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Statistics

Preface

StatisticsPreface
  1. Preface
  2. 1 Sampling and Data
    1. Introduction
    2. 1.1 Definitions of Statistics, Probability, and Key Terms
    3. 1.2 Data, Sampling, and Variation in Data and Sampling
    4. 1.3 Frequency, Frequency Tables, and Levels of Measurement
    5. 1.4 Experimental Design and Ethics
    6. 1.5 Data Collection Experiment
    7. 1.6 Sampling Experiment
    8. Key Terms
    9. Chapter Review
    10. Practice
    11. Homework
    12. Bringing It Together: Homework
    13. References
    14. Solutions
  3. 2 Descriptive Statistics
    1. Introduction
    2. 2.1 Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs
    3. 2.2 Histograms, Frequency Polygons, and Time Series Graphs
    4. 2.3 Measures of the Location of the Data
    5. 2.4 Box Plots
    6. 2.5 Measures of the Center of the Data
    7. 2.6 Skewness and the Mean, Median, and Mode
    8. 2.7 Measures of the Spread of the Data
    9. 2.8 Descriptive Statistics
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. Solutions
  4. 3 Probability Topics
    1. Introduction
    2. 3.1 Terminology
    3. 3.2 Independent and Mutually Exclusive Events
    4. 3.3 Two Basic Rules of Probability
    5. 3.4 Contingency Tables
    6. 3.5 Tree and Venn Diagrams
    7. 3.6 Probability Topics
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Bringing It Together: Practice
    13. Homework
    14. Bringing It Together: Homework
    15. References
    16. Solutions
  5. 4 Discrete Random Variables
    1. Introduction
    2. 4.1 Probability Distribution Function (PDF) for a Discrete Random Variable
    3. 4.2 Mean or Expected Value and Standard Deviation
    4. 4.3 Binomial Distribution (Optional)
    5. 4.4 Geometric Distribution (Optional)
    6. 4.5 Hypergeometric Distribution (Optional)
    7. 4.6 Poisson Distribution (Optional)
    8. 4.7 Discrete Distribution (Playing Card Experiment)
    9. 4.8 Discrete Distribution (Lucky Dice Experiment)
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. References
    16. Solutions
  6. 5 Continuous Random Variables
    1. Introduction
    2. 5.1 Continuous Probability Functions
    3. 5.2 The Uniform Distribution
    4. 5.3 The Exponential Distribution (Optional)
    5. 5.4 Continuous Distribution
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  7. 6 The Normal Distribution
    1. Introduction
    2. 6.1 The Standard Normal Distribution
    3. 6.2 Using the Normal Distribution
    4. 6.3 Normal Distribution—Lap Times
    5. 6.4 Normal Distribution—Pinkie Length
    6. Key Terms
    7. Chapter Review
    8. Formula Review
    9. Practice
    10. Homework
    11. References
    12. Solutions
  8. 7 The Central Limit Theorem
    1. Introduction
    2. 7.1 The Central Limit Theorem for Sample Means (Averages)
    3. 7.2 The Central Limit Theorem for Sums (Optional)
    4. 7.3 Using the Central Limit Theorem
    5. 7.4 Central Limit Theorem (Pocket Change)
    6. 7.5 Central Limit Theorem (Cookie Recipes)
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. References
    13. Solutions
  9. 8 Confidence Intervals
    1. Introduction
