This is an electronic version of the print textbook Due to electronic rights restrictions, some third party content may be suppressed Editorial review has deemed that any suppressed content does not materially affect the overall learning experience The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest Introduction to Probability and Statistics 14th EDITION William Mendenhall, III Robert J Beaver University of California, Riverside, Emeritus Barbara M Beaver University of California, Riverside, Emeritus Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Introduction to Probability and Statistics, Fourteenth Edition Mendenhall/Beaver/Beaver Editor in Chief: Michelle Julet Publisher: Richard Stratton Senior Sponsoring Editor: Molly Taylor Assistant Editor: Shaylin Walsh Editorial Assistant: Alexander Gontar © 2013, 2009 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher Associate Media Editor: Andrew Coppola Marketing Director: Mandee Eckersley Senior Marketing Manager: Barb Bartoszek Marketing Coordinator: Michael Ledesma Marketing Communications Manager: Mary Anne Payumo For product information and technology assistance, contact us at Cengage Learning Customer & Sales Support, 1-800-354-9706 For permission to use material from this text or product, submit all requests online at www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Content Project Manager: Jill Quinn Art Director: Linda Helcher Senior Manufacturing Print Buyer: Diane Gibbons Rights Acquisition Specialist: Shalice Shah-Caldwell Production Service: MPS Limited, a Macmillan Company Cover Designer: Rokusek Design Cover Image: Vera Volkova/© Shutterstock Compositor: MPS Limited, a Macmillan Company Library of Congress Control Number: 2011933688 Student Edition ISBN-13: 978-1-133-10375-2 ISBN-10: 1-133-10375-8 Brooks/Cole 20 Channel Center Street Boston, MA 02210 USA Cengage Learning is a leading provider of customized learning solutions with office locations around the globe, including Singapore, the United Kingdom, Australia, Mexico, Brazil and Japan Locate your local office at international.cengage.com/region Cengage Learning products are represented in Canada by Nelson Education, Ltd For your course and learning solutions, visit www.cengage.com Purchase any of our products at your local college store or at our preferred online store www.cengagebrain.com Instructors: Please visit login.cengage.com and log in to access instructor-specific resources Printed in United States of America 15 14 13 12 11 Preface Every time you pick up a newspaper or a magazine, watch TV, or surf the Internet, you encounter statistics Every time you fill out a questionnaire, register at an online website, or pass your grocery rewards card through an electronic scanner, your personal information becomes part of a database containing your personal statistical information You cannot avoid the fact that in this information age, data collection and analysis are an integral part of our day-to-day activities In order to be an educated consumer and citizen, you need to understand how statistics are used and misused in our daily lives THE SECRET TO OUR SUCCESS The first college course in introductory statistics that we ever took used Introduction to Probability and Statistics by William Mendenhall Since that time, this text—currently in the fourteenth edition—has helped several generations of students understand what statistics is all about and how it can be used as a tool in their particular area of application The secret to the success of Introduction to Probability and Statistics is its ability to blend the old with the new With each revision we try to build on the strong points of previous editions, while always looking for new ways to motivate, encourage, and interest students using new technological tools HALLMARK FEATURES OF THE FOURTEENTH EDITION The fourteenth edition retains the traditional outline for the coverage of descriptive and inferential statistics This revision maintains the straightforward presentation of the thirteenth edition In this spirit, we have continued to simplify and clarify the language and to make the language and style more readable and “user friendly”—without sacrificing the statistical integrity of the presentation Great effort has been taken to explain not only how to apply statistical procedures, but also to explain • • • • how to meaningfully describe real sets of data what the results of statistical tests mean in terms of their practical applications how to evaluate the validity of the assumptions behind statistical tests what to when statistical assumptions have been violated iv ❍ PREFACE Exercises In the tradition of all previous editions, the variety and number of real applications in the exercise sets is a major strength of this edition We have revised the exercise sets to provide new and interesting real-world situations and real data sets, many of which are drawn from current periodicals and journals The fourteenth edition contains over 1300 problems, many of which are new to this edition A set of classic exercises compiled from previous editions is available on the website (http://www.cengage com/statistics/ mendenhall) Exercises are graduated in level of difficulty; some, involving only basic techniques, can be solved by almost all students, while others, involving practical applications and interpretation of results, will challenge students to use more sophisticated statistical reasoning and understanding Organization and Coverage We believe that Chapters through 10—with the possible exception of Chapter 3— should be covered in the order presented The remaining chapters can be covered in any order The analysis of variance chapter precedes the regression chapter, so that the instructor can present the analysis of variance as part of a regression analysis Thus, the most effective presentation would order these three chapters as well Chapters 1–3 present descriptive data analysis for both one and two variables, using both MINITAB and Microsoft Excel® graphics Chapter includes a full presentation of probability and probability distributions Three optional sections—Counting Rules, the Total Law of Probability, and Bayes’ Rule—are placed into the general flow of text, and instructors will have the option of complete or partial coverage The sections that present event relations, independence, conditional probability, and the Multiplication Rule have been rewritten in an attempt to clarify concepts that often are difficult for students to grasp As in the thirteenth edition, the chapters on analysis of variance and linear regression include both calculational formulas and computer printouts in the basic text presentation These chapters can be used with equal ease by instructors who wish to use the “hands-on” computational approach to linear regression and ANOVA and by those who choose to focus on the interpretation of computer-generated statistical printouts One important feature in the hypothesis testing chapters involves the emphasis on p-values and their use in judging statistical significance With the advent of computergenerated p-values, these probabilities have become essential components in reporting the results of a statistical analysis As such, the observed value of the test statistic and its p-value are presented together at the outset of our discussion of statistical hypothesis testing as equivalent tools for decision-making Statistical significance is defined in terms of preassigned values of a, and the p-value approach is presented as an alternative to the critical value approach for testing a statistical hypothesis Examples are presented using both the p-value and critical value approaches to hypothesis testing Discussion of the practical interpretation of statistical results, along with the difference between statistical significance and practical significance, is emphasized in the practical