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1 Introductory Statistics By: OpenStax College Online: This selection and arrangement of content as a collection is copyrighted by OpenStax College Creative Commons Attribution License 4.0 http://creativecommons.org/licenses/by/4.0/ Collection structure revised: 2014/05/09 For copyright and attribution information for the modules contained in this collection, see the "Attributions" section at the end of the collection This content is available for free at http://legacy.cnx.org/content/col11562/1.17 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 13 29 37 41 43 67 68 76 86 94 98 103 108 118 163 164 168 175 180 185 194 225 226 228 235 240 244 247 252 255 289 291 294 303 314 339 340 345 352 354 371 372 377 380 388 391 413 415 424 429 436 438 440 471 472 474 476 477 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 content is available for free at http://legacy.cnx.org/content/col11562/1.17 480 496 527 528 536 539 543 549 579 580 581 590 594 597 598 600 604 635 636 638 641 647 652 653 660 662 664 695 696 697 701 708 711 735 761 815 819 825 829 835 847 848 PREFACE About Introductory Statistics Introductory Statistics is designed for the one-semester, 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 Coverage and Scope Chapter Sampling and Data Chapter Descriptive Statistics Chapter Probability Topics Chapter Discrete Random Variables Chapter Continuous Random Variables Chapter The Normal Distribution Chapter The Central Limit Theorem Chapter Confidence Intervals Chapter 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 Sampling and Data Chapter Descriptive Statistics Chapter 12 Linear Regression and Correlation Chapter Probability Topics Chapter Discrete Random Variables Chapter Continuous Random Variables Chapter The Normal Distribution Chapter The Central Limit Theorem Chapter Confidence Intervals Chapter 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 • 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 Ancillaries • Instructor’s Solutions Manual • Webassign Online Homework System • Video Lectures (http://cnx.org/content/m18746/latest/?collection=col10522/latest) delivered by Barbara Illowsky are provided for each chapter 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 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 This content is available for free at http://legacy.cnx.org/content/col11562/1.17 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 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 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 content is available for free at http://legacy.cnx.org/content/col11562/1.17 CHAPTER | SAMPLING AND DATA | 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 10 CHAPTER | 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; 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, you think the results would be the same? Why or why not? Where 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 or 0.5 Even though the outcomes of a few repetitions are uncertain, there is a regular pattern 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 probability began with the study of games of chance such as poker Predictions take the form of probabilities To predict the likelihood of an earthquake, of rain, or whether you will get an A in this course, we use probabilities Doctors use probability to determine the chance of a vaccination causing the disease the vaccination is supposed to prevent A stockbroker uses probability to determine the rate of return on a client's investments You might use probability to decide to buy a lottery ticket or not In your study of statistics, you will use the power of mathematics through probability calculations to analyze and interpret your data This content is available for free at http://legacy.cnx.org/content/col11562/1.17 APPENDIX H | APPENDIX H: TABLES APPENDIX H: TABLES The module contains links to government site tables used in statistics NOTE When you are finished with the table link, use the back button on your browser to return here Tables (NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, January 3, 2009) • Student t table (http://www.itl.nist.gov/div898/handbook/eda/section3/eda3672.htm) • Normal table (http://www.itl.nist.gov/div898/handbook/eda/section3/eda3671.htm) • Chi-Square table (http://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm) • F-table (http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm) • All four tables (http://www.itl.nist.gov/div898/handbook/eda/section3/eda367.htm) can be accessed by going to 95% Critical Values of the Sample Correlation Coefficient Table • 95% Critical Values of the Sample Correlation Coefficient 847 848 INDEX INDEX Symbols α, 479 A absolute value of a residual, 643 alternative hypothesis, 472 Analysis of Variance, 714 Area to the left, 345 Area to the right, 345 assumption, 477 average, 11 Average, 47, 396 B balanced design, 704 bar graph, 17 Bernoulli Trial, 235 Bernoulli Trials, 259 binomial distribution, 387, 429, 477 Binomial Distribution, 443, 500 Binomial Experiment, 259 binomial probability distribution, 235 Binomial Probability Distribution, 259 bivariate, 636 Blinding, 38, 47 Box plot, 121 Box plots, 94 box-and-whisker plots, 94 box-whisker plots, 94 C Categorical Variable, 47 Categorical variables, 11 central limit theorem, 371, 373, 380, 483 Central Limit Theorem, 396, 500 central limit theorem for means, 375 central limit theorem for sums, 377 chi-square distribution, 580 Cluster Sampling, 47 Coefficient of Correlation, 667 coefficient of