Mathematics

Introductory Statistics

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ISBN-10 1938168208 ISBN-13

978-1-938168-20-8

Revision

ST-1-000-RS

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Table of Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 1: Sampling and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1 Definitions of Statistics, Probability, and Key Terms . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Data, Sampling, and Variation in Data and Sampling . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Frequency, Frequency Tables, and Levels of Measurement . . . . . . . . . . . . . . . . . . 26 1.4 Experimental Design and Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1.5 Data Collection Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.6 Sampling Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Chapter 2: Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs . . . . . . . . . . . . . . 66 2.2 Histograms, Frequency Polygons, and Time Series Graphs . . . . . . . . . . . . . . . . . . 75 2.3 Measures of the Location of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 2.4 Box Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 2.5 Measures of the Center of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 2.6 Skewness and the Mean, Median, and Mode . . . . . . . . . . . . . . . . . . . . . . . . . 105 2.7 Measures of the Spread of the Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 2.8 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Chapter 3: Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 3.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 3.2 Independent and Mutually Exclusive Events . . . . . . . . . . . . . . . . . . . . . . . . . . 170 3.3 Two Basic Rules of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 3.4 Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 3.5 Tree and Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 3.6 Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Chapter 4: Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable . . . . . . . . . . . 228 4.2 Mean or Expected Value and Standard Deviation . . . . . . . . . . . . . . . . . . . . . . . 230 4.3 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 4.4 Geometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 4.5 Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 4.6 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 4.7 Discrete Distribution (Playing Card Experiment) . . . . . . . . . . . . . . . . . . . . . . . . 255 4.8 Discrete Distribution (Lucky Dice Experiment) . . . . . . . . . . . . . . . . . . . . . . . . . 258

Chapter 5: Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 5.1 Continuous Probability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293 5.2 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 5.3 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 5.4 Continuous Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

Chapter 6: The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 6.1 The Standard Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 6.2 Using the Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 6.3 Normal Distribution (Lap Times) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 6.4 Normal Distribution (Pinkie Length) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356

Chapter 7: The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 7.1 The Central Limit Theorem for Sample Means (Averages) . . . . . . . . . . . . . . . . . . 374 7.2 The Central Limit Theorem for Sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 7.3 Using the Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 7.4 Central Limit Theorem (Pocket Change) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391 7.5 Central Limit Theorem (Cookie Recipes) . . . . . . . . . . . . . . . . . . . . . . . . . . . 394

Chapter 8: Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 8.1 A Single Population Mean using the Normal Distribution . . . . . . . . . . . . . . . . . . . 417 8.2 A Single Population Mean using the Student t Distribution . . . . . . . . . . . . . . . . . . 427 8.3 A Population Proportion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 8.4 Confidence Interval (Home Costs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 8.5 Confidence Interval (Place of Birth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 8.6 Confidence Interval (Women’s Heights) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442

Chapter 9: Hypothesis Testing with One Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 9.1 Null and Alternative Hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 9.2 Outcomes and the Type I and Type II Errors . . . . . . . . . . . . . . . . . . . . . . . . . . 476 9.3 Distribution Needed for Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . 478 9.4 Rare Events, the Sample, Decision and Conclusion . . . . . . . . . . . . . . . . . . . . . . 479

9.5 Additional Information and Full Hypothesis Test Examples . . . . . . . . . . . . . . . . . . 482 9.6 Hypothesis Testing of a Single Mean and Single Proportion . . . . . . . . . . . . . . . . . . 498

Chapter 10: Hypothesis Testing with Two Samples . . . . . . . . . . . . . . . . . . . . . . . . . 529 10.1 Two Population Means with Unknown Standard Deviations . . . . . . . . . . . . . . . . . 530 10.2 Two Population Means with Known Standard Deviations . . . . . . . . . . . . . . . . . . 538 10.3 Comparing Two Independent Population Proportions . . . . . . . . . . . . . . . . . . . . 541 10.4 Matched or Paired Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 10.5 Hypothesis Testing for Two Means and Two Proportions . . . . . . . . . . . . . . . . . . . 551

Chapter 11: The Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 11.1 Facts About the Chi-Square Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 582 11.2 Goodness-of-Fit Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583 11.3 Test of Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592 11.4 Test for Homogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596 11.5 Comparison of the Chi-Square Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 11.6 Test of a Single Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 11.7 Lab 1: Chi-Square Goodness-of-Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602 11.8 Lab 2: Chi-Square Test of Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 606

Chapter 12: Linear Regression and Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . 637 12.1 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638 12.2 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640 12.3 The Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643 12.4 Testing the Significance of the Correlation Coefficient . . . . . . . . . . . . . . . . . . . . 649 12.5 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654 12.6 Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655 12.7 Regression (Distance from School) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663 12.8 Regression (Textbook Cost) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 12.9 Regression (Fuel Efficiency) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667

Chapter 13: F Distribution and One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 13.1 One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 13.2 The F Distribution and the F-Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701 13.3 Facts About the F Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705 13.4 Test of Two Variances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 13.5 Lab: One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715

Appendix A: Review Exercises (Ch 3-13) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739 Appendix B: Practice Tests (1-4) and Final Exams . . . . . . . . . . . . . . . . . . . . . . . . . . 765 Appendix C: Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 819 Appendix D: Group and Partner Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 Appendix E: Solution Sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829 Appendix F: Mathematical Phrases, Symbols, and Formulas . . . . . . . . . . . . . . . . . . . . 833 Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators . . . . . . . . . . . . . . . . . . . . . . 839 Appendix H: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 851 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853

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PREFACE

About Introductory Statistics Introductory Statistics is designed for the one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it.

The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean. Additional topics, examples, and ample opportunities for practice have been added to each chapter. The development choices for this textbook were made with the guidance of many faculty members who are deeply involved in teaching this course. These choices led to innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful, so that students can draw from it a working knowledge that will enrich their future studies and help them make sense of the world around them.

Coverage and Scope

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