 227

Appendix 5.1 Discrete Probability Distributions Using Minitab 230

Appendix 5.2 Discrete Probability Distributions Using Excel 230

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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

Contents xiii

Chapter 6 Continuous Probability Distributions 232

Statistics in Practice: Procter & Gamble 233

6.1 Uniform Probability Distribution 234

Area as a Measure of Probability 235

6.2 Normal Probability Distribution 238

Normal Curve 238

Standard Normal Probability Distribution 240

Computing Probabilities for Any Normal Probability Distribution 245

Grear Tire Company Problem 246

6.3 Normal Approximation of Binomial Probabilities 250

6.4 Exponential Probability Distribution 254

Computing Probabilities for the Exponential Distribution 254

Relationship Between the Poisson and Exponential Distributions 255

Summary 257

Glossary 258

Key Formulas 258

Supplementary Exercises 259

Case Problem: Specialty Toys 262

Appendix 6.1 Continuous Probability Distributions Using Minitab 263

Appendix 6.2 Continuous Probability Distributions Using Excel 263

Chapter 7 Sampling and Sampling Distributions 265

Statistics in Practice: Meadwestvaco Corporation 266

7.1 The Electronics Associates Sampling Problem 267

7.2 Selecting a Sample 268

Sampling from a Finite Population 268

Sampling from an Infinite Population 270

7.3 Point Estimation 273

Practical Advice 275

7.4 Introduction to Sampling Distributions 276

7.5 Sampling Distribution of

x 278

Expected Value of

x 279

Standard Deviation of

x 280

Form of the Sampling Distribution of

x 281

Sampling Distribution of

x for the EAI Problem 283

Practical Value of the Sampling Distribution of

x 283

Relationship Between the Sample Size and the Sampling

Distribution of

x 285

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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

xiv Contents

7.6 Sampling Distribution of

p 289

Expected Value of

p 289

Standard Deviation of

p 290

Form of the Sampling Distribution of

p 291

Practical Value of the Sampling Distribution of

p 291

7.7 Other Sampling Methods 295

Stratified Random Sampling 295

Cluster Sampling 295

Systematic Sampling 296

Convenience Sampling 296

Judgment Sampling 297

Summary 297

Glossary 298

Key Formulas 299

Supplementary Exercises 299

Appendix 7.1 Random Sampling Using Minitab 301

Appendix 7.2 Random Sampling Using Excel 302

Appendix 7.3 Random Sampling Using StatTools 302

Chapter 8 Interval Estimation 304

Statistics in Practice: Food Lion 305

8.1 Population Mean: Known 306

Margin of Error and the Interval Estimate 306

Practical Advice 310

8.2 Population Mean: Unknown 312

Margin of Error and the Interval Estimate 313

Practical Advice 316

Using a Small Sample 316

Summary of Interval Estimation Procedures 318

8.3 Determining the Sample Size 321

8.4 Population Proportion 324

Determining the Sample Size 326

Summary 329

Glossary 330

Key Formulas 331

Supplementary Exercises 331

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Contents xv

Case Problem 1: Young Professional Magazine 334

Case Problem 2: Gulf Real Estate Properties 335

Case Problem 3: Metropolitan Research, Inc. 337

Appendix 8.1 Interval Estimation Using Minitab 338

Appendix 8.2 Interval Estimation Using Excel 339

Appendix 8.3 Interval Estimation Using StatTools 341

Chapter 9 Hypothesis Tests 344

Statistics in Practice: John Morrell & Company 345

9.1 Developing Null and Alternative Hypotheses 346

The Alternative Hypothesis as a Research Hypothesis 346

The Null Hypothesis as an Assumption to Be Challenged 347

Summary of Forms for Null and Alternative Hypotheses 348

9.2 Type I and Type II Errors 349

9.3 Population Mean: Known 352

One-Tailed Test 352

Two-Tailed Test 358

Summary and Practical Advice 361

Relationship Between Interval Estimation and Hypothesis Testing 362

9.4 Population Mean: Unknown 367

One-Tailed Test 367

Two-Tailed Test 368

Summary and Practical Advice 370

9.5 Population Proportion 373

Summary 375

Summary 378

Glossary 378

Key Formulas 379

Supplementary Exercises 379

Case Problem 1: Quality Associates, Inc. 382

Case Problem 2: Ethical Behavior of Business Students at Bayview

Universtiy 383

Appendix 9.1 Hypothesis Testing Using Minitab 385

Appendix 9.2 Hypothesis Testing Using Excel 386

Appendix 9.3 Hypothesis Testing Using StatTools 391

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xvi Contents

Chapter 10 Comparisons Involving Means, Experimental Design,

and Analysis of Variance 392

Statistics in Practice: U.S. Food and Drug Administration 393

10.1 Inferences About the Difference Between Two Population Means:

1

and

2

Known 394

Interval Estimation of

1

2

394

Hypothesis Tests About

1

2

397

Practical Advice 398

10.2 Inferences About the Difference Between Two Population Means:

1

and

2

Unknown 401

Interval Estimation of

1

2

401

Hypothesis Tests About

1

2

403

Practical Advice 405

10.3 Inferences About the Difference Between Two Population Means:

Matched Samples 409

10.4 An Introduction to Experimental Design and Analysis of

Variance 414

Data Collection 416

Assumptions for Analysis of Variance 417

Analysis of Variance: A Conceptual Overview 417

10.5 Analysis of Variance and the Completely Randomized

Design 420

Between-Treatments Estimate of Population Variance 421

Within-Treatments Estimate of Population Variance 422

Comparing the Variance Estimates: The F Test 423

ANOVA Table 424

Computer Results for Analysis of Variance 425

Testing for the Equality of k Population Means: An Observational

Study 427

Summary 431

Glossary 431

Key Formulas 431

Supplementary Exercises 433

Case Problem 1: Par, Inc. 438

Case Problem 2: Wentworth Medical Center 438

Case Problem 3 Compensation for Sales Professionals 439

Appendix 10.1 Inferences About Two Populations Using Minitab 440

Appendix 10.2 Analysis of Variance Using Minitab 442

Appendix 10.3 Inferences About Two Populations Using Excel 442

Appendix 10.4 Analysis of Variance Using Excel 443

Appendix 10.5 Inferences About Two Populations Using StatTools 444

Appendix 10.6 Analysis of Variance Using StatTools 446

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Essentials of Business Statistics 4th Edition Chapter 3

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