introductory-statistics-21.2.pdf - Introductory Statistics SENIOR CONTRIBUTING AUTHORS BARBARA ILLOWSKY DE ANZA COLLEGE SUSAN DEAN DE ANZA COLLEGE

introductory-statistics-21.2.pdf - Introductory Statistics...

This preview shows page 1 out of 913 pages.

You've reached the end of your free preview.

Want to read all 913 pages?

Unformatted text preview: Introductory Statistics SENIOR CONTRIBUTING AUTHORS BARBARA ILLOWSKY, DE ANZA COLLEGE SUSAN DEAN, DE ANZA COLLEGE OpenStax Rice University 6100 Main Street MS-375 Houston, Texas 77005 To learn more about OpenStax, visit . Individual print copies and bulk orders can be purchased through our website. ©2018 Rice University. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0). Under this license, any user of this textbook or the textbook contents herein must provide proper attribution as follows: - - - - If you redistribute this textbook in a digital format (including but not limited to PDF and HTML), then you must retain on every page the following attribution: “Download for free at .” If you redistribute this textbook in a print format, then you must include on every physical page the following attribution: “Download for free at .” If you redistribute part of this textbook, then you must retain in every digital format page view (including but not limited to PDF and HTML) and on every physical printed page the following attribution: “Download for free at .” If you use this textbook as a bibliographic reference, please include in your citation. For questions regarding this licensing, please contact [email protected] Trademarks The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, OpenStax CNX logo, OpenStax Tutor name, Openstax Tutor logo, Connexions name, Connexions logo, Rice University name, and Rice University logo are not subject to the license and may not be reproduced without the prior and express written consent of Rice University. PRINT BOOK ISBN-10 PRINT BOOK ISBN-13 PDF VERSION ISBN-10 PDF VERSION ISBN-13 ENHANCED TEXTBOOK PART 1 ISBN-10 ENHANCED TEXTBOOK PART 1 ISBN-13 Revision Number Original Publication Year 1-938168-20-8 978-1-938168-20-8 1-947172-05-0 978-1-947172-05-0 1-938168-29-1 978-1-938168-29-1 ST-2013-002(03/18)-LC 2013 OPENSTAX OpenStax provides free, peer-reviewed, openly licensed textbooks for introductory college and Advanced Placement® courses and low-cost, personalized courseware that helps students learn. A nonprofit ed tech initiative based at Rice University, we’re committed to helping students access the tools they need to complete their courses and meet their educational goals. RICE UNIVERSITY OpenStax, OpenStax CNX, and OpenStax Tutor are initiatives of Rice University. As a leading research university with a distinctive commitment to undergraduate education, Rice University aspires to path-breaking research, unsurpassed teaching, and contributions to the betterment of our world. It seeks to fulfill this mission by cultivating a diverse community of learning and discovery that produces leaders across the spectrum of human endeavor. FOUNDATION SUPPORT OpenStax is grateful for the tremendous support of our sponsors. Without their strong engagement, the goal of free access to high-quality textbooks would remain just a dream. Laura and John Arnold Foundation (LJAF) actively seeks opportunities to invest in organizations and thought leaders that have a sincere interest in implementing fundamental changes that not only yield immediate gains, but also repair broken systems for future generations. LJAF currently focuses its strategic investments on education, criminal justice, research integrity, and public accountability. The William and Flora Hewlett Foundation has been making grants since 1967 to help solve social and environmental problems at home and around the world. The Foundation concentrates its resources on activities in education, the environment, global development and population, performing arts, and philanthropy, and makes grants to support disadvantaged communities in the San Francisco Bay Area. Calvin K. Kazanjian was the founder and president of Peter Paul (Almond Joy), Inc. He firmly believed that the more people understood about basic economics the happier and more prosperous they would be. Accordingly, he established the Calvin K. Kazanjian Economics Foundation Inc, in 1949 as a philanthropic, nonpolitical educational organization to support efforts that enhanced economic understanding. Guided by the belief that every life has equal value, the Bill & Melinda Gates Foundation works to help all people lead healthy, productive lives. In developing countries, it focuses on improving people’s health with vaccines and other life-saving tools and giving them the chance to lift themselves out of hunger and extreme poverty. In the United States, it seeks to significantly improve education so that all young people have the opportunity to reach their full potential. Based in Seattle, Washington, the foundation is led by CEO Jeff Raikes and Co-chair William H. Gates Sr., under the direction of Bill and Melinda Gates and Warren Buffett. The Maxfield Foundation supports projects with potential for high impact in science, education, sustainability, and other areas of social importance. Our mission at The Michelson 20MM Foundation is to grow access and success by eliminating unnecessary hurdles to affordability. 