Introductory statistics, 10th global edition

Introductory STATISTICS 10TH EDITION GLOBAL EDITION This page intentionally left blank Introductory STATISTICS 10TH EDITION GLOBAL EDITION Neil A Weiss, Ph.D School of Mathematical and Statistical Sciences Arizona State University Biographies by Carol A Weiss Boston Columbus Indianapolis New York San Francisco Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Editor in Chief: Deirdre Lynch Senior Acquisitions Editor: Suzanna Bainbridge Editorial Assistants: Justin Billing and Salena Casha Program Team Lead: Marianne Stepanian Program Manager: Chere Bemelmans Project Team Lead: Christina Lepre Acquisitions Editor, Global Edition: Sourabh Maheshwari Project Editor, Global Edition: Radhika Raheja Project Manager: Shannon Steed Senior Designer: Barbara T Atkinson Manager, Multimedia Production: Christine Stavrou Multimedia Producer: Stephanie Green Software Development: Bob Carroll, Marty Wright Senior Marketing Manager: Erin Kelly Marketing Coordinator: Kathleen DeChavez Senior Manufacturing Controller, Global Edition: Trudy Kimber Senior Author Support/Technology Specialist: Joe Vetere Rights and Permissions Advisor: Diahanne Lucas Senior Procurement Specialist: Carol Melville Media Production Manager, Global Edition: Vikram Kumar Text Design: Rokusek Design, Inc Production Coordination, Composition, and Illustrations: Aptara Corporation Cover Photo Credit: Acknowledgements of third party content appear on page C-1, which constitutes an extension of this copyright page Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: www.pearsonglobaleditions.com C Pearson Education Limited 2017 The rights of Neil A Weiss to be identified as the author(s) of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988 Authorized adaptation from the United States edition, Introductory Statistics, 10th edition, ISBN 9780321989178, by Neil A Weiss published by Pearson Education C 2017 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6−10 Kirby Street, London EC1N 8TS All trademarks used herein are the property of their respective owners The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library 10 ISBN 10: 1292099720 ISBN 13: 9781292099729 Typeset byAptara Printed and bound in Malaysia About the Author Neil A Weiss received his Ph.D from UCLA and subsequently accepted an assistant professor position at Arizona State University (ASU), where he was ultimately promoted to the rank of full professor Dr Weiss has taught statistics, probability, and mathematics—from the freshman level to the advanced graduate level—for more than 30 years In recognition of his excellence in teaching, Dr Weiss received the Dean’s Quality Teaching Award from the ASU College of Liberal Arts and Sciences He has also been runner-up twice for the Charles Wexler Teaching Award in the ASU School of Mathematical and Statistical Sciences Dr Weiss’s comprehensive knowledge and experience ensures that his texts are mathematically and statistically accurate, as well as pedagogically sound In addition to his numerous research publications, Dr Weiss is the author of A Course in Probability (Addison-Wesley, 2006) He has also authored or coauthored books in finite mathematics, statistics, and real analysis, and is currently working on a new book on applied regression analysis and the analysis of variance His texts— well known for their precision, readability, and pedagogical excellence—are used worldwide Dr Weiss is a pioneer of the integration of statistical software into textbooks and the classroom, first providing such integration in the book Introductory Statistics (AddisonWesley, 1982) He and Pearson Education continue that spirit to this day In his spare time, Dr Weiss enjoys walking, studying and practicing meditation, and playing hold’em poker He is married and has two sons Dedicated to Aaron and Greg Contents Preface 11 Supplements 16 Technology Resources 17 Data Sources 19 PART I Introduction C H A P T E R The Nature of Statistics 23 Case Study: Top Films of All Time 23 • 1.1 Statistics Basics 24 1.2 Simple Random Sampling 31 • 1.3 Other ∗ • Sampling Designs 39 1.4 Experimental Designs∗ 47 Chapter in Review 53 • Review Problems 53 • Focusing on Data Analysis 56 • Case Study Discussion 56 • Biography 56 P A R T II Descriptive Statistics C H A P T E R Organizing Data 58 Case Study: World’s Richest People 58 • 2.1 Variables and Data 59 2.2 Organizing Qualitative Data 64 • 2.3 Organizing Quantitative Data 74 • 2.4 Distribution Shapes 97 • 2.5 Misleading Graphs∗ 105 Chapter in Review 109 • Review Problems 110 • Focusing on Data Analysis 113 • Case Study Discussion 113 • Biography 114 C H A P T E R Descriptive Measures 115 Case Study: The Beatles’ Song Length 115 3.1 Measures of Center 116 • 3.2 Measures of Variation 127 • 3.3 Chebyshev’s Rule and the Empirical Rule∗ 139 • 3.4 The Five-Number Summary; Boxplots 147 • 3.5 Descriptive Measures for Populations; Use of Samples 139 Chapter in Review 172 • Review Problems 172 • Focusing on Data Analysis 175 • Case Study Discussion 176 • Biography 176 ∗ Indicates optional material CONTENTS P A R T III Probability, Random Variables, and Sampling Distributions C H A P T E R Probability Concepts 178 Case Study: Texas Hold’em 178 4.1 Probability Basics 179 • 4.2 Events 186 • 4.3 Some Rules of Probability 195 • 4.4 Contingency Tables; Joint and Marginal Probabilities∗ 201 • 4.5 Conditional Probability∗ 207 • 4.6 The Multiplication Rule; Independence∗ 215 • 4.7 Bayes’s Rule∗ 223 • 4.8 Counting Rules∗ 230 Chapter in Review 240 • Review Problems 240 • Focusing on Data Analysis 243 • Case Study Discussion 244 • Biography 244 C H A P T E R Discrete Random Variables∗ 245 Case Study: Aces Wild on the Sixth at Oak Hill 245 5.1 Discrete Random Variables and Probability Distributions∗ 246 • 5.2 The Mean and Standard Deviation of a Discrete Random Variable∗ 253 • 5.3 The Binomial Distribution∗ 260 • 5.4 The Poisson Distribution∗ 273 Chapter in Review 280 • Review Problems 281 • Focusing on Data Analysis 283 • Case Study Discussion 283 • Biography 283 C H A P T E R The Normal Distribution 284 Case Study: Chest Sizes of Scottish Militiamen 284 6.1 Introducing Normally Distributed Variables 285 • 6.2 Areas under the Standard Normal Curve 296 • 6.3 Working with Normally Distributed Variables 302 • 6.4 Assessing Normality; Normal Probability Plots 312 • 6.5 Normal Approximation to the Binomial Distribution∗ 296 Chapter in Review 325 • Review Problems 326 • Focusing on Data Analysis 328 • Case Study Discussion 328 • Biography 328 C H A P T E R The Sampling Distribution of the Sample Mean 329 