    2. 8.1 A Single Population Mean Using the Normal Distribution
    3. 8.2 A Single Population Mean Using the Student's t-Distribution
    4. 8.3 A Population Proportion
    5. 8.4 Confidence Interval (Home Costs)
    6. 8.5 Confidence Interval (Place of Birth)
    7. 8.6 Confidence Interval (Women's Heights)
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. References
    14. Solutions
  10. 9 Hypothesis Testing with One Sample
    1. Introduction
    2. 9.1 Null and Alternative Hypotheses
    3. 9.2 Outcomes and the Type I and Type II Errors
    4. 9.3 Distribution Needed for Hypothesis Testing
    5. 9.4 Rare Events, the Sample, and the Decision and Conclusion
    6. 9.5 Additional Information and Full Hypothesis Test Examples
    7. 9.6 Hypothesis Testing of a Single Mean and Single Proportion
    8. Key Terms
    9. Chapter Review
    10. Formula Review
    11. Practice
    12. Homework
    13. References
    14. Solutions
  11. 10 Hypothesis Testing with Two Samples
    1. Introduction
    2. 10.1 Two Population Means with Unknown Standard Deviations
    3. 10.2 Two Population Means with Known Standard Deviations
    4. 10.3 Comparing Two Independent Population Proportions
    5. 10.4 Matched or Paired Samples (Optional)
    6. 10.5 Hypothesis Testing for Two Means and Two Proportions
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. Bringing It Together: Homework
    13. References
    14. Solutions
  12. 11 The Chi-Square Distribution
    1. Introduction
    2. 11.1 Facts About the Chi-Square Distribution
    3. 11.2 Goodness-of-Fit Test
    4. 11.3 Test of Independence
    5. 11.4 Test for Homogeneity
    6. 11.5 Comparison of the Chi-Square Tests
    7. 11.6 Test of a Single Variance
    8. 11.7 Lab 1: Chi-Square Goodness-of-Fit
    9. 11.8 Lab 2: Chi-Square Test of Independence
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. Solutions
  13. 12 Linear Regression and Correlation
    1. Introduction
    2. 12.1 Linear Equations
    3. 12.2 The Regression Equation
    4. 12.3 Testing the Significance of the Correlation Coefficient (Optional)
    5. 12.4 Prediction (Optional)
    6. 12.5 Outliers
    7. 12.6 Regression (Distance from School) (Optional)
    8. 12.7 Regression (Textbook Cost) (Optional)
    9. 12.8 Regression (Fuel Efficiency) (Optional)
    10. Key Terms
    11. Chapter Review
    12. Formula Review
    13. Practice
    14. Homework
    15. Bringing It Together: Homework
    16. References
    17. Solutions
  14. 13 F Distribution and One-way Anova
    1. Introduction
    2. 13.1 One-Way ANOVA
    3. 13.2 The F Distribution and the F Ratio
    4. 13.3 Facts About the F Distribution
    5. 13.4 Test of Two Variances
    6. 13.5 Lab: One-Way ANOVA
    7. Key Terms
    8. Chapter Review
    9. Formula Review
    10. Practice
    11. Homework
    12. References
    13. Solutions
  15. A | Appendix A Review Exercises (Ch 3–13)
  16. B | Appendix B Practice Tests (1–4) and Final Exams
  17. C | Data Sets
  18. D | Group and Partner Projects
  19. E | Solution Sheets
  20. F | Mathematical Phrases, Symbols, and Formulas
  21. G | Notes for the TI-83, 83+, 84, 84+ Calculators
  22. H | Tables
  23. Index