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. The Bill and Stephanie Sick Fund supports innovative projects in the areas of Education, Art, Science and Engineering. I WOULDN’T THIS PENS I LOOK BETTER TUDENT E ON A BRAND MEET SC E NEW IPAD QUIREMENT I MINI? URSES. THESE AR EER-REVIEWED TEXTS WR ROFESSIONAL CONTENT EVELOPERS. ADOPT A BO ODAY FOR A TURNKEY LASSROOM SOLUTION OR TO SUIT YOUR TEACHING PPROACH. FREE ONLINE Knowing where our textbooks are used can help us provide better services to students and receive more grant support for future projects. If you’re using an OpenStax textbook, either as required for your course or just as an extra resource, send your course syllabus to [email protected] and you’ll be entered to win an iPad Mini. If you don’t win, don’t worry – we’ll be holding a new contest each semester. 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 5 . 5 10 26 35 39 41 67 68 77 87 96 100 106 110 120 175 176 181 188 193 199 209 243 244 247 253 259 263 266 271 274 311 313 316 326 338 365 366 371 379 381 399 400 405 408 417 420 443 445 456 460 467 469 471 505 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 . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . This OpenStax book is available for free at . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506 508 510 511 514 530 567 568 576 579 584 590 621 622 623 633 638 641 641 644 648 679 680 682 685 691 696 697 704 706 708 743 744 745 749 756 759 785 813 869 873 879 883 889 901 903 Preface 1 PREFACE Welcome to Introductory Statistics, an OpenStax resource. This textbook was written to increase student access to highquality learning materials, maintaining highest standards of academic rigor at little to no cost. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean. Additional topics, examples, and innovations in terminology and practical applications have been added, all with a goal of increasing relevance and accessibility for students. About OpenStax OpenStax is a nonprofit based at Rice University, and it’s our mission to improve student access to education. Our first openly licensed college textbook was published in 2012, and our library has since scaled to over 25 books for college and AP® courses used by hundreds of thousands of students. OpenStax Tutor, our low-cost personalized learning tool, is being used in college courses throughout the country. Through our partnerships with philanthropic foundations and our alliance with other educational resource organizations, OpenStax is breaking down the most common barriers to learning and empowering students and instructors to succeed. About OpenStax's resources Customization Introductory Statistics is licensed under a Creative Commons Attribution 4.0 International (CC BY) license, which means that you can distribute, remix, and build upon the content, as long as you provide attribution to OpenStax and its content contributors. Because our books are openly licensed, you are free to use the entire book or pick and choose the sections that are most relevant to the needs of your course. Feel free to remix the content by assigning your students certain chapters and sections in your syllabus, in the order that you prefer. You can even provide a direct link in your syllabus to the sections in the web view of your book. Instructors also have the option of creating a customized version of their OpenStax book. The custom version can be made available to students in low-cost print or digital form through their campus bookstore. Visit your book page on OpenStax.org for more information. Errata All OpenStax textbooks undergo a rigorous review process. However, like any professional-grade textbook, errors sometimes occur. Since our books are web based, we can make updates periodically when deemed pedagogically necessary. If you have a correction to suggest, submit it through the link on your book page on OpenStax.org. Subject matter experts review all errata suggestions. OpenStax is committed to remaining transparent about all updates, so you will also find a list of past errata changes on your book page on OpenStax.org. Format You can access this textbook for free in web view or PDF through OpenStax.org, and in low-cost print and iBooks editions. 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 Hypothes...
View Full Document

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture