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Unformatted text preview: 1 Introduction to Statistics I - STAT 213 University of Calgary - Ver2015RevB Collection edited by: Nancy Chibry Content authors: OpenStax, Claude Laflamme, and Nancy Chibry Based on: Introductory Statistics < ;. Online: < ; This selection and arrangement of content as a collection is copyrighted by Nancy Chibry. Creative Commons Attribution License 4.0 Collection structure revised: 2015/10/21 PDF Generated: 2019/03/14 11:51:12 For copyright and attribution information for the modules contained in this collection, see the "Attributions" section at the end of the collection. 2 This OpenStax book is available for free at Table of Contents Preface for STATS 213 -- University of Calgary -- Fall 2015 . . . . . . . . . . . . . . . . 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: Linear Regression and Correlation . . . . . . . . . . . . . . . . . . . . . . . 3.1 Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 The Regression Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Outliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Regression (Distance from School) . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 Regression (Textbook Cost) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Regression (Fuel Efficiency) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 4: Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Independent and Mutually Exclusive Events . . . . . . . . . . . . . . . . . . . . . 4.3 Two Basic Rules of Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Contingency Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Tree and Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Counting Rules - University of Calgary - BASE CONTENT - V2015 . . . . . . . . 4.7 Probability Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 5: Discrete Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Probability Distribution Function (PDF) for a Discrete Random Variable . . . . . . 5.2 Mean or Expected Value and Standard Deviation . . . . . . . . . . . . . . . . . . 5.3 Binomial Distribution - University of Calgary - BASE CONTENT - V2015 . . . . . . 5.4 Geometric Distribution - University of Calgary - BASE CONTENT - V2015 . . . . . 5.5 Hypergeometric Distribution - University of Calgary - BASE CONTENT - V2015RB 5.6 Poisson Di - University of Calgary - BASE CONTENT - V2015 . . . . . . . . . . . 5.7 Discrete Distribution (Playing Card Experiment) . . . . . . . . . . . . . . . . . . . 5.8 Discrete Distribution (Lucky Dice Experiment) . . . . . . . . . . . . . . . . . . . . Chapter 6: Continuous Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Continuous Probability Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 The Uniform Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 The Exponential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Continuous Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 7: The Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 The Standard Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Using the Normal Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Normal Distribution (Lap Times) . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Normal Distribution (Pinkie Length) . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 8: The Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 The Central Limit Theorem for Sample Means (Averages) . . . . . . . . . . . . . 8.2 The Central Limit Theorem for Sums . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Using the Central Limit Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 5 . 5 10 26 35 39 41 67 68 77 88 97 101 107 111 121 175 176 178 181 187 188 196 198 200 235 236 241 248 253 259 269 276 309 310 313 319 326 330 333 338 342 379 381 384 394 406 433 434 439 447 449 467 468 473 476 8.4 Central Limit Theorem (Pocket Change) . . . . . . . . . . . 8.5 Central Limit Theorem (Cookie Recipes) . . . . . . . . . . Chapter 9: Confidence Intervals . . . . . . . . . . . . . . . . . . . 9.1 A Single Population Mean using the Normal Distribution . . 9.2 A Single Population Mean using the Student t Distribution . 9.3 A Population Proportion . . . . . . . . . . . . . . . . . . . 9.4 Confidence Interval (Home Costs) . . . . . . . . . . . . . . 9.5 Confidence Interval (Place of Birth) . . . . . . . . . . . . . 9.6 Confidence Interval (Women's Heights) . . . . . . . . . . . Chapter 10: Hypothesis Testing with One Sample . . . . . . . . . 10.1 Null and Alternative Hypotheses . . . . . . . . . . . . . . 10.2 Outcomes and the Type I and Type II Errors . . . . . . . . 10.3 Distribution Needed for Hypothesis Testing . . . . . . . . 10.4 Rare Events, the Sample, Decision and Conclusion . . . . 10.5 Additional Information and Full Hypothesis Test Examples . 10.6 Hypothesis Testing of a Single Mean and Single Proportion 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 487 511 513 524 528 535 537 539 573 574 576 579 579 582 598 635 663 719 723 729 733 739 751 753 Preface 1 PREFACE FOR STATS 213 -UNIVERSITY OF CALGARY -- FALL 2015 About Introductory Statistics This version of Introductory Statistics has been adapted by Nancy Chibry from the original version specifically for the onesemester Statistics 213 course at the University of Calgary. 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. 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. • 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 interaction that will produce a meaningful application of statistics. Statistics Labs appear at the end of each chapter, and begin with student learning outcomes, general estimates for time on task, and any global implementation notes. Students are then provided step-by-step guidance, including sample data tables and calculation prompts. The detailed assistance will help the students successfully apply the concepts in the text and lay the groundwork for future collaborative or individual work. About Our Team Senior Contributing Authors Barbara Illowsky De Anza College Susan Dean De Anza College Contributors Abdulhamid Sukar Cameron University Abraham Biggs Broward Community College 2 Preface Adam Pennell Greensboro College Alexander Kolovos Andrew Wiesner Pennsylvania State University Ann Flanigan Kapiolani Community College Benjamin Ngwudike Jackson State University Birgit Aquilonius West Valley College Bryan Blount Kentucky Wesleyan 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 