Case Study: The Chesapeake and Ohio Freight Study 329 7.1 Sampling Error; the Need for Sampling Distributions 330 • 7.2 The Mean and Standard Deviation of the Sample Mean 335 • 7.3 The Sampling Distribution of the Sample Mean 341 Chapter in Review 348 • Review Problems 349 • Focusing on Data Analysis 351 • Case Study Discussion 351 • Biography 351 P A R T IV Inferential Statistics C H A P T E R Confidence Intervals for One Population Mean 353 Case Study: Bank Robberies: A Statistical Analysis 353 8.1 Estimating a Population Mean 354 • 8.2 Confidence Intervals for One Population Mean When σ Is Known 360 • 8.3 Confidence Intervals for One Population Mean When σ Is Unknown 374 Chapter in Review 385 • Review Problems 385 • Focusing on Data Analysis 388 • Case Study Discussion 388 • Biography 388 ∗ Indicates optional material CONTENTS C H A P T E R Hypothesis Tests for One Population Mean 389 Case Study: Gender and Sense of Direction 389 9.1 The Nature of Hypothesis Testing 390 • 9.2 Critical-Value Approach to Hypothesis Testing 398 • 9.3 P-Value Approach to Hypothesis Testing 403 • 9.4 Hypothesis Tests for One Population Mean When σ Is Known 409 • 9.5 Hypothesis Tests for One Population Mean When σ Is Unknown 421 • 9.6 The Wilcoxon Signed-Rank Test∗ 429 • 9.7 Type II Error Probabilities; Power∗ 444 • 9.8 Which Procedure Should Be Used?∗∗ Chapter in Review 455 • Review Problems 455 • Focusing on Data Analysis 459 • Case Study Discussion 459 • Biography 459 C H A P T E R 10 Inferences for Two Population Means 460 Case Study: Dexamethasone Therapy and IQ 460 10.1 The Sampling Distribution of the Difference between Two Sample Means for Independent Samples 461 • 10.2 Inferences for Two Population Means, Using Independent Samples: Standard Deviations Assumed Equal 468 • 10.3 Inferences for Two Population Means, Using Independent Samples: Standard Deviations Not Assumed Equal 480 • 10.4 The Mann–Whitney Test∗ 492 • 10.5 Inferences for Two Population Means, Using Paired Samples 507 • 10.6 The Paired Wilcoxon Signed-Rank Test∗ 520 • 10.7 Which Procedure Should Be Used?∗∗ Chapter in Review 530 • Review Problems 531 • Focusing on Data Analysis 533 • Case Study Discussion 533 • Biography 533 C H A P T E R 11 Inferences for Population Standard Deviations∗ 535 Case Study: Speaker Woofer Driver Manufacturing 535 11.1 Inferences for One Population Standard Deviation∗ 536 • 11.2 Inferences for Two Population Standard Deviations, Using Independent Samples∗ 549 Chapter in Review 563 • Review Problems 563 • Focusing on Data Analysis 565 • Case Study Discussion 565 • Biography 565 C H A P T E R 12 Inferences for Population Proportions 566 Case Study: Arrested Youths 566 12.1 Confidence Intervals for One Population Proportion 567 • 12.2 Hypothesis Tests for One Population Proportion 579 • 12.3 Inferences for Two Population Proportions 583 Chapter in Review 595 • Review Problems 595 • Focusing on Data Analysis 597 • Case Study Discussion 597 • Biography 597 C H A P T E R 13 Chi-Square Procedures 598 Case Study: Eye and Hair Color 598 13.1 The Chi-Square Distribution 599 • 13.2 Chi-Square Goodness-of-Fit Test 600 • 13.3 Contingency Tables; Association 609 • 13.4 Chi-Square Independence Test 619 • 13.5 Chi-Square Homogeneity Test 628 Chapter in Review 635 • Review Problems 636 • Focusing