determination, 647 Cohen's d, 534 complement, 165 conditional probability, 165, 299 Conditional Probability, 198, 318 confidence interval, 414, 425 Confidence Interval (CI), 443, 500 confidence intervals, 429 Confidence intervals, 471 confidence level, 415, 429 Confidence Level (CL), 443 contingency table, 180, 198, 590 Contingency Table, 607 continuity correction factor, 387 continuous, 14 Continuous Random Variable, 47 continuous random variable, 303 control group, 38 Control Group, 47 Convenience Sampling, 47 critical value, 347 cumulative distribution function (CDF), 304 Cumulative relative frequency, 30 Cumulative Relative Frequency, 47 D data, Data, 11, 47 decay parameter, 318 degrees of freedom, 425 Degrees of Freedom (df), 443, 553 degrees of freedom (df), 529 Dependent Events, 198 descriptive statistics, 10 discrete, 14 Discrete Random Variable, 47 double-blind experiment, 38 Double-blinding, 47 E Empirical Rule, 342 empirical rule, 414 equal standard deviations, 696 Equally likely, 164 Equally Likely, 198 equally likely, 295 error bound, 429 error bound for a population mean, 415, 425 Error Bound for a Population Mean (EBM), 443 Error Bound for a Population Proportion (EBP), 443 event, 164 Event, 198 expected value, 228 Expected Value, 259 expected values, 581 experiment, 164 Experiment, 198 experimental unit, 37 Experimental Unit, 47 This content is available for free at http://legacy.cnx.org/content/col11562/1.17 explanatory variable, 37 Explanatory Variable, 47 exponential distribution, 303, 383 Exponential Distribution, 318, 396 extrapolation, 653 F F distribution, 697 F ratio, 697 fair, 164 first quartile, 87 First Quartile, 121 frequency, 30, 76 Frequency, 47, 121 Frequency Polygon, 121 Frequency Table, 121 G geometric distribution, 242 Geometric Distribution, 259 Geometric Experiment, 259 goodness-of-fit test, 581 H histogram, 76 Histogram, 121 hypergeometric experiment, 261 Hypergeometric Experiment, 259 hypergeometric probability, 244 Hypergeometric Probability, 259 hypotheses, 472 Hypothesis, 500 hypothesis test, 477, 480, 501 hypothesis testing, 472 Hypothesis Testing, 500 I independent, 168, 176 Independent Events, 198 Independent groups, 528 inferential statistics, 10, 414 Inferential Statistics, 443 influential points, 653 informed consent, 40 Informed Consent, 47 Institutional Review Board, 47 Institutional Review Boards (IRB), 40 interpolation, 653 interquartile range, 87 Interquartile Range, 121 Interval, 121 interval scale, 29 L law of large numbers, 164, 380 INDEX Least-Squares Line, 641 least-squares regression line, 642 level of measurement, 29 Level of Significance of the Test , 500 Line of Best Fit, 641 linear regression, 641 long-term relative frequency, 164 Lurking Variable, 47 lurking variables, 37 P p-value, 477, 480, 500 paired data set, 84 Paired Data Set, 121 parameter, 11, 414 Parameter, 47, 443 Pareto chart, 17 Pearson, 10 Percentile, 121 percentile, 379 percentiles, 86 M pie chart, 17 placebo, 38 margin of error, 414 Placebo, 47 matched pairs, 528 point estimate, 414 mean, 11, 98, 228, 372, 375, 381 Point Estimate, 443 Mean, 121, 259, 396 Poisson distribution, 318 Mean of a Probability Distribution, Poisson probability distribution, 259 247, 261 mean square, 697 Poisson Probability Distribution, median, 86, 98 260 Median, 121 Pooled Proportion, 553 memoryless property, 318 population, 11, 27 Midpoint, 121 Population, 47 mode, 100 population variance, 598 Mode, 121 potential outlier, 656 multivariate, 636 Probability, 10, 47, 198 mutually exclusive, 170, 176 probability, 164 Mutually Exclusive, 198 probability density function, 290 probability distribution function, N 226 Probability Distribution Function nominal scale, 29 (PDF), 260 Nonsampling Error, 47 proportion, 11 normal approximation to the Proportion, 47 binomial, 387 Normal Distribution, 357, 396, Q 443, 500 normal distribution, 425, 429, 476 Qualitative data, 13 Normal distribution, 536 Qualitative Data, 48 normally distributed, 372, 377, quantitative continuous data, 14 477 Quantitative data, 14 null hypothesis, 472, 477, 477, Quantitative Data, 48 479 quantitative discrete data, 14 Numerical Variable, 47 quartiles, 86 Numerical variables, 11 Quartiles, 87, 121 O observed values, 581 One-Way ANOVA, 714 ordinal scale, 29 outcome, 164 Outcome, 198 outlier, 69, 87 Outlier, 121, 667 outliers, 653 R random assignment, 37 Random Assignment, 48 Random Sampling, 48 random variable, 226 Random variable, 529 Random Variable, 536 Random Variable (RV), 260 ratio scale, 29 relative frequency, 30, 76 Relative Frequency, 48, 121 replacement, 168 Representative Sample, 48 residual, 643 response variable, 37 Response Variable, 48 S sample, 11 Sample, 48 sample mean, 373 sample size, 373, 377 sample space, 164, 175, 186 Sample Space, 198 samples, 27 sampling, 11 Sampling Bias, 48 sampling distribution, 101 Sampling Distribution, 396 Sampling Error, 48 sampling variability of a statistic, 109 Sampling with Replacement, 48, 198 Sampling without Replacement, 48, 198 simple random sample, 477 Simple Random Sampling, 48 single population mean, 476 single population proportion, 476 Skewed, 121 standard deviation, 108, 424, 476, 477, 478, 482 Standard Deviation, 121, 443, 500, 553 Standard Deviation of a Probability Distribution, 260 standard error, 528 Standard Error of the Mean, 396 standard error of the mean., 373 standard normal distribution, 340 Standard Normal Distribution, 357 statistic, 11 Statistic, 48 statistics, Stratified Sampling, 48 Student's t-distribution, 425, 476, 477 Student's t-Distribution, 443, 500 