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Unformatted text preview: Introductory Statistics OpenStax College Rice University 6100 Main Street MS-375 Houston, Texas 77005 To learn more about OpenStax College, visit . Individual print copies and bulk orders can be purchased through our website. © 2013 Rice University. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution 4.0 International License. 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We support the creation, sharing, and proliferation of more effective, more affordable educational content by leveraging disruptive technologies, open educational resources, and new models for collaboration between for-profit, nonprofit, and public entities. Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1: Sampling and Data . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Definitions of Statistics, Probability, and Key Terms . . . . . . . . . . . 1.2 Data, Sampling, and Variation in Data and Sampling . . . . . . . . . . 1.3 Frequency, Frequency Tables, and Levels of Measurement . . . . . . . 1.4 Experimental Design and Ethics . . . . . . . . . . . . . . . . . . . . . 1.5 Data Collection Experiment . . . . . . . . . . . . . . . . . . . . . . . 1.6 Sampling Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 2: Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs . . . 2.2 Histograms, Frequency Polygons, and Time Series Graphs . . . . . . . 2.3 Measures of the Location of the Data . . . . . . . . . . . . . . . . . . 2.4 Box Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Measures of the Center of the Data . . . . . . . . . . . . . . . . . . . 2.6 Skewness and the Mean, Median, and Mode . . . . . . . . . . . . . . 2.7 Measures of the Spread of the Data . . . . . . . . . . . . . . . . . . . 2.8 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 3: Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Independent and Mutually Exclusive Events . . . . . . . . . . . . . . . 3.3 Two Basic Rules of Probability . . . . . . . . . . . . . . . . . . . . . . 3.4 Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Tree and Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 4: Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable 4.2 Mean or Expected Value and Standard Deviation . . . . . . . . . . . . 4.3 Binomial Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Geometric Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Hypergeometric Distribution . . . . . . . . . . . . . . . . . . . . . . . 4.6 Poisson Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Discrete Distribution (Playing Card Experiment) . . . . . . . . . . . . . 4.8 Discrete Distribution (Lucky Dice Experiment) . . . . . . . . . . . . . . Chapter 5: Continuous Random Variables . . . . . . . . . . . . . . . . . . . 5.1 Continuous Probability Functions . . . . . . . . . . . . . . . . . . . . 5.2 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . 5.4 Continuous Distribution . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 6: The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . 6.1 The Standard Normal Distribution . . . . . . . . . . . . . . . . . . . . 6.2 Using the Normal Distribution . . . . . . . . . . . . . . . . . . . . . . 6.3 Normal Distribution (Lap Times) . . . . . . . . . . . . . . . . . . . . . 6.4 Normal Distribution (Pinkie Length) . . . . . . . . . . . . . . . . . . . Chapter 7: The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . 7.1 The Central Limit Theorem for Sample Means (Averages) . . . . . . . 7.2 The Central Limit Theorem for Sums . . . . . . . . . . . . . . . . . . 7.3 Using the Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . 7.4 Central Limit Theorem (Pocket Change) . . . . . . . . . . . . . . . . . 7.5 Central Limit Theorem (Cookie Recipes) . . . . . . . . . . . . . . . . Chapter 8: Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 A Single Population Mean using the Normal Distribution . . . . . . . . 8.2 A Single Population Mean using the Student t Distribution . . . . . . . 8.3 A Population Proportion . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Confidence Interval (Home Costs) . . . . . . . . . . . . . . . . . . . . 8.5 Confidence Interval (Place of Birth) . . . . . . . . . . . . . . . . . . . 8.6 Confidence Interval (Women's Heights) . . . . . . . . . . . . . . . . . Chapter 9: Hypothesis Testing with One Sample . . . . . . . . . . . . . . . . 9.1 Null and Alternative Hypotheses . . . . . . . . . . . . . . . . . . . . . 9.2 Outcomes and the Type I and Type II Errors . . . . . . . . . . . . . . . 9.3 Distribution Needed for Hypothesis Testing . . . . . . . . . . . . . . . 9.4 Rare Events, the Sample, Decision and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5 5 9 26 34 38 40 65 66 75 85 94 99 105 109 119 165 166 170 177 182 188 197 227 228 230 237 243 247 250 255 258 291 293 296 305 316 341 342 347 354 356 373 374 379 383 391 394 415 417 427 431 438 440 442 473 474 476 478 479 9.5 Additional Information and Full Hypothesis Test Examples . 9.6 Hypothesis Testing of a Single Mean and Single Proportion . Chapter 10: Hypothesis Testing with Two Samples . . . . . . . . 10.1 Two Population Means with Unknown Standard Deviations 10.2 Two Population Means with Known Standard Deviations . 10.3 Comparing Two Independent Population Proportions . . . 10.4 Matched or Paired Samples . . . . . . . . . . . . . . . . 