on Data Analysis 639 • Case Study Discussion 639 • Biography 639 ∗ Indicates optional material ∗∗ Indicates optional material on the WeissStats site CONTENTS PART V Regression, Correlation, and ANOVA C H A P T E R 14 Descriptive Methods in Regression and Correlation 640 Case Study: Healthcare: Spending and Outcomes 640 14.1 Linear Equations with One Independent Variable 641 • 14.2 The Regression Equation 646 • 14.3 The Coefficient of Determination 660 • 14.4 Linear Correlation 667 Chapter in Review 675 • Review Problems 676 • Focusing on Data Analysis 677 • Case Study Discussion 678 • Biography 678 C H A P T E R 15 Inferential Methods in Regression and Correlation 679 Case Study: Shoe Size and Height 679 15.1 The Regression Model; Analysis of Residuals 680 • 15.2 Inferences for the Slope of the Population Regression Line 692 • 15.3 Estimation and Prediction 700 • 15.4 Inferences in Correlation 710 • 15.5 Testing for Normality∗∗ Chapter in Review 716 • Review Problems 716 • Focusing on Data Analysis 718 • Case Study Discussion 718 • Biography 719 C H A P T E R 16 Analysis of Variance (ANOVA) 720 Case Study: Self-Perception and Physical Activity 720 16.1 The F-Distribution 721 • 16.2 One-Way ANOVA: The Logic 723 • 16.3 One-Way ANOVA: The Procedure 729 • 16.4 Multiple Comparisons∗ 742 • 16.5 The Kruskal–Wallis Test∗ 750 Chapter in Review 760 • Review Problems 760 • Focusing on Data Analysis 762 • Case Study Discussion 763 • Biography 763 P A R T VI Multiple Regression and Model Building; Experimental Design and ANOVA∗∗ M O D U L E A Multiple Regression Analysis A-0 Case Study: Automobile Insurance Rates A-0 A.1 The Multiple Linear Regression Model A-1 • A.2 Estimation of the Regression Parameters A-6 • A.3 Inferences Concerning the Utility of the Regression Model A-21 • A.4 Inferences Concerning the Utility of Particular Predictor Variables A-31 • A.5 Confidence Intervals for Mean Response; Prediction Intervals for Response A-37 • A.6 Checking Model Assumptions and Residual Analysis A-47 Module in Review A-59 • Review Problems A-59 • Focusing on Data Analysis A-62 • Case Study Discussion A-63 • Answers to Selected Exercises A-65 • Index A-68 M O D U L E B Model Building in Regression B-0 Case Study: Automobile Insurance Rates—Revisited B-0 B.1 Transformations to Remedy Model Violations B-1 • B.2 Polynomial Regression Model B-32 • B.3 Qualitative Predictor Variables B-64 • ∗ Indicates optional material ∗∗ Indicates optional material on the WeissStats site TABLE IV Values of t ␣ t␣ NOTE: See the version of Table IV in Appendix A for additional values of t df t 0.10 t 0.05 t 0.025 t 0.01 t 0.005 df 3.078 1.886 1.638 1.533 6.314 2.920 2.353 2.132 12.706 4.303 3.182 2.776 31.821 6.965 4.541 3.747 63.657 9.925 5.841 4.604 1.476 1.440 1.415 1.397 1.383 2.015 1.943 1.895 1.860 1.833 2.571 2.447 2.365 2.306 2.262 3.365 3.143 2.998 2.896 2.821 4.032 3.707 3.499 3.355 3.250 10 11 12 13 14 1.372 1.363 1.356 1.350 1.345 1.812 1.796 1.782 1.771 1.761 2.228 2.201 2.179 2.160 2.145 2.764 2.718 2.681 2.650 2.624 3.169 3.106 3.055 3.012 2.977 10 11 12 13 14 15 16 17 18 19 1.341 1.337 1.333 1.330 1.328 1.753 1.746 1.740 1.734 1.729 2.131 2.120 2.110 2.101 2.093 2.602 2.583 2.567 2.552 2.539 2.947 2.921 2.898 2.878 2.861 15 16 17 18 19 20 21 22 23 24 1.325 1.323 1.321 1.319 1.318 