Sum of Squared Errors (SSE), 643 sum of squares, 697 Systematic Sampling, 48 T test for homogeneity, 594 test of a single variance, 598 test of independence, 590 849 850 INDEX test statistic, 536 The AND Event, 198 The Complement Event, 198 The Conditional Probability of A GIVEN B, 198 The Conditional Probability of One Event Given Another Event, 198 The Law of Large Numbers, 260 The Or Event, 198 The OR of Two Events, 198 The standard deviation, 536 third quartile, 87 treatments, 37 Treatments, 48 tree diagram, 185 Tree Diagram, 198 Type Error, 500 Type Error, 500 Type I error, 474, 479 Type II error, 474 U unfair, 165 Uniform Distribution, 318, 396 uniform distribution, 381 V variable, 11 Variable, 48 Variable (Random Variable), 553 variance, 109 Variance, 121, 714 Variance between samples, 697 Variance within samples, 697 variances, 696 Variation, 27 Venn diagram, 191 Venn Diagram, 199 Z z-score, 357, 425 z-scores, 340 This content is available for free at http://legacy.cnx.org/content/col11562/1.17 INDEX ATTRIBUTIONS Collection: Introductory Statistics Edited by: OpenStax College URL: http://legacy.cnx.org/content/col11562/1.17/ Copyright: OpenStax College License: http://creativecommons.org/licenses/by/4.0/ Module: Preface By: OpenStax College URL: http://legacy.cnx.org/content/m47830/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m46913/1.11/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Definitions of Statistics, Probability, and Key Terms By: OpenStax College URL: http://legacy.cnx.org/content/m46909/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Data, Sampling, and Variation in Data and Sampling By: OpenStax College URL: http://legacy.cnx.org/content/m46885/1.12/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Frequency, Frequency Tables, and Levels of Measurement By: OpenStax College URL: http://legacy.cnx.org/content/m46882/1.9/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Experimental Design and Ethics By: OpenStax College URL: http://legacy.cnx.org/content/m46919/1.8/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Data Collection Experiment By: OpenStax College URL: http://legacy.cnx.org/content/m50252/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Sampling Experiment By: OpenStax College URL: http://legacy.cnx.org/content/m50243/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m46925/1.5/ Copyright: Rice University 851 852 INDEX License: http://creativecommons.org/licenses/by/3.0/ Module: Stem-and-Leaf Graphs (Stemplots), Line Graphs, and Bar Graphs By: OpenStax College URL: http://legacy.cnx.org/content/m46934/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Histograms, Frequency Polygons, and Time Series Graphs By: OpenStax College URL: http://legacy.cnx.org/content/m46924/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Measures of the Location of the Data By: OpenStax College URL: http://legacy.cnx.org/content/m46930/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Box Plots By: OpenStax College URL: http://legacy.cnx.org/content/m46920/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Measures of the Center of the Data By: OpenStax College URL: http://legacy.cnx.org/content/m46928/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Skewness and the Mean, Median, and Mode By: OpenStax College URL: http://legacy.cnx.org/content/m46931/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Measures of the Spread of the Data By: OpenStax College URL: http://legacy.cnx.org/content/m46922/1.10/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Descriptive Statistics By: OpenStax College URL: http://legacy.cnx.org/content/m50253/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m46938/1.7/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Terminology By: OpenStax College URL: http://legacy.cnx.org/content/m46942/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Independent and Mutually Exclusive Events By: OpenStax College This content is available for free at http://legacy.cnx.org/content/col11562/1.17 INDEX URL: http://legacy.cnx.org/content/m46948/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Two Basic Rules of Probability By: OpenStax College URL: http://legacy.cnx.org/content/m46947/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Contingency Tables By: OpenStax College URL: http://legacy.cnx.org/content/m46935/1.8/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Tree and Venn Diagrams By: OpenStax College URL: http://legacy.cnx.org/content/m46944/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Probability Topics By: OpenStax College URL: http://legacy.cnx.org/content/m50256/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m46955/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Probability Distribution Function (PDF) for a Discrete Random Variable By: OpenStax College URL: http://legacy.cnx.org/content/m46963/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Mean or Expected Value and Standard Deviation By: OpenStax College URL: http://legacy.cnx.org/content/m46959/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Binomial Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m46950/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Geometric Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m46953/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Hypergeometric Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m46964/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ 853 854 INDEX Module: Poisson Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m46961/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Discrete