examples in the text Special Features of the Fourteenth Edition • NEED TO KNOW .: A special feature of this edition are highlighted sections called “NEED TO KNOW .” and identified by this icon These sections provide information consisting of definitions, procedures or step-by-step PREFACE • • ❍ v hints on problem solving for specific questions such as “NEED TO KNOW… How to Construct a Relative Frequency Histogram?” or “NEED TO KNOW… How to Decide Which Test to Use?” Applets: Easy access to the Internet has made it possible for students to visualize statistical concepts using an interactive webtool called an applet Applets written by Gary McClelland, author of Seeing StatisticsTM, are found on the CourseMate Website that accompanies the text Following each applet, appropriate exercises are available that provide visual reinforcement of the concepts presented in the text Applets allow the user to perform a statistical experiment, to interact with a statistical graph, to change its form, or to access an interactive “statistical table.” Graphical and numerical data description includes both traditional and EDA methods, using computer graphics generated by MINITAB 16 for Windows and MS Excel vi ❍ PREFACE • All examples and exercises in the text contain printouts based on MINITAB 16 and consistent with earlier versions of MINITAB or MS Excel Printouts are provided for some exercises, while other exercises require the student to obtain solutions without using a computer 1.47 Presidential Vetoes Here is a list of the 44 presidents of the United States along with the number of regular vetoes used by each:5 EX0147 Washington J Adams Jefferson Madison Monroe J Q Adams Jackson Van Buren W H Harrison Tyler Polk Taylor Fillmore Pierce Buchanan Lincoln A Johnson Grant Hayes Garfield Arthur Cleveland 0 5 0 0 21 45 12 304 B Harrison Cleveland McKinley T Roosevelt Taft Wilson Harding Coolidge Hoover F D Roosevelt Truman Eisenhower Kennedy L Johnson Nixon Ford Carter Reagan G H W Bush Clinton G W Bush Obama 19 42 42 30 33 20 21 372 180 73 12 16 26 48 13 39 29 36 11 Source: The World Almanac and Book of Facts 2011 Use an appropriate graph to describe the number of vetoes cast by the 44 presidents Write a summary paragraph describing this set of data 1.48 Windy Cities Are some cities more EX0148 windy than others? Does Chicago deserve to be (1950) (1960) (1970) (1980) (1990) (2000) (2010) 121.3 122.2 123.2 122.0 122.0 121.0 124.4 122.3 124.0 123.1 122.0 123.0 119.97 121.3 120.2 121.4 122.2 123.0 121.13 122.0 121.4 119.2† 122.1 122.2 121.19 123.0 120.0 124.0 122.2 123.3 124.06 121.4 121.1 122.0 120.1 121.1 122.75 123.2 122.0 121.3 122.4 121.0 121.36 122.1 120.3 122.1 123.2 122.4 122.17 125.0 122.1 121.1 122.2 122.2 121.86 122.1 121.4 122.2 125.0 123.2 122.66 † Record time set by Secretariat in 1973 Source: www.kentuckyderby.com a Do you think there will be a trend in the winning times over the years? Draw a line chart to verify your answer b Describe the distribution of winning times using an appropriate graph Comment on the shape of the distribution and look for any unusual observations 1.50 Gulf Oil Spill Cleanup On April 20, 2010, the United States experienced a major environmental disaster when a Deepwater Horizon drilling rig exploded in the Gulf of Mexico The number of personnel and equipment used in the Gulf oil spill cleanup, beginning May 2, 2010 (Day 13) through June 9, 2010 (Day 51) is given in the following table.13 EX0150 Day 13 Day 26 Day 39 Day 51 Number of personnel (1000s) Federal Gulf fishing areas closed Booms laid (miles) Dispersants used (1000 gallons) 3.0 3% 46 156 17.5 8% 315 500 20.0 25% 644 870 24.0 32% 909 1143 The Role of Computers in the Fourteenth Edition—TECHNOLOGY TODAY Computers are now a common tool for college students in all disciplines Most students are accomplished users of word processors, spreadsheets, and databases, and they have no trouble navigating through software packages in the Windows environment We believe, however, that advances in computer technology should not turn statistical analyses into a “black box.” Rather, we choose to use the computational shortcuts and interactive visual tools that modern technology provides to give us more time to emphasize statistical reasoning as well as the understanding and interpretation of statistical results In this edition, students will be able to use computers for both standard statistical analyses and as a tool for reinforcing and visualizing statistical concepts Both MS Excel and MINITAB 16 (consistent with earlier versions of MINITAB) are used exclusively as the computer packages for statistical analysis However, we have chosen to isolate the instructions for generating computer output into individual sections called Technology Today at the end of each chapter Each discussion uses numerical examples to guide the student through the MS Excel commands and option necessary for the procedures presented in that chapter, and then present the equivalent steps and commands needed to produce the same or similar results using MINITAB We have included screen captures from both MS Excel and MINITAB 16, so that the student can actually work through these sections as “mini-labs.” If you not need “hands-on” knowledge of MINITAB or MS Excel, or if you are using another software package, you may choose to skip these sections and simply use the printouts as guides for the basic understanding of computer printouts PREFACE ❍ vii Numerical Descriptive Measures in Excel MS Excel provides most of the basic descriptive statistics presented in Chapter a single command on the Data tab Other descriptive statistics can be calculate the Function command on the Formulas tab E XA MPL E 2.15 The following data are the front and rear leg rooms (in inches) for nine differen utility vehicles:14 Make & Model Acura MDX Buick Enclave Chevy TrailBlazer Chevy Tahoe Hybrid V8 CVT GMC Terrain 1LT 4-cyl Front Leg Room Rear Leg Room 41.0 41.5 40.0 41.0 43 28.5 30.0 25.5 27.5 31 Numerical Descriptive Measures in MINITAB MINITAB provides most of the basic descriptive statistics presented in Chapter using a single command in the drop-down menus The following data are the front and rear leg rooms (in inches) for nine different sports utility vehicles:14 Make and Model Acura MDX Buick Enclave Chevy TrailBlazer Chevy Tahoe Hybrid V8 CVT GMC Terrain 1LT 4-cyl Honda CR-V H ndai T cson Front Leg Room Rear Leg Room 41.0 41.5 40.0 41.0 43.0 41.0 42 28.5 30.0 25.5 27.5 31.0 29.5 29 Any student who has Internet access can use the applets found on the CourseMate Website to visualize a variety of statistical concepts (access instructions for the CourseMate Website are listed on the Printed Access Card that is an optional bundle with this text) In addition, some of the applets can be used instead of computer software to perform simple statistical analyses Exercises written specifically for use with these applets also appear on the CourseMate Website Students can use the applets at home or in a computer lab They can use them as they read through the text material, once they have finished reading the entire chapter, or as a tool for exam review Instructors can use the applets as a tool in a lab setting, or use them for visual demonstrations during lectures We believe that these applets will be a powerful tool that will increase student enthusiasm for, and understanding of, statistical concepts and procedures STUDY AIDS The many and varied exercises in the text provide the best learning tool for students embarking on a first course in statistics The answers to all odd-numbered exercises are given in the back of the text, and a detailed solution appears in the Student Solutions Manual, which is available as a supplement for students Each application exercise has viii ❍ PREFACE a title, making it easier for students and instructors to immediately identify both the context of