1.725 1.721 1.717 1.714 1.711 2.086 2.080 2.074 2.069 2.064 2.528 2.518 2.508 2.500 2.492 2.845 2.831 2.819 2.807 2.797 20 21 22 23 24 25 26 27 28 29 1.316 1.315 1.314 1.313 1.311 1.708 1.706 1.703 1.701 1.699 2.060 2.056 2.052 2.048 2.045 2.485 2.479 2.473 2.467 2.462 2.787 2.779 2.771 2.763 2.756 25 26 27 28 29 30 35 40 50 60 1.310 1.306 1.303 1.299 1.296 1.697 1.690 1.684 1.676 1.671 2.042 2.030 2.021 2.009 2.000 2.457 2.438 2.423 2.403 2.390 2.750 2.724 2.704 2.678 2.660 30 35 40 50 60 70 80 90 100 1000 2000 1.294 1.292 1.291 1.290 1.282 1.282 1.667 1.664 1.662 1.660 1.646 1.646 1.994 1.990 1.987 1.984 1.962 1.961 2.381 2.374 2.369 2.364 2.330 2.328 2.648 2.639 2.632 2.626 2.581 2.578 70 80 90 100 1000 2000 1.282 1.645 1.960 2.326 2.576 z 0.10 z 0.05 z 0.025 z 0.01 z 0.005 TABLE II Second decimal place in z Areas under the standard normal curve 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0.00 z 3.9 3.8 3.7 3.6 3.5 † z 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0002 0.0002 0.0000 0.0001 0.0001 0.0002 0.0002 0.0002 0.0003 0.0005 0.0007 0.0010 0.0003 0.0004 0.0005 0.0007 0.0010 0.0003 0.0004 0.0005 0.0008 0.0011 0.0003 0.0004 0.0006 0.0008 0.0011 0.0003 0.0004 0.0006 0.0008 0.0011 0.0003 0.0004 0.0006 0.0008 0.0012 0.0003 0.0004 0.0006 0.0009 0.0012 0.0003 0.0005 0.0006 0.0009 0.0013 0.0003 0.0005 0.0007 0.0009 0.0013 0.0003 0.0005 0.0007 0.0010 0.0013 3.4 3.3 3.2 3.1 3.0 0.0014 0.0019 0.0026 0.0036 0.0048 0.0014 0.0020 0.0027 0.0037 0.0049 0.0015 0.0021 0.0028 0.0038 0.0051 0.0015 0.0021 0.0029 0.0039 0.0052 0.0016 0.0022 0.0030 0.0040 0.0054 0.0016 0.0023 0.0031 0.0041 0.0055 0.0017 0.0023 0.0032 0.0043 0.0057 0.0018 0.0024 0.0033 0.0044 0.0059 0.0018 0.0025 0.0034 0.0045 0.0060 0.0019 0.0026 0.0035 0.0047 0.0062 2.9 2.8 2.7 2.6 2.5 0.0064 0.0084 0.0110 0.0143 0.0183 0.0066 0.0087 0.0113 0.0146 0.0188 0.0068 0.0089 0.0116 0.0150 0.0192 0.0069 0.0091 0.0119 0.0154 0.0197 0.0071 0.0094 0.0122 0.0158 0.0202 0.0073 0.0096 0.0125 0.0162 0.0207 0.0075 0.0099 0.0129 0.0166 0.0212 0.0078 0.0102 0.0132 0.0170 0.0217 0.0080 0.0104 0.0136 0.0174 0.0222 0.0082 0.0107 0.0139 0.0179 0.0228 2.4 2.3 2.2 2.1 2.0 0.0233 0.0294 0.0367 0.0455 0.0559 0.0239 0.0301 0.0375 0.0465 0.0571 0.0244 0.0307 0.0384 0.0475 0.0582 0.0250 0.0314 0.0392 0.0485 0.0594 0.0256 0.0322 0.0401 0.0495 0.0606 0.0262 0.0329 0.0409 0.0505 0.0618 0.0268 0.0336 0.0418 0.0516 0.0630 0.0274 0.0344 0.0427 0.0526 0.0643 0.0281 0.0351 0.0436 0.0537 0.0655 0.0287 0.0359 0.0446 0.0548 0.0668 1.9 1.8 1.7 1.6 1.5 0.0681 0.0823 0.0985 0.1170 0.1379 0.0694 0.0838 0.1003 0.1190 0.1401 0.0708 0.0853 0.1020 0.1210 0.1423 0.0721 0.0869 0.1038 0.1230 0.1446 0.0735 0.0885 0.1056 0.1251 0.1469 0.0749 0.0901 0.1075 0.1271 0.1492 0.0764 0.0918 0.1093 0.1292 0.1515 0.0778 0.0934 0.1112 0.1314 0.1539 0.0793 0.0951 0.1131 0.1335 0.1562 0.0808 0.0968 0.1151 0.1357 0.1587 1.4 1.3 1.2 1.1 1.0 0.1611 0.1867 0.2148 0.2451 0.2776 0.1635 0.1894 0.2177 0.2483 0.2810 0.1660 0.1922 0.2206 0.2514 0.2843 0.1685 0.1949 0.2236 0.2546 0.2877 0.1711 0.1977 0.2266 0.2578 0.2912 0.1736 0.2005 0.2296 0.2611 0.2946 0.1762 0.2033 0.2327 0.2643 0.2981 0.1788 0.2061 0.2358 0.2676 0.3015 0.1814 0.2090 0.2389 0.2709 0.3050 0.1841 0.2119 0.2420 0.2743 0.3085 0.9 0.8 0.7 0.6 0.5 0.3121 0.3483 0.3859 0.4247 0.4641 0.3156 0.3520 