Distribution (Playing Card Experiment) By: OpenStax College URL: http://legacy.cnx.org/content/m50257/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Discrete Distribution (Lucky Dice Experiment) By: OpenStax College URL: http://legacy.cnx.org/content/m50259/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m46967/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Continuous Probability Functions By: OpenStax College URL: http://legacy.cnx.org/content/m46965/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: The Uniform Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m46972/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: The Exponential Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m46969/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Continuous Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m50260/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m46977/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: The Standard Normal Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m46980/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Using the Normal Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m46973/1.8/ This content is available for free at http://legacy.cnx.org/content/col11562/1.17 INDEX Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Normal Distribution (Lap Times) By: OpenStax College URL: http://legacy.cnx.org/content/m50261/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Normal Distribution (Pinkie Length) By: OpenStax College URL: http://legacy.cnx.org/content/m50264/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m46983/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: The Central Limit Theorem for Sample Means (Averages) By: OpenStax College URL: http://legacy.cnx.org/content/m46994/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: The Central Limit Theorem for Sums By: OpenStax College URL: http://legacy.cnx.org/content/m46997/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Using the Central Limit Theorem By: OpenStax College URL: http://legacy.cnx.org/content/m46992/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Central Limit Theorem (Pocket Change) By: OpenStax College URL: http://legacy.cnx.org/content/m50268/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Central Limit Theorem (Cookie Recipes) By: OpenStax College URL: http://legacy.cnx.org/content/m50269/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m47008/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: A Single Population Mean using the Normal Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m47002/1.9/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: A Single Population Mean using the Student t Distribution 855 856 INDEX By: OpenStax College URL: http://legacy.cnx.org/content/m47001/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: A Population Proportion By: OpenStax College URL: http://legacy.cnx.org/content/m46999/1.7/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Confidence Interval (Home Costs) By: OpenStax College URL: http://legacy.cnx.org/content/m50270/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Confidence Interval (Place of Birth) By: OpenStax College URL: http://legacy.cnx.org/content/m50272/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Confidence Interval (Women's Heights) By: OpenStax College URL: http://legacy.cnx.org/content/m50274/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m47041/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Null and Alternative Hypotheses By: OpenStax College URL: http://legacy.cnx.org/content/m47033/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Outcomes and the Type I and Type II Errors By: OpenStax College URL: http://legacy.cnx.org/content/m47029/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Distribution Needed for Hypothesis Testing By: OpenStax College URL: http://legacy.cnx.org/content/m47036/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Rare Events, the Sample, Decision and Conclusion By: OpenStax College URL: http://legacy.cnx.org/content/m47044/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Additional Information and Full Hypothesis Test Examples By: OpenStax College URL: http://legacy.cnx.org/content/m47019/1.6/ Copyright: Rice University This content is available for free at http://legacy.cnx.org/content/col11562/1.17 INDEX License: http://creativecommons.org/licenses/by/4.0/ Module: Hypothesis Testing of a Single Mean and Single Proportion By: OpenStax College URL: http://legacy.cnx.org/content/m50277/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m47057/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Two Population Means with Unknown Standard Deviations By: OpenStax College URL: http://legacy.cnx.org/content/m47050/1.7/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Two Population Means with Known Standard Deviations By: OpenStax College URL: http://legacy.cnx.org/content/m47061/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Comparing Two Independent Population Proportions By: OpenStax College URL: http://legacy.cnx.org/content/m47060/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Matched or Paired Samples By: OpenStax College URL: http://legacy.cnx.org/content/m47045/1.8/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Hypothesis Testing for Two Means and Two Proportions By: OpenStax College URL: http://legacy.cnx.org/content/m50278/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m47088/1.7/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Facts