the problem and the area of application Students should be encouraged to use the “NEED TO KNOW .” sections as they occur in the text The placement of these sections is intended to answer questions as they would normally arise in discussions In addition, there are numerous hints called “NEED A TIP?” that appear in the margins of the text The tips are short and concise Finally, sections called Key Concepts and Formulas appear in each chapter as a review in outline form of the material covered in that chapter INDEX ❍ Chi-square variable, 395 Cholesterol level case study, nonparametric procedures, 653–654 Cluster sampling, 246 Coefficient of determination, 498–499 multiple regression analysis, 536–537 Coefficients, correlation in Excel, 110–112 in MINITAB, 113–114 Pearson product moment sample coefficient of correlation, 513–517 quantitative bivariate data, 102–107 Colorblindness Bayes’ rule, 152–156 conditional probabilities and, 146 multiplication rule and, 145 Combinations, counting rule for, 136–137 Common variance, analysis of variance, 427 Complement of events, 139–140 addition rule, 142 probability calculations, 141–142 Completely randomized design analysis of variance, 428–437 Kruskal-Wallis H-test, 627–631 residual plots and, 468–469 Conditional data distributions, 97 Conditional probability, 144–149 Conditional proportions, chi-square test of independence, 584–586 Confidence bounds, one-sided, 311–312 Confidence coefficient, interval estimation, 291–293 Confidence interval, 284 binomial proportion, large-sample confidence interval, 308–309 construction of, 292–293 hypothesis testing and, 343 interpretation, 295–298 large-sample, 292–298 linear regression inferences, 496–497 paired-difference testing, small-sample inference, 389–391 population variance, 397–399 equality of two variances, 404 prediction intervals, 509–511 sample size and, 313–316 single treatment mean and difference between two means, 435–436 small-sample inference, 369–373 independent random samples, 378–382 two-sided, 311–312 Congo, probability and decision making in, 174 Constant variance assumption, analysis of variance, 468–469 Contingency tables, 581–586 multidimensional, 594 Continuity correction, binomial probability distribution, normal approximation, 226–227 Continuous probability distribution, 210–213 Continuous random variables continuity correction, 226–227 defined, 158 expected value calculation, 163 probability distribution, 210–213 Continuous variable, 10–11 Control charts, statistical process control, 267–270 Control limits, statistical process control chart, 267–269 Convenience sample, 246 Correction for the mean (CM), analysis of variance, 429–430 Correlation analysis, 513–517 population rank correlation coefficient, 641 rank correlation, 637–641 Correlation coefficient in Excel, 110–112 in MINITAB, 113–114 Pearson product moment sample coefficient of correlation, 513–517 quantitative bivariate data, 102–107 Counting rules, 133–137 combinations, 136–137 extended mn rule, 134–137 mn counting rule, 133–134 n item arrangement, 135–136 permutations, 134–135 Covariance, quantitative bivariate data, 102–107 Critical values, 666–668 difference between two population means, 343 hypothesis testing, 328 left-tailed, 677–678 population mean, 330 population variance, inferences concerning, 398–399 p-value calculations, 334–335 small-sample inference, 371–373 Spearman’s rank correlation coefficient, 680 Wilcoxon signed-rank test, 679 Cumulative area, standard normal distribution, 215 Cumulative binomial probabilities, 180–184, 658 Cumulative distribution function, 183 Cumulative Poisson tables, 190–193, 662–663 Curvilinear relationship, 540–542 correlation analysis, 515–517 linear regression analysis, 499 D Data bivariate, categorical, 11–14 distribution, 11 distribution location, 22 distribution shape, 22 graphs for, 8–14 numerical measurements, 51–55 quantitative, 17–24 univariate, Decision making, probability and, 174 Defective items, 269–270 Degrees of freedom analysis of variance, 430 chi-square testing, 594 linear regression, 489–491, 498 715 multiple regression analysis, 534–535 Pearson’s chi-square statistic, 576–577 randomized block design, 446–452 small-sample inferences, difference between two population means, 377–382 Student’s t distribution, 366–369 a ϫ b factorial experiment, two-way classification, 459–462 Density of probability, 183 Dependent error terms, 503 Dependent events, probability, 144–149 Dependent samples, paired-difference testing, 388–391 Dependent variable, 104–107 Descriptive statistics, Design variables, defined, 469 Determination, coefficient of, 498–499 multiple regression analysis, 536 Deterministic model, 483–486 Deviation standard binomial random variable, 178–179 defined, 60–62 discrete random variables, 160–163 point estimation, 288–289 practical significance of, 63–67 variability and, 59 Diagnostic tools, linear regression assumptions, 503–504 Difference between means, confidence interval, 435–436 Discrete probability distribution binomial, 176–184 in Excel, 167 in MINITAB, 167–168 Discrete random variables continuity correction, 226–227 defined, 158 mean and standard deviation, 160–163 probability distributions, 158–160 Discrete variable, 10 Dispersion See Variability Distribution See also Probability distribution; Sampling distribution; specific types of distribution bimodal, 23 graphic representation of, 22–25 skewed, 22–23, 54 symmetric, 22 unimodal, 23 Dotplots distribution data, 23–25 in MINITAB, 41–42 for quantitative data, 20 Dummy variables, 547–551 E Empirical Rule basic principles, 65–67 z score, 73 Equally likely probabilities counting rules, 133–137 simple events, 128–130 Equivalence, of statistical test, 592–593 Equivalent test statistic, linear regression, 498 716 ❍ INDEX Error dependent error terms, 503 of estimation, 286 random error, 484–486 residual error, 491 standard error, 508–509 Type I error, 328 Type II error, 335–336 Estimation applications, 283–284 fitted line, 507–511 interval estimation, 291–298 multiple regression analysis, 538–539 point estimation, 283–289 small-sample inferences, population mean, 369–373 statistical inference, 282 Estimators classification of, 283–284 interval estimator, 283 point estimator, 283 Events dependent events, probability, 144–149 independent events, probability, 144–149 probability and relations between, 137–142 probability calculations, 127–130 sample space and, 124–127 Excel program analysis of variance procedures, 470–472 binomial and Poisson probability in, 198–200 bivariate data in, 109–112 Central Limit Theorem in, 273–274 chi-square testing, 595–596 discrete probability distribution in, 167 graphing with, 33–37 linear regression analysis, 520–521 multiple regression analysis, 563 normal probability distribution calculation in, 232–234 numerical descriptive measures in, 84–85 quartile calculations, 76–77 small-sample testing, 410–413 Student’s t test in, 373 Exclusive events, 153 Exhaustive events, 153 Expected value, discrete random variables, 160–163 Experimental design analysis of variance, 426–427 blocking and, 451–452 sample size, 312–316 sampling plans, 243–246 Experimental error, residual plots, 467–469 Experimental unit analysis of variance, 426 defined, observational studies, 245 Experiments binomial, 176 counting rules, 133–137 defined, 124–125 total variation partitioning, 444–452 Exponential random variable, 212 Extended mn counting rule, 134–137 Extrapolation, linear regression analysis, 499 F Factor analysis of variance, 427 defined, 426 Factorial experiment blocking and, 451–452 a ϫ b factorial experiment, two-way classification, 458–462 Factorial notation, counting rules, 135 False negative, 154 False positive, 154 First-order model, quantitative and qualitative predictor variables, 547–551 Fit, residual plots and, 467–469 Fitted line, estimation and prediction using, 507–511 Five-number