Introductory Statistics, International Adaptation

PREM S. MANN has a Bachelor’s degree in mathematics, economics, and English, and a Master’s degree in economics, with a specialization in statistics, from Punjab University, India. Prem taught economics and statistics at a Punjab University college for four years. In 1975 he left India for the United Kingdom, where he studied at the University of Manchester and received his second Master’s degree in economics. Then he attended the London School of Economics where he studied operations research. In January 1980, Prem moved to Los Angeles, California, to study for his Ph.D. in Economics at UCLA. One of his fields of specialization in his Ph.D. studies was statistics and quantitative methods. While working on his Ph.D. at UCLA, Prem Mann taught statistics and quantitative methods at the Los Angeles and Fullerton campuses of California State University, first as an adjunct instructor and then as a full-time faculty member. In 1986, he joined Eastern Connecticut State University as a faculty member, where he taught statistics, mathematics for economics, and econometrics for 29 years. He also served as chair of the Department of Economics at Eastern Connecticut State University for 20 years before retiring in 2015. Currently, Prem Mann lives with his wife and close to his children and grandchildren in New York City. In addition to Introductory Statistics, which is currently in its 10th edition, Prem Mann has authored Introductory Statistics Using Technology and Statistics for Business and Economics. He has also coauthored Practitioner’s Guide to Statistics and Lean Six Sigma for Process Improvements with Mikel J. Harry, Ofelia C. De Hodgins, Richard L. Hulbert, and Christopher J. Lacke. All these books are Wiley publications. Prem Mann’s Introductory Statistics book has been translated into Chinese, Serbian, and Portuguese. His Statistics for Business and Economics was also translated into Chinese.

1 Introduction 1

1.1 Statistics and Types of Statistics 1

Case Study 1.1 Deaths Due to Red-Light Running in the United States 3

Case Study 1.2 Is Anxiety and Depression a Major Problem Among Teens? 4

1.2 Basic Terms 5

1.3 Types of Variables 7

1.4 Types of Scales 10

1.5 Cross-Section Versus Time-Series Data 12

1.6 Population Versus Sample 13

1.7 Design of Experiments 22

1.8 Summation Notation 26

Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Project / Decide for  ourself / Chapter 1 Technology Instructions

2 Organizing and Graphing Data 41

2.1 Organizing and Graphing Qualitative Data 42

Case Study 2.1 Confidence in Charitable and Nongovernmental Organizations 46

Case Study 2.2 Single-Payer Health-Care System Where the Federal Government Provides Coverage for Everyone 47

2.2 Organizing and Graphing Quantitative Data 48

Case Study 2.3 Average Starting Salaries of Teachers in the United States 53

Case Study 2.4 Mom, I Am Hungry 54

Case Study 2.5 How Many Cups of Coffee Do You Drink a Day? 58

2.3 Stem-and-Leaf Displays 66

2.4 Dotplots 71

Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 2 Technology Instructions

3 Numerical Descriptive Measures 87

3.1 Measures of Center for Ungrouped Data 88

Case Study 3.1 Coffee Consumption Statistics 91

Case Study 3.2 Median Prices of Homes in Selected Metro Areas of the United States 94

3.2 Measures of Dispersion for Ungrouped Data 103

3.3 Mean, Variance, and Standard Deviation for Grouped Data 111

3.4 Use of Standard Deviation 117

Case Study 3.3 Does Spread Mean the Same as Variability and Dispersion? 121

3.5 Measures of Position 122

3.6 Box-and-Whisker Plot 127

Uses and Misuses of Statistics / Glossary / Exercises / Appendix 3.1 / Self-Review Test / Mini-Projects /

Decide for Yourself / Chapter 3 Technology Instructions

4 Probability 147

4.1 Experiment, Outcome, and Sample Space 148

4.2 Calculating Probability 153

4.3 Marginal Probability, Conditional Probability, and Related Probability Concepts 160

Case Study 4.1 Vegetarians, Gender, and Ideology 163

4.4 Intersection of Events and the Multiplication Rule 171

4.5 Union of Events and the Addition Rule 177

4.6 Counting Rule, Factorials, Combinations, and Permutations 184

Case Study 4.2 Probability of Winning a Mega Millions Lottery Jackpot 189

Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 4 Technology Instructions

5 Discrete Random Variables and Their Probability Distributions 203

5.1 Random Variables 204

5.2 Probability Distribution of a Discrete Random Variable 206

5.3 Mean and Standard Deviation of a Discrete Random Variable 212

Case Study 5.1 All State Lottery 214

5.4 The Binomial Probability Distribution 219

5.5 Negative Binomial Probability Distribution 230

5.6 The Hypergeometric Probability Distribution 234

5.7 The Poisson Probability Distribution 237

Case Study 5.2 Global Birth and Death Rates 240

Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 5 Technology Instructions

6 Continuous Random Variables and the Normal Distribution 257

6.1 Continuous Probability Distribution and the Normal Probability Distribution 258

Case Study 6.1 Distribution of Time Taken to Run a Road Race 261

6.2 Standardizing a Normal Distribution 272

6.3 Applications of the Normal Distribution 278

6.4 Determining the Z and X Values When An Area Under the Normal Distribution Curve Is Known 283

6.5 The Normal Approximation to the Binomial Distribution 288

Uses and Misuses of Statistics / Glossary / Exercises /Appendix 6.1 / Self-Review Test / Mini-Projects /