About the Chi-Square Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m47062/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Goodness-of-Fit Test By: OpenStax College URL: http://legacy.cnx.org/content/m47064/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Test of Independence By: OpenStax College 857 858 INDEX URL: http://legacy.cnx.org/content/m47077/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Test for Homogeneity By: OpenStax College URL: http://legacy.cnx.org/content/m47091/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Comparison of the Chi-Square Tests By: OpenStax College URL: http://legacy.cnx.org/content/m47082/1.7/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Test of a Single Variance By: OpenStax College URL: http://legacy.cnx.org/content/m47085/1.6/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Lab 1: Chi-Square Goodness-of-Fit By: OpenStax College URL: http://legacy.cnx.org/content/m50279/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Lab 2: Chi-Square Test of Independence By: OpenStax College URL: http://legacy.cnx.org/content/m50280/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m47098/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Linear Equations By: OpenStax College URL: http://legacy.cnx.org/content/m47100/1.2/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Scatter Plots By: OpenStax College URL: http://legacy.cnx.org/content/m47109/1.2/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: The Regression Equation By: OpenStax College URL: http://legacy.cnx.org/content/m47117/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Testing the Significance of the Correlation Coefficient By: OpenStax College URL: http://legacy.cnx.org/content/m47111/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ This content is available for free at http://legacy.cnx.org/content/col11562/1.17 INDEX Module: Prediction By: OpenStax College URL: http://legacy.cnx.org/content/m47105/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Outliers By: OpenStax College URL: http://legacy.cnx.org/content/m47107/1.7/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Regression (Distance from School) By: OpenStax College URL: http://legacy.cnx.org/content/m50283/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Regression (Textbook Cost) By: OpenStax College URL: http://legacy.cnx.org/content/m50285/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Regression (Fuel Efficiency) By: OpenStax College URL: http://legacy.cnx.org/content/m50287/1.1/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Introduction By: OpenStax College URL: http://legacy.cnx.org/content/m47121/1.2/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: One-Way ANOVA By: OpenStax College URL: http://legacy.cnx.org/content/m47124/1.2/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: The F Distribution and the F-Ratio By: OpenStax College URL: http://legacy.cnx.org/content/m47128/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Facts About the F Distribution By: OpenStax College URL: http://legacy.cnx.org/content/m47119/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Test of Two Variances By: OpenStax College URL: http://legacy.cnx.org/content/m47125/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Lab: One-Way ANOVA By: OpenStax College URL: http://legacy.cnx.org/content/m50288/1.1/ 859 860 INDEX Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Appendix A: Review Exercises (Ch 3-13) By: OpenStax College URL: http://legacy.cnx.org/content/m47864/1.10/ Copyright: Rice University License: http://creativecommons.org/licenses/by/4.0/ Module: Appendix B: Practice Tests (1-4) and Final Exams By: OpenStax College URL: http://legacy.cnx.org/content/m47865/1.7/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Appendix C: Data Sets By: OpenStax College URL: http://legacy.cnx.org/content/m47873/1.3/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Appendix D: Group and Partner Projects By: OpenStax College URL: http://legacy.cnx.org/content/m47874/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Appendix E: Solution Sheets By: OpenStax College URL: http://legacy.cnx.org/content/m47882/1.5/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Appendix F: Mathematical Phrases, Symbols, and Formulas By: OpenStax College URL: http://legacy.cnx.org/content/m47891/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Appendix G: Notes for the TI-83, 83+, 84, 84+ Calculators By: OpenStax College URL: http://legacy.cnx.org/content/m47896/1.4/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ Module: Appendix H: Tables By: OpenStax College URL: http://legacy.cnx.org/content/m47875/1.7/ Copyright: Rice University License: http://creativecommons.org/licenses/by/3.0/ This content is available for free at http://legacy.cnx.org/content/col11562/1.17 INDEX ABOUT CONNEXIONS Since 1999, Connexions has been pioneering a global system where anyone can create course materials and make them fully accessible and easily reusable free of charge We are a Web-based authoring, teaching and learning environment open to anyone interested in education, including students, teachers, professors and lifelong learners We connect ideas and facilitate educational communities Connexions's modular, interactive courses are in use worldwide by universities, community colleges, K-12 schools, distance learners, and lifelong learners Connexions materials are in many languages, including 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