summary, 77–80 F probability distribution assumptions concerning, 401–402 comparison of two population variances, 401–407 percentage points, 669–676 Frequencies, categorical variables, 96–97 Frequency categorical data, 11 histograms, 24–28 Friedman Fr-test, randomized block designs, 633–636 F-test factorial experiments, 462 linear regression, 498 multiple regression analysis, 536 population means comparison, 433–434 qualitative and quantitative predictor variables, 550–551 G General Multiplication Rule, 146–149 Goodness-of-fit test, 593 cell probabilities, 577–579 Goodness of the inference, 283 Grading on the curve case study, probability distribution, 241 Graphs categorical data, 11–14 categorical variables, 95–97 critical interpretation, 22–25 data and variables in, 8–14 in Excel, 33–37 in MINITAB, 37–42 quantitative data, 17–24 H Histograms in MINITAB, 41–42 probability, 159–160 relative frequency, 24–28 Homogeneity, tests of, 589–590, 592–593 Hypergeometric probability distribution, 194–196 Hypothesis testing confidence intervals and, 343–344 correlation coefficient, 516–517 factorial experiments, 460–462 guidelines for, 356–357 independent random samples, difference between two population means, 378–382 one-tailed test, 326 paired-difference testing, 388–391 population variance, 396–399 equality of two variances, 403–404 slope of line, linear regression inferences, 495–497 small-sample inferences, population mean, 369–373 statistical inference, 282–283 two-tailed test, 326 Hypothetical populations, observational studies, 245 I Independent events chi-square test of independence, 582–586 multiplication rule, 146–149 mutually exclusive events vs., 148–149 probability, 144–149 Independent random samples analysis of variance, 430–431 difference between two means, smallsample inferences, 387–391 Kruskal-Wallis H-test, multiple population comparisons, 630–631 small-sample inferences, 409 difference between two population means, 376–382 Wilcoxon rank sum test, 607–614 Independent variable, 104–107 Indicator variables, 547–551 Inference Central Limit Theorem and, 251–256, 267–269, 273–275 goodness of, 283 hypothesis testing and, 282–283 linear regression, 495–497 Inferential statistics, Information contributors, regression analysis misinterpretation, 561 Interacting factors, blocking and, 451–452 Interaction sum of squares, a ϫ b factorial experiment, two-way classification, 458–462 Interaction term, quantitative and qualitative predictor variables, 547–551 Interquartile range (IQR), 76–80 Intersection of events, 139 Interval estimation, 284, 291–298 J Judgment sampling, 246 K Kendall tau (␶) rank correlation coefficient, 637–641 Kruskal-Wallis H-test, completely randomized design, 627–631 INDEX ❍ L M Large-sample confidence interval, 292–298 binomial proportion, 308–309 population mean, 292–297 difference between two means, 302–304 population proportion, 297–298 Large-sample point estimation, population mean, difference between two means, 302–304 Large-sample tests of hypotheses binomial proportion, 347–350 difference between two binomial proportions, 351–354 difference between two population means, 341–344 population mean, 328–339 population parameters, 325 research issues, 354–357 sign test, 618 statistical testing, 325–328 Wilcoxon rank sum test, 612–614 Wilcoxon signed-rank test, 625 Law of Total Probability, 153–155 Least-squares estimators, 487 Least-squares line, 104–106 Least-squares method basic principles, 486–488 multiple regression analysis, 533 Least-squares regression line, bivariate data, 104–106 Left inclusion, method of, relative frequency histograms, 25 Left-tailed test, 327 critical values, 677–678 Level of significance hypothesis testing, 328 Type I error and, 336 Level variable, defined, 426 Linear correlation, 515–517 Linearity, quantitative bivariate data, 101–107 Linear probabilistic model, 483–486 Linear regression analysis, 469 analysis of variance, 488–491 car manufacturing case study, 528–529 coefficient of determination, 498–499 Excel, 520–521 fitted line estimation and prediction, 507–511 MINITAB, 521–523 multiple linear regression, 531–532 significant regression results, 499 usability testing, 494–500 Line charts in Excel, 33–37, 109–112 in MINITAB, 40–42, 112–114 for quantitative data, 19 Line of means estimation and prediction, 507–511 linear regression inferences, 495–497 multiple regression analysis, 532–533 Location distribution data, 22 relative frequency histogram, 28 Log-linear models, 594 Lower confidence limit, 293, 311–312 Lower quartile, 74–75 Main effect sums of squares, a ϫ b factorial experiment, two-way classification, 458–462 Mann-Whitney U-test, independent random samples, 607–614 Marginal probabilities, chi-square test of independence, 582–586 Margin of error, sample size and, 313–316 Matched pairs testing difference between two means, smallsample inferences, 388–391 sign test, 616–618 Maximum tolerable risk, hypothesis testing, 328 Means binomial random variable, 178–179 confidence interval, single treatment and difference between two means, 435–436 difference between two means, smallsample inferences, 386–391 discrete random variables, 160–163 equality testing of treatment means, 432–433 measure of center and, 52 population mean, large-sample test for, 294–298 sampling distribution and, 248–250 standard error of, 255 Mean squares analysis of variance, 430 equality testing of treatment means, 432–433, 448–452 linear regression, 489–491 multiple regression analysis, 537 a ϫ b factorial experiment, two-way classification, 459–462 Measurement experimental unit, sample size and, 313–316 Tchebysheff’s theorem concerning, 63–67 Measure of central tendency, 51–55 Median defined, 53 fiftieth percentile as, 74 sampling distribution and, 248–250 Minimum variability, unbiased estimators, 286–289 MINITAB analysis of variance procedures, 470–472 binomial and Poisson probabilities in, 200–202 bivariate data in, 112–114 Central Limit Theorem in, 274–275 chi-square testing, 596–598 discrete probability distribution in, 167–168 graphing with, 37–42 linear regression analysis, 521–523 multiple regression analysis, 564–565 nonparametric procedures, 645–647 normal probability distribution, 234–236 numerical descriptive measures in, 85–87 quartile calculations, 76–77 small-sample testing, 413–416 Student’s t test in, 373 717 mn counting rule, 133–137 Modal class, 54–55 Mode, measure of center as, 54–55 Monte Carlo procedure, sampling applications, 279–280 Multicollinearity, 560–561 Multidimensional contingency tables, 594 Multinomial experiments, 575, 588–590 time-dependent multinomials, 593–594 Multiple regression analysis, 469 analysis of variance, 534–535 assumptions validation, 538 basic principles, 531 car construction case study, 572–573 construction procedures, 562 estimation and prediction, 538–542 Excel, 563 general model and assumptions, 531–532 least squares method, 533–534 MINITAB, 564–565 misinterpretation of, 560–561 polynomial regression model, 539–540 quantitative and qualitative predictor variables, 546–551 regression coefficient testing, 555–557 residual plots, 558–559 significant regression interpretation, 536–538 stepwise regression analysis, 559–560 usability testing of, 535–536 Multiplication rule independent events, 146–149 probability and, 144–149 Multivariate data, defined, Mutually exclusive events, 125–127 addition rule and, 141–142 colorblindness, Bayes’ rule, 153 independent events vs., 148–149 N Negative differences, Wilcoxon signed-rank test, 621–623 95% confidence interval, linear regression inferences, 496–497 n item arrangement, counting rule, 135–136 Nonlinear function, 517 Nonnormal distribution population mean, difference between two means, 302–304 sample mean and, 254–255 Nonparametric statistics basic principles, 607 cholesterol level case study, 653–654 Friedman Fr-test, randomized block designs, 633–636 Kruskal-Wallis