Decide for Yourself / Chapter 6 Technology Instructions

7 Sampling Distributions 309

7.1 Sampling Distribution, Sampling Error, and Nonsampling Errors 310

7.2 Mean and Standard Deviation of ​x̄ 315

7.3 Shape of the Sampling Distribution of ​x̄ 318

7.4 Applications _ of the Sampling Distribution of ​ x̄ 324

7.5 Population and Sample Proportions; and the Mean, Standard Deviation, and Shape of the Sampling Distribution of ​p̂ 329

Case Study 7.1 2016 U.S. Election and Sampling Error 331

7.6 Applications of the Sampling Distribution of ​p̂​ 336

Uses and Misuses of Statistics / Glossary / Exercises / Self- Review Test / Mini-Projects / Decide for Yourself /Chapter 7 Technology Instructions

8 Estimation of the Mean and Proportion 349

8.1 Estimation, Point Estimate, and Interval Estimate 349

8.2 Estimation of a Population Mean: σ Known 353

Case Study 8.1 2019 National Average Salaries of U.S. Doctors 357

8.3 Estimation of a Population Mean: σ Not Known 362

8.4 Estimation of a Population Proportion: Large Samples 370

Case Study 8.2 Is Government, Poor Leadership, or Politicians the Most Important Problem Facing the United States? 373

Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 8 Technology Instructions

9 Hypothesis Tests About the Mean and Proportion 389

9.1 Hypothesis Tests: An Introduction 390

9.2 Hypothesis Tests About μ: σ Known 397

Case Study 9.1 Class of 2018 Average Loan Debt for U.S. Students 407

9.3 Hypothesis Tests About μ: σ Not Known 410

9.4 Hypothesis Tests About a Population Proportion: Large Samples 419

Case Study 9.2 Are Parents Doing Too Much for Their Adult Children? 425

Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself / Chapter 9 Technology Instructions

10 Estimation and Hypothesis Testing: Two Populations 441

10.1 Inferences About the Difference Between Two Population Means for Independent Samples:
σ1 and σ2Known 442

10.2 Inferences About the Difference Between Two Population Means for Independent Samples:
σ1 and σ2 Unknown but Equal 449

10.3 Inferences About the Difference Between Two Population Means for Independent Samples:
σ1 and σ2 Unknown and Unequal 457

10.4 Inferences About the Mean of Paired Samples (Dependent Samples) 462

10.5 Inferences About the Difference Between Two Population Proportions for Large and Independent Samples 471

Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 10 Technology Instructions

11 Chi-Square Tests 497

11.1 The Chi-Square Distribution 498

11.2 A Goodness-of-Fit Test 501

Case Study 11.1 How Are the Economic Conditions in the United States Affecting the Middle Class? 507

11.3 A Test of Independence or Homogeneity 509

11.4 Inferences About the Population Variance 519

Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 11 Technology Instructions

12 Analysis of Variance 537

12.1 The F Distribution 538

12.2 One-Way Analysis of Variance 540

12.3 Two-Way Analysis of Variance 550

Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 12 Technology Instructions

13 Simple Linear Regression 573

13.1 Simple Linear Regression 573

Case Study 13.1 Regression of Weights on Heights for NFL Players 583

13.2 Standard Deviation of Errors and Coefficient of Determination 588

13.3 Inferences About B 594

13.4 Linear Correlation 599

13.5 Regression Analysis: A Complete Example 604

13.6 Using the Regression Model 610

Uses and Misuses of Statistics / Glossary / Exercises /Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 13 Technology Instructions

14 Multiple Regression 629

14.1 Multiple Regression Analysis 629

14.2 Assumptions of the Multiple Regression Model 631

14.3 Standard Deviation of Errors 632

14.4 Coefficient of Multiple Determination 633

14.5 Computer Solution of Multiple Regression 634

Uses and Misuses of Statistics / Glossary / Self-Review Test / Mini-Project / Decide for Yourself / Chapter 14 Technology Instructions

15 Nonparametric Methods 649

This chapter is not included in this text but is available in the book’s product page on
www.wiley.com.

15.1 The Sign Test 650

15.2 The Wilcoxon Signed-Rank Test for Two Dependent Samples 663

15.3 The Wilcoxon Rank Sum Test for Two Independent Samples 669

15.4 The Kruskal-Wallis Test 675

15.5 The Spearman Rho Rank Correlation Coefficient Test 680

15.6 The Runs Test for Randomness 683

Uses and Misuses of Statistics / Glossary / Exercises / Self-Review Test / Mini-Projects / Decide for Yourself /Chapter 15 Technology Instructions

Appendix A Explanation of Data Sets A- 1

Appendix B Statistical Tables B- 1

Appendix C Lists of Formulas C- 1

Answers to Selected Odd-numbered Exercises And Self-review Tests An- 1

Index I- 1