Welcome to Statistics, an OpenStax resource. This textbook was written to increase teacher and student access to high-quality learning materials, maintaining the highest standards of academic rigor at little to no cost.

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 35 books used by hundreds of thousands of students for college and AP® courses. OpenStax Tutor and Rover, our low-cost personalized learning tools, are being used in college and high school 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 Resources

Customization

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Art Attribution in Statistics

In Statistics, most art contains attribution to its title, creator or rights holder, host platform, and license within the caption. For art that is openly licensed, anyone may reuse the art as long as they provide the same attribution to its original source. Some art has been provided through permissions and should only be used with the attribution or limitations provided in the credit.

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Format

You can access this textbook for free in web view or PDF through openstax.org, and for a low cost in print.

About Statistics

This instructional material was initially created through a Texas Education Agency (TEA) initiative to provide high-quality open-source instructional materials to districts free of charge. Funds were allocated by the 84th Texas Legislature (2015) for the creation of state-developed, open-source instructional materials with the request that advanced secondary courses supporting the study of science, technology, engineering, and mathematics should be prioritized.

Statistics covers the scope and sequence requirements of a typical one-year statistics course. The text provides comprehensive coverage of statistical concepts, including quantitative examples, collaborative activities, and practical applications. Statistics was designed to meet and exceed the requirements of the relevant Texas Essential Knowledge and Skills (TEKS), while allowing significant flexibility for instructors.

Qualified and experienced Texas faculty were involved throughout the development process, and the textbooks were reviewed extensively to ensure effectiveness and usability in each course. Reviewers considered each resource’s clarity, accuracy, student support, assessment rigor and appropriateness, alignment to TEKS, and overall quality. Their invaluable suggestions provided the basis for continually improved material and helped to certify that the books are ready for use. The writers and reviewers also considered common course issues, effective teaching strategies, and student engagement to provide instructors and students with useful, supportive content and drive effective learning experiences.

Coverage and Scope

Statistics presents the appropriate statistical concepts and skills in a logical and engaging progression that should be familiar to faculty.

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

Flexibility

Like any OpenStax content, this textbook can be modified as needed for use by the instructor depending on the needs of the students in the course. Each set of materials created by OpenStax is organized into units and chapters and can be used like a traditional textbook as the entire syllabus for each course. The materials can also be accessed in smaller chunks for more focused use with a single student or an entire class. Instructors are welcome to download and assign the PDF version of the textbook through a learning management system or can use their LMS to link students to specific chapters and sections of the book relevant to the concept being studied. The entire textbook will be available during the fall of 2020 in an editable Google document, and until then instructors are welcome to copy and paste content from the textbook to modify as needed prior to instruction.

Student-Centered Focus

Statistics was developed with detailed and practical guidance from experienced high school teachers and curriculum experts. Their contributions helped create a resource that provides easy-to-follow explanations with ample opportunities for enrichment and practice. In addition to clear and grade-level appropriate main text coverage, the following features are meant to enhance student understanding of statistics concepts:

  • 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, including examples from academic 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. Like the Examples, the Try It problems are usually based on practical and familiar topics.
  • Collaborative Exercises provide an in-class scenario for students to work together and learn from each other as they explore course concepts.
  • Calculator Guidance shows students step-by-step instructions for input using the TI-83, 83+, 84, and 84+ calculators and helps them consider how to use these tools in their studies. 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 including real-world scenarios to engage students.

Statistics Labs

These innovative activities were developed by Barbara Illowsky and Susan Dean (both of De Anza College) and allow students to design, implement, and interpret statistical analyses. They are drawn from actual experiments and data-gathering processes and offer a unique hands-on and collaborative experience. Statistics Labs appear at the end of each chapter and begin with student learning outcomes, general estimates for time on task, and global implementation notes. Students are then provided with step-by-step guidance, including sample data tables and calculation prompts. This detailed assistance will help the students successfully apply statistics concepts and lay the groundwork for future collaborative or individual work.

Additional Resources

Student and Instructor Resources

We’ve compiled additional resources for both students and instructors, including Getting Started Guides, PowerPoint slides, and an instructor answer guide. Instructor resources require a verified instructor account, which you can apply for when you log in or create your account on OpenStax.org. Take advantage of these resources to supplement your OpenStax book.

Partner Resources

OpenStax Partners are our allies in the mission to make high-quality learning materials affordable and accessible to students and instructors everywhere. Their tools integrate seamlessly with our OpenStax titles at a low cost. To access the partner resources for your text, visit your book page on OpenStax.org.

About the Authors

Senior Contributing Authors

Barbara Illowsky, De Anza College
Susan Dean, De Anza College

Contributing Authors

Daniel Birmajer, Nazareth College
Bryan Blount, Kentucky Wesleyan College
Sheri Boyd, Rollins College
Matthew Einsohn, Prescott College
James Helmreich, Marist College
Lynette Kenyon, Collin County Community College
Sheldon Lee, Viterbo University
Jeff Taub, Maine Maritime Academy

