Introductory Statistics

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Introductory Statistics

OpenStax CollegeRice University6100 Main Street MS-375Houston, Texas 77005To learn more about OpenStax College, visit http://openstaxcollege.org.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 4.0International License. Under this license, any user of this textbook or the textbook contents herein must provide proper attribution asfollows:---If you redistribute this textbook in a digital format (including but not limited to EPUB, PDF, and HTML), then you must retain onevery page the following attribution:“Download for free at http://cnx.org/content/col11562/latest/.”If you redistribute this textbook in a print format, then you must include on every physical page the following attribution:“Download for free at http://cnx.org/content/col11562/latest/.”If you redistribute part of this textbook, then you must retain in every digital format page view (including but not limited toEPUB, PDF, and HTML) and on every physical printed page the following attribution:“Download for free at http://cnx.org/content/col11562/latest/.”If you use this textbook as a bibliographic reference, then you should cite it as follows: OpenStax College, IntroductoryStatistics. OpenStax College. 19 September 2013. http://cnx.org/content/col11562/latest/ .For questions regarding this licensing, please contact partners@openstaxcollege.org.TrademarksThe OpenStax College name, OpenStax College logo, OpenStax College book covers, OpenStax CNX name, OpenStax CNX logo,Connexions name, and Connexions logo are not subject to the license and may not be reproduced without the prior and express writtenconsent of Rice -8RevisionST-1-000-RS

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Table of ContentsPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .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 Variable4.2 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 . . . . . . . . . . 2473474476478479

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 Deviations10.2 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 content is available for free at 29833839851853

1PREFACEAbout Introductory StatisticsIntroductory Statistics is designed for the one-semester, introduction to statistics course and is geared toward studentsmajoring 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 textbookwere made with the guidance of many faculty members who are deeply involved in teaching this course. These choices ledto innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility forstudents. We strove to make the discipline meaningful, so that students can draw from it a working knowledge that willenrich their future studies and help them make sense of the world around them.Coverage and ScopeChapter 1 Sampling and DataChapter 2 Descriptive StatisticsChapter 3 Probability TopicsChapter 4 Discrete Random VariablesChapter 5 Continuous Random VariablesChapter 6 The Normal DistributionChapter 7 The Central Limit TheoremChapter 8 Confidence IntervalsChapter 9 Hypothesis Testing with One SampleChapter 10 Hypothesis Testing with Two SamplesChapter 11 The Chi-Square DistributionChapter 12 Linear Regression and CorrelationChapter 13 F Distribution and One-Way ANOVAAlternate SequencingIntroductory Statistics was conceived and written to fit a particular topical sequence, but it can be used flexibly toaccommodate 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 theproposed alternate sequence should be carefully considered for student preparation and textual consistency.Chapter 1 Sampling and DataChapter 2 Descriptive StatisticsChapter 12 Linear Regression and CorrelationChapter 3 Probability TopicsChapter 4 Discrete Random VariablesChapter 5 Continuous Random VariablesChapter 6 The Normal DistributionChapter 7 The Central Limit TheoremChapter 8 Confidence IntervalsChapter 9 Hypothesis Testing with One SampleChapter 10 Hypothesis Testing with Two SamplesChapter 11 The Chi-Square DistributionChapter 13 F Distribution and One-Way ANOVAPedagogical Foundation and Features Examples are placed strategically throughout the text to show students the step-by-step process of interpreting andsolving statistical problems. To keep the text relevant for students, the examples are drawn from a broad spectrum ofpractical topics; these include examples about college life and learning, health and medicine, retail and business, andsports and entertainment. Try It practice problems immediately follow many examples and give students the opportunity to practice as they readthe 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 theircalculator. 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 difficultywhile also including real-world scenarios to engage students.Statistics LabsThese innovative activities were developed by Barbara Illowsky and Susan Dean in order to offer students the experience ofdesigning, implementing, and interpreting statistical analyses. They are drawn from actual experiments and data-gatheringprocesses, and offer a unique hands-on and collaborative experience. The labs provide a foundation for further learning andclassroom 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 ontask, and any global implementation notes. Students are then provided step-by-step guidance, including sample data tablesand calculation prompts. The detailed assistance will help the students successfully apply the concepts in the text and laythe groundwork for future collaborative or individual work.Ancillaries Instructor’s Solutions Manual Webassign Online Homework System Video Lectures (http://cnx.org/content/m18746/latest/?collection col10522/latest) delivered by BarbaraIllowsky are provided for each chapter.About Our TeamSenior Contributing AuthorsBarbara Illowsky De Anza CollegeSusan DeanDe Anza CollegeContributorsAbdulhamid SukarCameron UniversityAbraham BiggsBroward Community CollegeAdam PennellGreensboro CollegeAlexander KolovosAndrew WiesnerPennsylvania State UniversityAnn FlaniganKapiolani Community CollegeBenjamin NgwudikeJackson State UniversityBirgit AquiloniusWest Valley CollegeBryan BlountKentucky Wesleyan CollegeCarol OlmsteadDe Anza CollegeCarol WeidemanSt. Petersburg CollegeCharles AshbacherUpper Iowa University, Cedar RapidsCharles KleinDe Anza CollegeCheryl WartmanUniversity of Prince Edward IslandCindy MossSkyline CollegeDaniel BirmajerNazareth CollegeDavid BosworthHutchinson Community CollegeDavid FrenchTidewater Community CollegeDenn

PREFACE AboutIntroductory Statistics IntroductoryStatisticsis designed for the one-semester, introduction to statistics course and is geared toward students .

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