H-test, completely randomized designs, 627–631 MINITAB procedures, 645–647 rank correlation coefficient, 637–641 sign test, paired experiment, 616–618 statistical test comparisons, 620 Wilcoxon rank sum test, independent random sample, 607–614 Wilcoxon signed-rank test, paired experiment, 621–625 Nonparametric testing, analysis of variance, 468–469 718 ❍ INDEX Nonrandom sampling, 246 Nonresponse, observational studies, 244 Normal approximation binomial probability distribution, 224–228 sign test, 617–618 Wilcoxon rank sum test, 611–612 Wilcoxon signed-rank test, 624–625 Normal distribution analysis of variance, 427 Empirical rule and, 65–67 population mean, difference between two means, 302–304 sample mean and, 254–255 Normal probability distribution, 213–221 in Excel, 232–234 linear regression assumptions, 504 in MINITAB, 234–236 multiple regression analysis, 538 residual plots, 467–469 Normal random variable, probability distribution, 213–221 Notation factorial, 135 variability measures, 55–62 Null hypothesis defined, 325 population mean, 330 population variance, 396 small-sample inference, 370 Wilcoxon rank sum and Mann-Whitney U-tests, 608–614 Wilcoxon signed-rank test, 622 Number of degrees of freedom, Student’s t distribution, 366–369 Numbers, random, 244 Numerical measures of center, 51–55 of data, 51–55 quantitative bivariate data, 101–107 O Observational studies, 244–246 analysis of variance, 426 1-in-k systematic random sample, 246 One-sided confidence bounds, 311–312 Wilcoxon signed-rank test, 622 One-tailed test of hypothesis, 326 Spearman rank correlation coefficient, critical values, 680 One-way classification, analysis of variance, 428–437 Orderings, counting rules, 134–135 Outliers box plot construction, 78–80 measure of central tendency, 54 relative frequency histogram, 28 z score, 73 P Paired comparisons ranking of population mean, 440–443 sign test for, 616–618 Wilcoxon signed-rank test, 621–625 Paired-difference testing analysis of variance, 428 difference between two means, smallsample inferences, 386–391 sign test, 616–618 Parameters numerical measures, 51 point estimation, 283–285 sampling distribution, 243 statistical inference, 282 Pareto charts, 12 Partial regression coefficients multiple regression analysis, 532–533 significance testing, 536–537 Partial slope, multiple regression analysis, 532–533 Partitioning, total variation partitioning, 444–452 p chart, 269–270 Pearson product moment sample coefficient of correlation, 513–517 Pearson’s chi-square statistic See Chi-square statistic basic principles, 576–577 multinomial experiments, 575, 594 Percentage measurements, categorical data, 11 Percentiles, 74 Permutations, counting rules, 134–135 Pie charts categorical data, 12 in Excel, 33–37 in MINITAB, 37–42 for quantitative data, 17–19 side-by-side, 95–97 Plane, multiple regression analysis, 532–533 Plot of residuals vs fit, 503–504 Point estimation, 283–289 confidence intervals and, 298 large-sample estimation, 308–309 population parameter, 286–289 Poisson approximation, binomial probability, 191–193 Poisson probability distribution, 188–193 cancer risk case study, 208 in Excel, 198–200 in MINITAB, 200–201 Poisson random variable, 188–193 Polling data, sampling data in, 322–323 Polynomial regression model, 539–542 Pooled sampling, 381–382 Pooled t test difference between two means, smallsample inferences, 387–391 independent random samples, 381–382 Population mean difference estimation, two means, 301–304, 341 large-sample confidence interval for, 292–298 large-sample test of hypotheses for, 325, 328–329 ranking, 440–443 sampling distribution and, 248–250 small-sample inferences, 369–373 difference between two means, 376–382 Population parameter, point estimation of, 286–289 Population rank correlation coefficient, 641 Populations correlation coefficient, 515–517 defined, hypothetical, 284 known and unknown, 124 Kruskal-Wallis H-test, multiple population comparisons, 630–631 linear probabilistic model, 483–486 multinomial, two-way classification, 588–590 proportion, large-sample confidence interval for, 297–298 sign test comparing, 616–618 standard deviation, 161–163 Population variance calculation of, 59–61 comparison of two variances, 401–407 defined, 60 inferences concerning, 394–399 Positive differences, Wilcoxon signed-rank test, 621–622 Power of statistical test, 336–337 Practical importance, binomial proportions, large-sample test of hypothesis for, 349–350 Prediction confidence and prediction intervals, 509–511 fitted line, 507–511 multiple regression analysis, 538–539 Predictor variable linear probabilistic model, 484–486 multiple regression analysis, 531–532 quantitative and qualitative, multiple regression analysis, 546–551 Principle of least squares, 486–488 Probabilistic models, linear models, 483–486 Probability complements, 141–142 conditional probability, 144–149 counting rules, 136–137 cumulative binomial probabilities, 180–184 decision making and, 174 event relations and, 139–142 histogram, 159–160 independence and, 144–149 multiplication rule, 144–149 normal random variable calculations, 218–221 sample events, calculation of, 127–130 statistics and, 124 unions, 141–142 Probability density function, 183 Probability distribution binomial, 176–184 chi-square, 395 continuous random variables, 210–213 discrete random variables, 158–160 in Excel, 167 grading on the curve case study, 241 hypergeometric, 194–196 in MINITAB, 167–168 normal probability distribution, 213–221 Poisson probability, 188–193 Probability table event relations, 143 simple events, 127 INDEX ❍ Process mean control chart for, 267–269 statistical process control, 267–269 Proportion binomial difference estimation, 307–309, 351–354 large-sample test of hypothesis for, 347–350 conditional, chi-square test of independence, 584–586 defective measurements, 269–270 population, large-sample confidence interval for, 297–298 sample proportion, 260–264 Proportion defective measurements, statistical process control chart, 269–270 pth percentile, 74 p-value calculation of, 332–335 difference between two population means, calculation of, 343 equivalence of statistical test, 593 factorial experiments, 462 population variance, inferences concerning, 398–399 qualitative and quantitative predictor variables, 550–551 small-sample inference, 371–373 test statistic, 327 Q Quadratic model, polynomial regression, 539–542 Qualitative variables analysis of variance assumptions, 466–469 contingency tables, two-way classification, 581–586 defined, 9–10 dishwasher case study, 121–122 in MINITAB, 112–114 multiple regression analysis, 546–551 Quantitative data analysis of variance assumptions, 466–469 bivariate data, numerical measures, 101–107 graphs for, 17–24 in MINITAB, 112–114 scatterplots for, 99–101 Quantitative variables defined, 9–10 discrete and continuous, 10 multiple regression analysis, 546–551 Quartiles, 74–75 Quota sampling, 246 R Random error component, linear probabilistic model, 484–486 Randomized assignment, analysis of variance, 429 Randomized block design Friedman Fr-test, 633–636 paired-difference testing, small-sample inference, 390–391 tests for, 449–452 two-way classification, 444–452 Random numbers, 244, 681–682 Random sampling, 243–246 confidence intervals and, 298 independent samples, 376–382 small-sample inferences, 409 Random selection, multiplication rule and, 145–149 Random variables binomial, 176–184 continuous, 158, 163, 210–213 discrete, 158–163 exponential, 212 hypergeometric variability, 194–196 normal random variable, 213–214 Poisson probability distribution, 188–193 uniform, 212 Random variation linear regression, coefficient of determination, 498–499 statistical process control, 266–269 Range defined, 58 interquartile range, 76–80 Rank correlation coefficient, 637–641 Rank sum, Wilcoxon signed-rank test, 621–623 R chart, 270 Regression See also Linear regression