Reviewers of Prior Editions

Laurel Chiappetta, University of Pittsburgh
Lenore Desilets, De Anza College
Lisa Markus, De Anza College
Mary Teegarden, San Diego Mesa College
Carol Olmstead, De Anza College
Carol Weideman, St. Petersburg College
Charles Ashbacher, Upper Iowa University, Cedar Rapids
Charles Klein, De Anza College
Cheryl Wartman, University of Prince Edward Island
David French, Tidewater Community College
Dennis Walsh, Middle Tennessee State University
Diane Mathios, De Anza College
John Thomas, College of Lake County
Jing Chang, College of Saint Mary
Sara Lenhart, Christopher Newport University
Sarah Boslaugh, Kennesaw State University
Abdulhamid Sukar, Cameron University
Abraham Biggs, Broward Community College
Adam Pennell, Greensboro College
Alexander Kolovos
Ann Flanigan, Kapiolani Community College
Robert McDevitt, Germanna Community College
Roberta Bloom, De Anza College
Rupinder Sekhon, De Anza College
Sudipta Roy, Kankakee Community College
Cindy Moss, Skyline College
Ernest Bonat, Portland Community College
Kathy Plum, De Anza College
Andrew Wiesner, Pennsylvania State University
Jonathan Oaks, Macomb Community College
Michael Greenwich, College of Southern Nevada
Miriam Masullo, SUNY Purchase
Mo Geraghty, De Anza College
Larry Green, Lake Tahoe Community College
Nydia Nelson, St. Petersburg College
Philip J. Verrecchia, York College of Pennsylvania
Robert Henderson, Stephen F. Austin State University
Benjamin Ngwudike, Jackson State University
Mel Jacobsen, Snow College
Birgit Aquilonius, West Valley College
Jim Lucas, De Anza College
David Bosworth, Hutchinson Community College
Frank Snow, De Anza College
George Bratton, University of Central Arkansas
Inna Grushko, De Anza College
Janice Hector, De Anza College
Javier Rueda, De Anza College
Lisa Rosenberg, Elon University
Mark Mills, Central College
Mary Jo Kane, De Anza College
Travis Short, St. Petersburg College
Valier Hauber, De Anza College
Vladimir Logvenenko, De Anza College
Wendy Lightheart, Lane Community College
Yvonne Sandoval, Pima Community College

Editorial Review Board

Linda Gann (6-12 Mathematics Coordinator, Boerne ISD) taught mathematics and statistics for over twenty-five years at Northside ISD, and currently serves as the 6-12 Mathematics Coordinator in Boerne ISD. She was awarded the Presidential Award for Excellence in Teaching, the Radio Shack National Teacher Award, the HEB Teaching Excellence Award (State Finalist), and the AP Siemens Award. For many years, Linda worked for the College Board as a consultant for AP Calculus AB, BC, and Statistics, and as a reader for AP Statistics. She has also served as the co-chair for the College and Career Readiness Standards for Mathematics for all three writing phases. Her educational background consists of a B.S. in Mathematics from Illinois State University and an M.S. in Mathematics from the University of Texas, San Antonio. Additionally, she is nearing completion of her Ph.D. in Interdisciplinary of Learning and Teaching from UTSA. She presently serves as president of the Alamo District Council of Teachers of Mathematics and scholarship chair for the Priest Holmes Foundation.

Wendy Martinez (Cedar Park High School) has been a teacher since 1994. She currently teaches PreAP Geometry and on-level Statistics at Cedar Park High School in Leander ISD. She has taught at Rouse High School, Lake Travis High School, and Pflugerville Middle School.

Alexander Teich (Rice University Graduate Student, Master’s Degree in Applied Mathematics) has teaching experience back to 2004 and has taught math classes at Spring Woods High School, in Cambridge, Massachusetts, and Philadelphia, Pennsylvania. He formerly sponsored the Spring Wood Chess Club, and has a wealth of varied practical experience outside the classroom.

Amanda Yowell (Pleasant Grove High School) earned a Bachelors of Science in Business Administration and Finance from the University of Arkansas and worked in Financial Management. She teaches Mathematics classes at Pleasant Grove High School in Texarkana, TX. In her free time, she enjoys spending time with her husband and their three children.

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