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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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15 Nonparametric Methods 649

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

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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

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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