analysis; Multiple regression analysis assumptions, diagnostic tools for validation of, 503–504 bivariate data, 104–106 coefficients, 555–557 in Excel, 110–112 in MINITAB, 113–114 Rejection region, 330 hypothesis testing, 327 small-sample inference, 370 Relative frequency categorical data, 11, 97 event probability, 127–130 histograms, 24–28 probability distribution, 158–160 Relative standing, measures of, 72–77 Residual error, linear regression, 491 Residual plots analysis of variance assumptions, 467–469 multiple regression analysis, 538, 558–559 regression assumptions, 503–504 Response variable defined, 426 linear probabilistic model, 484–486 multiple regression analysis, 531–532 Right-tailed test, 327 equality testing of treatment means, 433 Pearson’s chi-square statistic, 576–577 randomized block design, 449 Robustness analysis of variance, 427 Student’s t distribution, 368–369 719 S s2 calculation, small-sample inferences, difference between two population means, 377–382 Sample defined, polling data case study, 322–323 short cut method, variance calculation, 61–62 variance of, 59–62 Sample mean defined, 52–53 large-sample test of hypothesis, 329 sampling distribution of, 254–258 Sample proportion, sampling distribution for, 260–264 Sample size See also Large-sample confidence interval large sample estimation, 282 selection criteria, 312–316 Sample space, events and, 124–127 Sample z score, 73 Sampling Monte Carlo procedure, 279–280 statistics and, 248 Sampling distribution binomial proportions, 307–309 Central Limit Theorem, 251–254, 273–275 in Excel, 273–274 in MINITAB, 274–275 Monte Carlo roulette case study, 279–280 parameters, 243 point estimation, 283–289 population mean, difference between two means, 301–304 sample mean, 254–258 sample proportion, 260–264 sampling plans and experimental designs, 243–246 statistical process control, 266–270 statistics and, 248–250 Sampling error, point estimation, 289 Sampling plans and designs, 243–246 sample size, 312–316 Scales, graph interpretation, 22–25 Scatterplots in Excel, 110–112 in MINITAB, 113–114 quantitative variables, 99–101 Second-order model polynomial regression, 539–542 quantitative and qualitative predictor variables, 547–551 Sequential sums of squares, multiple regression analysis, 535 Shape distribution data, 22 relative frequency histogram, 28 Shortcut method of sample variance calculation, 61–62 Tchebysheff’s theorem and Empirical rule, 67–68 Side-by-side pie charts, 95–97 Significance level of ␣ hypothesis testing, 328 large-sample test of hypothesis, 329 720 ❍ INDEX Sign test large samples, 618 normal approximation, 617–618 paired experiment, 616–618 Simple event defined, 125–127 probability calculations, 127–130 Simple random sampling See also Random sampling defined, 243–246 observational studies, 244–246 Single treatment mean, confidence interval, 435–436 Skewed left distribution, 23 Skewed right distribution, 22 Slope, 104 linear regression inferences, 495–497 multiple regression analysis, 532–533 Small-sample inference See also Inference assumptions concerning, 409 basic principles, 365 confidence interval, 369–373 in Excel, 410–413 independent random samples, difference between two population means, 373–382 in MINITAB, 413–416 paired-difference tests, difference between two means, 376–391 population mean, 369–373 population variance, 394–399 comparison of two variances, 401–407 school accountability case study, 424 student’s t distribution, 365–369 two population variances, 401–407 Sources of variation randomized block design, 446–452 a ϫ b factorial experiment, two-way classification, 458–462 Spearman rank correlation coefficient, 637–641 critical values, 680 Spread, point estimation, 285–289 Stacked bar charts, 95–97 Standard deviation binomial random variable, 178–179 defined, 60–62 discrete random variables, 160–163 point estimation, 288–289 practical significance of, 63–67 Standard error of estimator, 255, 287–289, 508–509 of mean, 255, 360–373 point estimation, 287–289 small-sample inference, 369–373 Standardized test statistic, 330 Standard normal distribution, 215, 218–221 Standard normal random variable, 213–215 Statistical inference, 282–283 Statistical process control (SPC) proportion defective measurements, 269–270 sampling application, 266–270 Statistical significance binomial proportions, large-sample test of hypothesis for, 349–350 p-value calculations, 333–335 Statistical table, 11–12 Statistical tests basic principles, 325–328 comparison of, 620–621 equivalence of, 592–593 large-sample, 347–354 population mean, 325 power of, 336–337 Statistical theorems, sampling distribution and, 248–249 Statistics descriptive, estimators as, 283–284 inferential, nonparametric, 607–654 numerical measures, 51 probability and, 124 sampling distribution, 248–249 Stem and leaf plots in MINITAB, 41–42 for quantitative data, 20 Stepwise regression analysis, 559–560 Stratified random sampling, 245–246 Studentized range percentage points, 683–686 ranking of population mean, 441–443 Student’s t distribution analysis of variance, 428 assumptions behind, 368–369 population mean, 369–373 small-sample inference, 365–369 Sum of squares for blocks (SSB), randomized block design, 446–452 Sum of squares for error (SSE) analysis of variance, 430 least-squares method, 486–488 Sum of squares for treatments (SST), analysis of variance, 429–430 Sums of squares least-squares method, 487–488 linear regression, 488–491 a ϫ b factorial experiment, two-way classification, 458–462 Symmetric distribution, 22 T Tchebysheff’s theorem basic principles, 63–67 z score, 73 Test of hypothesis, statistical inference, 283 Tests of homogeneity, 589–590 Test statistic defined, 326–327 large value of, 327 population mean, 330 small-sample inference, 370 Tied observations, sign test of populations, 616–618 Time-dependent multinomials, 593–594 Time series data set, 19 Total sum of squares (TSS), analysis of variance, 429–430 Treatment variable defined, 426, 469 difference estimation, 434–435 difference identification, block means, 450–452 equality testing of, 432–433, 448–452 randomized block design, 444–452 Tree diagram, sample space, 126–127 Trend, quantitative data, line charts for, 19 Tukey’s method for paired comparisons, 441–443 factorial experiments, 462 treatment difference identification, 450–452 Two-sided confidence interval, 311–312 Two-tailed test of hypothesis, 326 population mean, 330 Wilcoxon signed-rank test, 622 Two-way classification contingency tables, 581–586 multinomial populations, 588–590 randomized block design, 444–452 a ϫ b factorial experiment, 458–462 Type I error, hypothesis testing, 328, 335–336 Type II error, 328, 335–336 U Unbiased parameters, point estimation, 285 Unconditional probabilities, chi-square test of independence, 582–586 Undercoverage, observational studies, 245 Uniform random variable, 212 Unimodal distribution, 23 Union of events, 139 probability calculations, 141–142 Univariate data, defined, Unpaired t test, analysis of variance, 428 Upper confidence limit, 293, 311–312 Upper quartile, 74–75 V Variability defined, 58 measures of, 55–62 Variables categorical variables, graphs for, 95–97 chi-square, 395 classification, 9–11 defined, dependent variable, 104–107 independent variable, 104–107 quantitative variables, 99–101 residual plots and, 467–469 Variance calculation of, 59–61 discrete random variable, 161–163 point estimation spread, 285–289 population, 60 sample, 59–60 Venn diagram complement of events and, 139–141 sample space, 126–127 W Weighted average, small-sample inferences, difference between two population means, 377–382 INDEX ❍ Wilcoxon rank sum test formulas for, 609 independent random sample, 607–614 large samples, 612–614 normal approximation, 611–612 notation, 609–610 Wilcoxon signed-rank test critical values, 679 large sample tests, 625 paired experiment, 621–625 Wording bias, observational