10.5 Hypothesis Testing for Two Means and Two Proportions . . Chapter 11: The Chi-Square Distribution . . . . . . . . . . . . . . 11.1 Facts About the Chi-Square Distribution . . . . . . . . . . 11.2 Goodness-of-Fit Test . . . . . . . . . . . . . . . . . . . . 11.3 Test of Independence . . . . . . . . . . . . . . . . . . . . 11.4 Test for Homogeneity . . . . . . . . . . . . . . . . . . . . 11.5 Comparison of the Chi-Square Tests . . . . . . . . . . . . 11.6 Test of a Single Variance . . . . . . . . . . . . . . . . . . 11.7 Lab 1: Chi-Square Goodness-of-Fit . . . . . . . . . . . . . 11.8 Lab 2: Chi-Square Test of Independence . . . . . . . . . . Chapter 12: Linear Regression and Correlation . . . . . . . . . . 12.1 Linear Equations . . . . . . . . . . . . . . . . . . . . . . 12.2 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . 12.3 The Regression Equation . . . . . . . . . . . . . . . . . . 12.4 Testing the Significance of the Correlation Coefficient . . . 12.5 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . 12.6 Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.7 Regression (Distance from School) . . . . . . . . . . . . . 12.8 Regression (Textbook Cost) . . . . . . . . . . . . . . . . 12.9 Regression (Fuel Efficiency) . . . . . . . . . . . . . . . . Chapter 13: F Distribution and One-Way ANOVA . . . . . . . . . . 13.1 One-Way ANOVA . . . . . . . . . . . . . . . . . . . . . . 13.2 The F Distribution and the F-Ratio . . . . . . . . . . . . . 13.3 Facts About the F Distribution . . . . . . . . . . . . . . . 13.4 Test of Two Variances . . . . . . . . . . . . . . . . . . . . 13.5 Lab: One-Way ANOVA . . . . . . . . . . . . . . . . . . . Appendix A: Review Exercises (Ch 3-13) . . . . . . . . . . . . . . Appendix B: Practice Tests (1-4) and Final Exams . . . . . . . . . Appendix C: Data Sets . . . . . . . . . . . . . . . . . . . . . . . . Appendix D: Group and Partner Projects . . . . . . . . . . . . . . Appendix E: Solution Sheets . . . . . . . . . . . . . . . . . . . . . Appendix F: Mathematical Phrases, Symbols, and Formulas . . . Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators . . . . . Appendix H: Tables . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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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 Chapter 1 Sampling and Data Chapter 2 Descriptive Statistics Chapter 3 Probability Topics Chapter 4 Discrete Random Variables Chapter 5 Continuous Random Variables Chapter 6 The Normal Distribution Chapter 7 The Central Limit Theorem Chapter 8 Confidence Intervals Chapter 9 Hypothesis Testing with One Sample Chapter 10 Hypothesis Testing with Two Samples Chapter 11 The Chi-Square Distribution Chapter 12 Linear Regression and Correlation Chapter 13 F Distribution and One-Way ANOVA Alternate Sequencing Introductory Statistics was conceived and written to fit a particular topical sequence, but it can be used flexibly to accommodate other course structures. One such potential structure, which will fit reasonably well with the textbook content, is provided. Please consider, however, that the chapters were not written to be completely independent, and that the proposed alternate sequence should be carefully considered for student preparation and textual consistency. Chapter 1 Sampling and Data Chapter 2 Descriptive Statistics Chapter 12 Linear Regression and Correlation Chapter 3 Probability Topics Chapter 4 Discrete Random Variables Chapter 5 Continuous Random Variables Chapter 6 The Normal Distribution Chapter 7 The Central Limit Theorem Chapter 8 Confidence Intervals Chapter 9 Hypothesis Testing with One Sample Chapter 10 Hypothesis Testing with Two Samples Chapter 11 The Chi-Square Distribution Chapter 13 F Distribution and One-Way ANOVA Pedagogical Foundation and Features • Examples are placed strategically throughout the text to show students the step-by-step process of interpreting and solving statistical problems. To keep the text relevant for students, the examples are drawn from a broad spectrum of practical topics; these include examples about college life and learning, health and medicine, retail and business, and sports and entertainment. • Try It practice problems immediately follow many examples and give students the opportunity to practice as they read the text. They are usually based on practical and familiar topics, like the Examples themselves. • Collaborative Exercises provide an in-class scenario for students to work together to explore presented concepts. 2 • Using the TI-83, 83+, 84, 84+ Calculator shows students step-by-step instructions to input problems into their calculator. • The Technology Icon indicates where the use of a TI calculator or computer software is recommended. • Practice, Homework, and Bringing It Together problems give the students problems at various degrees of difficulty while also including real-world scenarios to engage students. Statistics Labs These innovative activities were developed by Barbara Illowsky and Susan Dean in order to offer students the experience of designing, implementing, and interpreting statistical analyses. They are drawn from actual experiments and data-gathering processes, and offer a unique hands-on and collaborative experience. The labs provide a foundation for further learning and classroom in...
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