Cindy Moss Skyline College Daniel Birmajer Nazareth College David Bosworth Hutchinson Community College David French Tidewater Community College Dennis Walsh Middle Tennessee State University Diane Mathios De Anza College Ernest Bonat Portland 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 Jeffery Taub Maine Maritime Academy Jim Helmreich Marist College Jim Lucas De Anza College Jing Chang College of Saint Mary John Thomas College of Lake County Jonathan Oaks Macomb Community College Kathy Plum De Anza College Larry Green Lake Tahoe Community College Laurel Chiappetta University of Pittsburgh Lenore Desilets De Anza College Lisa Markus De Anza College Lisa Rosenberg Elon University Lynette Kenyon Collin County Community College Mark Mills Central College Mary Jo Kane De Anza College Mary Teegarden San Diego Mesa College Matthew Einsohn Prescott College This OpenStax book is available for free at Preface 3 Mel Jacobsen Snow College Michael Greenwich College of Southern Nevada Miriam Masullo SUNY Purchase Mo Geraghty De Anza College Nydia Nelson St. Petersburg College Philip J. Verrecchia York College of Pennsylvania Robert Henderson Stephen F. Austin State University Robert McDevitt Germanna Community College Roberta Bloom De Anza College Rupinder Sekhon De Anza College Sara Lenhart Christopher Newport University Sarah Boslaugh Kennesaw State University Sheldon Lee Viterbo University Sheri Boyd Rollins College Sudipta Roy Kankakee Community 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 4 Preface Sample TI Technology Disclaimer: The original calculator image(s) by Texas Instruments, Inc. are provided under CC-BY. Any subsequent modifications to the image(s) should be noted by the person making the modification. (Credit: ETmarcom TexasInstruments) This OpenStax book is available for free at Chapter 1 | Sampling and Data 5 1 | SAMPLING AND DATA Figure 1.1 We encounter statistics in our daily lives more often than we probably realize and from many different sources, like the news. (credit: David Sim) Introduction Chapter Objectives By the end of this chapter, the student should be able to: • Recognize and differentiate between key terms. • Apply various types of sampling methods to data collection. • Create and interpret frequency tables. You are probably asking yourself the question, "When and where will I use statistics?" If you read any newspaper, watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a television news program, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or "fact." Statistical methods can help you make the "best educated guess." Since you will undoubtedly be given statistical information at some point in your life, you need to know some techniques for analyzing the information thoughtfully. Think about buying a house or managing a budget. Think about your chosen profession. The fields of economics, business, psychology, education, biology, law, computer science, police science, and early childhood development require at least one course in statistics. Included in this chapter are the basic ideas and words of probability and statistics. You will soon understand that statistics and probability work together. You will also learn how data are gathered and what "good" data can be distinguished from "bad." 1.1 | Definitions of Statistics, Probability, and Key Terms The science of statistics deals with the collection, analysis, interpretation, and presentation of data. We see and use data in our everyday lives. 6 Chapter 1 | Sampling and Data In your classroom, try this exercise. Have class members write down the average time (in hours, to the nearest halfhour) they sleep per night. Your instructor will record the data. Then create a simple graph (called a dot plot) of the data. A dot plot consists of a number line and dots (or points) positioned above the number line. For example, consider the following data: 5; 5.5; 6; 6; 6; 6.5; 6.5; 6.5; 6.5; 7; 7; 8; 8; 9 The dot plot for this data would be as follows: Figure 1.2 Does your dot plot look the same as or different from the example? Why? If you did the same example in an English class with the same number of students, do you think the results would be the same? Why or why not? Where do your data appear to cluster? How might you interpret the clustering? The questions above ask you to analyze and interpret your data. With this example, you have begun your study of statistics. In this course, you will learn how to organize and summarize data. Organizing and summarizing data is called descriptive statistics. Two ways to summarize data are by graphing and by using numbers (for example, finding an average). After you have studied probability and probability distributions, you will use formal methods for drawing conclusions from "good" data. The formal methods are called inferential statistics. Statistical inference uses probability to determine how confident we can be that our conclusions are correct. Effective interpretation of data (inference) is based on good procedures for producing data and thoughtful examination of the data. You will encounter what will seem to be too many mathematical formulas for interpreting data. The goal of statistics is not to perform numerous calculations using the formulas, but to gain an understanding of your data. The calculations can be done using a calculator or a computer. The understanding must come from you. If you can thoroughly grasp the basics of statistics, you can be more confident in the decisions you make in life. Probability Probability is a mathematical tool used to study randomness. It deals with the chance (the likelihood) of an event occurring. For example, if you toss a fair coin four times, the outcomes may not be two heads and two tails. However, if you toss the same coin 4,000 times, the outcomes will be close to half heads and half tails. The expected theoretical probability of heads in any one toss is 1 or 0.5. Even though the outcomes of a few repetitions are uncertain, there is a regular pattern 2 of outcomes when there are many repetitions. After reading about the English statistician Karl Pearson who tossed a coin 24,000 times with a result of 12,012 heads, one of the authors tossed a coin 2,000 times. The results were 996 heads. The fraction 996 is equal to 0.498 which is very close to 0.5, the expected probability. 2000 The theory of probab...
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