studies, 245 Working women case study, categorical data in, 604–605 X x– chart, 267–269 Y y-intercept, 104, 510 Z z score, basic properties, 73 z values, confidence interval, 293 721 This page intentionally left blank Area TABLE z Areas under the Normal Curve, pages 664–665 z 00 01 02 03 04 05 06 07 08 09 Ϫ3.4 Ϫ3.3 Ϫ3.2 Ϫ3.1 Ϫ3.0 0003 0005 0007 0010 0013 0003 0005 0007 0009 0013 0003 0005 0006 0009 0013 0003 0004 0006 0009 0012 0003 0004 0006 0008 0012 0003 0004 0006 0008 0011 0003 0004 0006 0008 0011 0003 0004 0005 0008 0011 0003 0004 0005 0007 0010 0002 0003 0005 0007 0010 Ϫ2.9 Ϫ2.8 Ϫ2.7 Ϫ2.6 Ϫ2.5 0019 0026 0035 0047 0062 0018 0025 0034 0045 0060 0017 0024 0033 0044 0059 0017 0023 0032 0043 0057 0016 0023 0031 0041 0055 0016 0022 0030 0040 0054 0015 0021 0029 0039 0052 0015 0021 0028 0038 0051 0014 0020 0027 0037 0049 0014 0019 0026 0036 0048 Ϫ2.4 Ϫ2.3 Ϫ2.2 Ϫ2.1 Ϫ2.0 0082 0107 0139 0179 0228 0080 0104 0136 0174 0222 0078 0102 0132 0170 0217 0075 0099 0129 0166 0212 0073 0096 0125 0162 0207 0071 0094 0122 0158 0202 0069 0091 0119 0154 0197 0068 0089 0116 0150 0192 0066 0087 0113 0146 0188 0064 0084 0110 0143 0183 Ϫ1.9 Ϫ1.8 Ϫ1.7 Ϫ1.6 Ϫ1.5 0287 0359 0446 0548 0668 0281 0351 0436 0537 0655 0274 0344 0427 0526 0643 0268 0336 0418 0516 0630 0262 0329 0409 0505 0618 0256 0322 0401 0495 0606 0250 0314 0392 0485 0594 0244 0307 0384 0475 0582 0239 0301 0375 0465 0571 0233 0294 0367 0455 0559 Ϫ1.4 Ϫ1.3 Ϫ1.2 Ϫ1.1 Ϫ1.0 0808 0968 1151 1357 1587 0793 0951 1131 1335 1562 0778 0934 1112 1314 1539 0764 0918 1093 1292 1515 0749 0901 1075 1271 1492 0735 0885 1056 1251 1469 0722 0869 1038 1230 1446 0708 0853 1020 1210 1423 0694 0838 1003 1190 1401 0681 0823 0985 1170 1379 Ϫ0.9 Ϫ0.8 Ϫ0.7 Ϫ0.6 Ϫ0.5 1841 2119 2420 2743 3085 1814 2090 2389 2709 3050 1788 2061 2358 2676 3015 1762 2033 2327 2643 2981 1736 2005 2296 2611 2946 1711 1977 2266 2578 2912 1685 1949 2236 2546 2877 1660 1922 2206 2514 2843 1635 1894 2177 2483 2810 1611 1867 2148 2451 2776 Ϫ0.4 Ϫ0.3 Ϫ0.2 Ϫ0.1 Ϫ0.0 3446 3821 4207 4602 5000 3409 3783 4168 4562 4960 3372 3745 4129 4522 4920 3336 3707 4090 4483 4880 3300 3669 4052 4443 4840 3264 3632 4013 4404 4801 3228 3594 3974 4364 4761 3192 3557 3936 4325 4721 3156 3520 3897 4286 4681 3121 3483 3859 4247 4641 This page intentionally left blank TABLE (continued) z 00 01 02 03 04 05 06 07 08 09 0.0 0.1 0.2 0.3 0.4 5000 5398 5793 6179 6554 5040 5438 5832 6217 6591 5080 5478 5871 6255 6628 5120 5517 5910 6293 6664 5160 5557 5948 6331 6700 5199 5596 5987 6368 6736 5239 5636 6026 6406 6772 5279 5675 6064 6443 6808 5319 5714 6103 6480 6844 5359 5753 6141 6517 6879 0.5 0.6 0.7 0.8 0.9 6915 7257 7580 7881 8159 6950 7291 7611 7910 8186 6985 7324 7642 7939 8212 7019 7357 7673 7967 8238 7054 7389 7704 7995 8264 7088 7422 7734 8023 8289 7123 7454 7764 8051 8315 7157 7486 7794 8078 8340 7190 7517 7823 8106 8365 7224 7549 7852 8133 8389 1.0 1.1 1.2 1.3 1.4 8413 8643 8849 9032 9192 8438 8665 8869 9049 9207 8461 8686 8888 9066 9222 8485 8708 8907 9082 9236 8508 8729 8925 9099 9251 8531 8749 8944 9115 9265 8554 8770 8962 9131 9279 8577 8790 8980 9147 9292 8599 8810 8997 9162 9306 8621 8830 9015 9177 9319 1.5 1.6 1.7 1.8 1.9 9332 9452 9554 9641 9713 9345 9463 9564 9649 9719 9357 9474 9573 9656 9726 9370 9484 9582 9664 9732 9382 9495 9591 9671 9738 9394 9505 9599 9678 9744 9406 9515 9608 9686 9750 9418 9525 9616 9693 9756 9429 9535 9625 9699 9761 9441 9545 9633 9706 9767 2.0 2.1 2.2 2.3 2.4 9772 9821 9861 9893 9918 9778 9826 9864 9896 9920 9783 9830 9868 9898 9922 9788 9834 9871 9901 9925 9793 9838 9875 9904 9927 9798 9842 9878 9906 9929 9803 9846 9881 9909 9931 9808 9850 9884 9911 9932 9812 9854 9887 9913 9934 9817 9857 9890 9916 9936 2.5 2.6 2.7 2.8 2.9 9938 9953 9965 9974 9981 9940 9955 9966 9975 9982 9941 9956 9967 9976 9982 9943 9957 9968 9977 9983 9945 9959 9969 9977 9984 9946 9960 9970 9978 9984 9948 9961 9971 9979 9985 9949 9962 9972 9979 9985 9951 9963 9973 9980 9986 9952 9964 9974 9981 9986 3.0 3.1 3.2 3.3 3.4 9987 9990 9993 9995 9997 9987 9991 9993 9995 9997 9987 9991 9994 9995 9997 9988 9991 9994 9996 9997 9988 9992 9994 9996 9997 9989 9992 9994 9996 9997 9989 9992 9994 9996 9997 9989 9992 9995 9996 9997 9990 9993 9995 9996 9997 9990 9993 9995 9997 9998 How to Construct a Stem and Leaf Plot 20 How to Construct a Relative Frequency Histogram 27 How to Calculate Sample Quartiles 76 How to Calculate the Correlation Coefficient 106 How to Calculate the Regression Line 106 How to Calculate the Probability of an Event 130 The Difference between Mutually Exclusive and Independent Events 148 How to Use Table to Calculate Binomial Probabilities 182 How to Use Table to Calculate Poisson Probabilities 190 How to Use Table to Calculate Probabilities under the Standard Normal Curve 217 How to Calculate Binomial Probabilities Using the Normal Approximation 227 When the Sample Size is Large Enough to Use the Central Limit Theorem 253 Index of Applets on the CourseMate Web site CHAPTER Building a Dotplot applet Building a Histogram applet Flipping Fair Coins applet CHAPTER How Extreme Values Affect the Mean and Median applet Why Divide n Ϫ 1? Building a Box Plot applet How to Calculate Probabilities for the Sample Mean ෆx 255 How to Calculate Probabilities for the Sample Proportion pˆ 263 How to Estimate a Population Mean or Proportion 287 How to Choose the Sample Size 314 Rejection Regions, p-Values, and Conclusions 335 How to Calculate b 339 How to Decide Which Test to Use 408 How to Determine Whether My Calculations Are Accurate 437 How to Make Sure That My Calculations Are Correct 488 How to Determine the Appropriate Number of Degrees of Freedom 584, 589 CHAPTER Central Limit Theorem applet Normal Probabilities for Means applet CHAPTER Interpreting Confidence Intervals applet CHAPTER Large Sample Test of a Population Mean applet Power of a z-Test applet CHAPTER Tossing Dice applet Flipping Fair Coins applet Flipping Weighted Coins applet CHAPTER 10 Student’s t Probabilities applet Comparing t and z applet Small Sample Test of a Population Mean applet Two-Sample t Test: Independent Samples applet Chi-Square Probabilities applet F Probabilities applet CHAPTER Calculating Binomial Probabilities applet CHAPTER 11 F Probabilities applet CHAPTER Visualizing Normal Curves applet Normal Distribution Probabilities applet Normal Probabilities and z-Scores applet Normal Approximation to Binomial Probabilities applet CHAPTER 12 Method of Least Squares applet t Test for the Slope applet Exploring Correlation applet CHAPTER Building a Scatterplot applet Exploring Correlation applet How a Line Works applet CHAPTER 14 Goodness-of-Fit applet Chi-Square Test of Independence applet a ta TABLE Critical Values of t page 667 df t.100 t.050 t.025 t.010 t.005 df 3.078 1.886 1.638 1.533 1.476 6.314 2.920 2.353 2.132 2.015 12.706 4.303 3.182 2.776 2.571 31.821 6.965 4.541 3.747 3.365 63.657 9.925 5.841 4.604 4.032 10 1.440 1.415 1.397 1.383 1.372 1.943 1.895 1.860 1.833 1.812 2.447 2.365 2.306 2.262 2.228 3.143 2.998 2.896 2.821 2.764 3.707 3.499 3.355 3.250 3.169 10 11 12 13 14 15 1.363 1.356 1.350 1.345 1.341 1.796 1.782 1.771 1.761 1.753 2.201 2.179 2.160 2.145 2.131 2.718 2.681 2.650 2.624 2.602 3.106 3.055 3.012 2.977 2.947 11 12 13 14 15 16 17 18 19 20 1.337 1.333 1.330 1.328 1.325 1.746 1.740 1.734 1.729 1.725 2.120 2.110 2.101 2.093 2.086 2.583 2.567 2.552 2.539 2.528 2.921 2.898 2.878 2.861 2.845 16 17 18 19 20 21 22 23 24 25 1.323 1.321 1.319 1.318 1.316 1.721 1.717 1.714 1.711 1.708 2.080 2.074 2.069 2.064 2.060 2.518 2.508 2.500 2.492 2.485 2.831 2.819 2.807 2.797 2.787 21 22 23 24 25 26 27 28 29 ϱ 1.315 1.314 1.313 1.311 1.282 1.706 1.703 1.701 1.699 1.645 2.056 2.052 2.048 2.045 1.960 2.479 2.473 2.467 2.462 2.326 2.779 2.771 2.763 2.756 2.576 26 27 28 29 ϱ SOURCE: From “Table of Percentage Points of the t-Distribution,” Biometrika 32 (1941):300 Reproduced by permission of the Biometrika Trustees List of Applications Business and