Summary

Statistics: Unlocking the Power of Data, 2^nd Edition continues to utilize these intuitive methods like randomization and bootstrap intervals to introduce the fundamental idea of statistical inference. These methods are brought to life through authentically relevant examples, enabled through easy to use statistical software, and are accessible at very early stages of a course. The program includes the more traditional methods like t-tests, chi-square texts, etc. but only after students have developed a strong intuitive understanding of inference through randomization methods. The focus throughout is on data analysis and the primary goal is to enable students to effectively collect data, analyze data, and interpret conclusions drawn from data. The program is driven by real data and real applications.

Author Biography

Patti Frazer Lock is the Cummings Professor of Mathematics in the Department of Mathematics, Computer Science, and Statistics at St. Lawrence University. She is a member of the Calculus Consortium for Higher Education (formerly the Calculus Consortium based at Harvard). She is a co-author with the Consortium of texts in Calculus, Applied Calculus, Multivariable Calculus, Precalculus, and Algebra. She is currently working on a text in Introductory Statistics. She does workshops around the country on the teaching of undergraduate mathematics. She is a member of the Committee on the Undergraduate Program in Mathematics of the Mathematics Association of America, is on the Editorial Board of PRIMUS Journal, and is a Consultant to Project NExT of the MAA. She loves to teach and teaches courses across the spectrum of mathematics and statistics, and she enjoys collaborating with undergraduates on her research in graph theory. She received her BA from Colgate University and her Ph.D. from the University of Massachusetts at Amherst.

Preface ix

Unit A: Data 1

Chapter 1. Collecting Data 2

1.1. The Structure of Data 4

1.2. Sampling from a Population 16

1.3. Experiments and Observational Studies 29

Chapter 2. Describing Data 46

2.1. Categorical Variables 48

2.2. One Quantitative Variable: Shape and Center 63

2.3. One Quantitative Variable: Measures of Spread 77

2.4. Boxplots and Quantitative/Categorical Relationships 93

2.5. Two Quantitative Variables: Scatterplot and Correlation 106

2.6. Two Quantitative Variables: Linear Regression 123

2.7. Data Visualization and Multiple Variables 137

Unit A: Essential Synthesis 161

Review Exercises 174

Unit B: Understanding Inference 193

Chapter 3. Confidence Intervals 194

3.1. Sampling Distributions 196

3.2. Understanding and Interpreting Confidence Intervals 213

3.3. Constructing Bootstrap Confidence Intervals 228

3.4. Bootstrap Confidence Intervals using Percentiles 242

Chapter 4. Hypothesis Tests 256

4.1. Introducing Hypothesis Tests 258

4.2. Measuring Evidence with P-values 272

4.3. Determining Statistical Significance 288

4.4. A Closer Look at Testing 303

4.5. Making Connections 318

Unit B: Essential Synthesis 341

Review Exercises 351

Unit C: Inference with Normal and t-Distributions 369

Chapter 5. Approximating with a Distribution 370

5.1. Hypothesis Tests Using Normal Distributions 372

5.2. Confidence Intervals Using Normal Distributions 387

Chapter 6. Inference for Means and Proportions 402

6.1. Inference for a Proportion

6.1-D Distribution of a Proportion 404

6.1-CI Confidence Interval for a Proportion 407

6.1-HT Hypothesis Test for a Proportion 414

6.2. Inference for a Mean

6.2-D Distribution of a Mean 419

6.2-CI Confidence Interval for a Mean 424

6.2-HT Hypothesis Test for a Mean 433

6.3. Inference for a Difference in Proportions

6.3-D Distribution of a Difference in Proportions 438

6.3-CI Confidence Interval for a Difference in Proportions 441

6.3-HT Hypothesis Test for a Difference in Proportions 446

6.4. Inference for a Difference in Means

6.4-D Distribution of a Difference in Means 452

6.4-CI Confidence Interval for a Difference in Means 455

6.4-HT Hypothesis Test for a Difference in Means 461

6.5. Paired Difference in Means 468

Unit C: Essential Synthesis 477

Review Exercises 489

Unit D: Inference for Multiple Parameters 505

Chapter 7. Chi-Square Tests for Categorical Variables 506

7.1. Testing Goodness-of-Fit for a Single Categorical Variable 508

7.2. Testing for an Association between Two Categorical Variables 523

Chapter 8. ANOVA to Compare Means 538

8.1. Analysis of Variance 540

8.2. Pairwise Comparisons and Inference after ANOVA 563

Chapter 9. Inference for Regression 574

9.1. Inference for Slope and Correlation 576

9.2. ANOVA for Regression 591

9.3. Confidence and Prediction Intervals 603

Chapter 10. Multiple Regression 610

10.1. Multiple Predictors 612

10.2. Checking Conditions for a Regression Model 624

10.3. Using Multiple Regression 633

Unit D: Essential Synthesis 647

Review Exercises 661

The Big Picture: Essential Synthesis 669

Exercises for the Big Picture: Essential Synthesis 683

Chapter P. Probability Basics 688

P.1. Probability Rules 690

P.2. Tree Diagrams and Bayes’ Rule 702

P.3. Random Variables and Probability Functions 709

P.4. Binomial Probabilities 716

P.5. Density Curves and the Normal Distribution 724

Appendix A. Chapter Summaries 737

Appendix B. Selected Dataset Descriptions 749

Partial Answers 761

Index

General Index 783

Data Index 786

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