Economics Actuaries 166 Advertising campaigns 632 Airline occupancy rates 340 America’s market basket 392 Auto accidents 311 Auto insurance 56, 391, 455 Baseball bats 272 Bidding on construction jobs 455 Black jack 271 Brass rivets 271 Choosing a camera 545 Coal burning power plant 271 Coffee breaks 165 Coldstone Creamery 518 College textbooks 543 Construction projects 554 Consumer confidence 290 Consumer Price Index 98 Corporate profits 545 Cost of lumber 440, 444 Deli sales 260 Does college pay off? 340 Drilling oil wells 165 Economic forecasts 223 Education pays off 30 Electric cars 300 Flextime 340 Fortune 500 revenues 56 Gas mileage 453 Gasoline tax 48 Glare in rearview mirrors 453 Grant funding 150 Grocery costs 108 Hamburger meat 81, 222, 300, 340, 375 Health care reform 586 Hotel costs 290, 306, 346 Housing defaults 118 Housing prices 512, 513 How to choose a TV 108 Illegal Immigration 290, 317 Inspection lines 151 Interstate commerce 170 Landlines passe 351 Light bulbs 400 Line length 31 Lithium batteries 407 Loading grain 223 Lumber specs 271 Movie money 116 Multimedia kids 290 Nintendo’s Wii 57 Nuclear power plant 271 Operating expenses 316 Packaging hamburger meat 69 Paper strength 259 Property values 619, 626 Raisins 385 Rating tobacco leaves 643 Real estate prices 108 School workers 321 Service times 31 Shipping charges 166 Smart phones 120, 204, 480 Sports salaries 57 Starbucks 46, 48, 57, 528 Store brand vs name brand 652 Strawberries 494, 502, 513 Supermarket prices 636 Taste testing 351 Tax assessors 393 Tax audits 223 Teaching credentials 197 Telecommuting 588 Telemarketers 186 Timber tracts 70 Tire performance 569 Tuna fish 57, 71, 88, 374, 384, 408, 439 Utility bills in Southern California 63, 82 Vacation destinations 208 Water resistance in textiles 453 Where to shop 455 Whistle blowers 169 Worker error 156 Working spouses 173, 299 General Interest 100-meter run 132, 139 900 numbers 291 9-1-1 305 Aaron Rodgers 71, 117 Accident prone 194 Airport safety 193 Airport security 156 Armspan and height 494, 502 Art critics 642 Barry Bonds 91 Baseball fans 310 Baseball stats 519 Basketball tickets 320 Batting champions 31 Ben Roethlisberger 375 Birth order and college success 310 Birthday problem 151 Braking distances 222 Car colors 48, 186 Cellphone etiquette 239 Cheaper airfares 346 Cheating on taxes 157 Christmas trees 222 Comparing NFL quarterbacks 81, 385, 407, 615 Competitive running 642 Cramming 139 Creation 132 Defective computer chips 197 Defective equipment 165 Dieting 305 Dinner at Gerards 138 Drew Brees 513 Driving emergencies 69 Election 2012 16 Elevator capacities 222 Eyeglasses 131 Facebook 16, 99, 115 Fast food 188, 320 Food safety 602 Football strategies 157 Free time 98 Freestyle swimmers 385 Going to the moon 247 Golfing 152 Gourmet cooking 619, 626 GPAs 317 GRE scores 444 Hard hats 400 Hockey 518 Home security systems 186 How long is it? 493, 525 Human heights 222 Hunting season 317 Instrument precision 400 Insuring your diamonds 165 Itineraries 138 JFK assassination 587 Kobe and Lamar 152 M&Ms 98, 309, 355 Machine breakdowns 626 Major World Lakes 43 Man’s best friend 188, 351 Men on Mars 291 National Hockey League 187 Noise and stress 306, 346 Old Faithful 71 PGA 165 Phosphate mine 222 Playing poker 138 Presidential vetoes 44, 81 President’s kids 71 Professor Asimov 492, 501, 505 Rating political candidates 642 Red dye 393 Roulette 131, 170 RU texting? 164 Sandwich generation 591 Smoke detectors 151 Soccer injuries 152 Starbucks or Peets 151 SUVs 300 Tennis 165, 223, 642 Time on task 57 Tomatoes 259 Top 20 movies 32 Traffic control 626 Traffic problems 138 Vacation plans 138 What to wear 138 WNBA 138 Life Sciences Achilles tendon injuries 260, 341 Acid rain 299 Alzheimer’s disease 614 Archeological find 46, 63, 71, 386 Avocado research 525, 526 Baby’s sleeping position 356, 599 Back pain 187 Bacteria in water 194, 223, 259 Bees 418 Biomass 290 Biotin intake in chicks 565 Birth order and personality 56 Blood types 186 Body temperature and heart rate 518 Breathing rates 69, 223 Bulimia 375 Calcium 439 Calcium content 31 California whitefly 477 Cerebral blood flow 222 Chemical experiment 492 Chemotherapy 615 Chicago weather 186 Childhood obesity 350 Chirping crickets 108, 500, 505 Cholesterol 376 Clopidogel and aspirin 355 Color preferences in mice 187 Cotton versus cucumber 553 Cure for insomnia 351 Cure for the common cold 345 Deep-sea research 592 Digitalis and calcium uptake 454 Disinfectants 384 Dissolved O2 content 374, 385, 439, 615 Drug potency 400 E coli outbreaks 194 Early detection of breast cancer 350 Evolution 592 Excedrin or Tylenol 311 FDA testing 165 Fruit flies 132 Geothermal power 518 Gestation times and longevity 118, 501 Glucose tolerance 444 Good tasting medicine 637 Ground or air 393 Gulf oil spill 44 Hazardous waste 32, 117 Healthy eating 345 Healthy teeth 383, 392 Heart rate and exercise 632 Hormone therapy and Alzheimer’s Disease 355 Human body temperatures 48, 82, 260, 300, 306, 341,347 Hungry rats 291 Impurities 408 Invasive species 340 Jigsaw puzzles 626 Lead levels in blood 619 Lead levels in drinking water 345 Less red meat 317, 552 Lobsters 374, 517 Long-Term care 591 Measurement error 259 Medical diagnostics 157 Mercury concentration in dolphins 80, 568 Monkey business 139 Nematodes 524 Omega-3 Fats 247 Ore samples 70 pH in rainfall 317 pH levels in water 632 Physical fitness 479 Plant genetics 151, 350 Plant science 523 Polluted rain 317 Potassium levels 260 Potency of an antibiotic 340 Pulse rates 224 Purifying organic compounds 375 Rain and snow 120 Recovery rates 620 Recurring illness 30 Recycling 229, 265 Red blood cell count 31, 398 Runners and cyclists 384, 392, 408 San Andreas Fault 290 Screening tests 157 Seed treatments 197 Selenium 305, 317 Shade or sun? 419 Slash pine seedlings 454 Sleep deprivation 492 Smoking and lung capacity 374 Sunflowers 222 Survival times 29, 70, 82 Swampy sites 438, 443, 632 Sweet potato whitefly 350 Tai Chi and fibromyalgia 247, 355 Taste test for PTC 188 Titanium 385 Toxic chemicals 637 Weights of turtles 615 Whitefly infestation 187 Social Sciences Achievement scores 553 Achievement tests 493 Adolescents and social stress 359 American Presidents 31 Animation helps 464 Anxious infants 587 Back to work 17 Biology skills 306 Books or iPads? 424 Boomers, Xers and Millennial Men 358 Catching a cold 310 Choosing a mate 152 Disabled students 108 Discovery-based teaching 599 Drug offenders 151 Drug testing 150 Eye movement 615 Faculty salaries 240, 259 Gender bias 139, 165, 197 Generation Next 311, 358 Graduate teaching assistants 601 Hospital survey 138 Household size 99 Images and word recall 627 Intensive care 193 Jury duty 131 Laptops and learning 502, 506 Math and art 649 Medical bills 187 Memory experiments 393 Midterm Scores 119 Music in the workplace 394 Native American youth 247 No pass-no play rule for athletics 157 Organized religion 30 Political corruption 317 Preschool 30 Racial bias 247 Reducing hostility 438 SAT scores 186, 407 Smoking and cancer 151 Social Security numbers 70 Social skills training 517, 643 Spending patterns 587 Starting salaries 305, 346 Student ratings 642 Teaching biology 305 Test interviews 493 Union Yes! 310 Violent crime 156 Want to be President? 16 ... understanding and interpretation of statistical results In this edition, students will be able to use computers for both standard statistical analyses and as a tool for reinforcing and visualizing statistical... statistics is all about and how it can be used as a tool in their particular area of application The secret to the success of Introduction to Probability and Statistics is its ability to blend the old... consumer and citizen, you need to understand how statistics are used and misused in our daily lives THE SECRET TO OUR SUCCESS The first college course in introductory statistics that we ever took