0.3897 0.4286 0.4681 0.3192 0.3557 0.3936 0.4325 0.4721 0.3228 0.3594 0.3974 0.4364 0.4761 0.3264 0.3632 0.4013 0.4404 0.4801 0.3300 0.3669 0.4052 0.4443 0.4840 0.3336 0.3707 0.4090 0.4483 0.4880 0.3372 0.3745 0.4129 0.4522 0.4920 0.3409 0.3783 0.4168 0.4562 0.4960 0.3446 0.3821 0.4207 0.4602 0.5000 0.4 0.3 0.2 0.1 0.0 † For z 3.90, the areas are 0.0000 to four decimal places TABLE II (cont.) Second decimal place in z Areas under the standard normal curve z † z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.1 0.2 0.3 0.4 0.5000 0.5398 0.5793 0.6179 0.6554 0.5040 0.5438 0.5832 0.6217 0.6591 0.5080 0.5478 0.5871 0.6255 0.6628 0.5120 0.5517 0.5910 0.6293 0.6664 0.5160 0.5557 0.5948 0.6331 0.6700 0.5199 0.5596 0.5987 0.6368 0.6736 0.5239 0.5636 0.6026 0.6406 0.6772 0.5279 0.5675 0.6064 0.6443 0.6808 0.5319 0.5714 0.6103 0.6480 0.6844 0.5359 0.5753 0.6141 0.6517 0.6879 0.5 0.6 0.7 0.8 0.9 0.6915 0.7257 0.7580 0.7881 0.8159 0.6950 0.7291 0.7611 0.7910 0.8186 0.6985 0.7324 0.7642 0.7939 0.8212 0.7019 0.7357 0.7673 0.7967 0.8238 0.7054 0.7389 0.7704 0.7995 0.8264 0.7088 0.7422 0.7734 0.8023 0.8289 0.7123 0.7454 0.7764 0.8051 0.8315 0.7157 0.7486 0.7794 0.8078 0.8340 0.7190 0.7517 0.7823 0.8106 0.8365 0.7224 0.7549 0.7852 0.8133 0.8389 1.0 1.1 1.2 1.3 1.4 0.8413 0.8643 0.8849 0.9032 0.9192 0.8438 0.8665 0.8869 0.9049 0.9207 0.8461 0.8686 0.8888 0.9066 0.9222 0.8485 0.8708 0.8907 0.9082 0.9236 0.8508 0.8729 0.8925 0.9099 0.9251 0.8531 0.8749 0.8944 0.9115 0.9265 0.8554 0.8770 0.8962 0.9131 0.9279 0.8577 0.8790 0.8980 0.9147 0.9292 0.8599 0.8810 0.8997 0.9162 0.9306 0.8621 0.8830 0.9015 0.9177 0.9319 1.5 1.6 1.7 1.8 1.9 0.9332 0.9452 0.9554 0.9641 0.9713 0.9345 0.9463 0.9564 0.9649 0.9719 0.9357 0.9474 0.9573 0.9656 0.9726 0.9370 0.9484 0.9582 0.9664 0.9732 0.9382 0.9495 0.9591 0.9671 0.9738 0.9394 0.9505 0.9599 0.9678 0.9744 0.9406 0.9515 0.9608 0.9686 0.9750 0.9418 0.9525 0.9616 0.9693 0.9756 0.9429 0.9535 0.9625 0.9699 0.9761 0.9441 0.9545 0.9633 0.9706 0.9767 2.0 2.1 2.2 2.3 2.4 0.9772 0.9821 0.9861 0.9893 0.9918 0.9778 0.9826 0.9864 0.9896 0.9920 0.9783 0.9830 0.9868 0.9898 0.9922 0.9788 0.9834 0.9871 0.9901 0.9925 0.9793 0.9838 0.9875 0.9904 0.9927 0.9798 0.9842 0.9878 0.9906 0.9929 0.9803 0.9846 0.9881 0.9909 0.9931 0.9808 0.9850 0.9884 0.9911 0.9932 0.9812 0.9854 0.9887 0.9913 0.9934 0.9817 0.9857 0.9890 0.9916 0.9936 2.5 2.6 2.7 2.8 2.9 0.9938 0.9953 0.9965 0.9974 0.9981 0.9940 0.9955 0.9966 0.9975 0.9982 0.9941 0.9956 0.9967 0.9976 0.9982 0.9943 0.9957 0.9968 0.9977 0.9983 0.9945 0.9959 0.9969 0.9977 0.9984 0.9946 0.9960 0.9970 0.9978 0.9984 0.9948 0.9961 0.9971 0.9979 0.9985 0.9949 0.9962 0.9972 0.9979 0.9985 0.9951 0.9963 0.9973 0.9980 0.9986 0.9952 0.9964 0.9974 0.9981 0.9986 3.0 3.1 3.2 3.3 3.4 0.9987 0.9990 0.9993 0.9995 0.9997 0.9987 0.9991 0.9993 0.9995 0.9997 0.9987 0.9991 0.9994 0.9995 0.9997 0.9988 0.9991 0.9994 0.9996 0.9997 0.9988 0.9992 0.9994 0.9996 0.9997 0.9989 0.9992 0.9994 0.9996 0.9997 0.9989 0.9992 0.9994 0.9996 0.9997 0.9989 0.9992 0.9995 0.9996 0.9997 0.9990 0.9993 0.9995 0.9996 0.9997 0.9990 0.9993 0.9995 0.9997 0.9998 3.5 3.6 3.7 3.8 3.9 0.9998 0.9998 0.9999 0.9999 1.0000† 0.9998 0.9998 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 For z 3.90, the areas are 1.0000 to four decimal places This page intentionally left blank Indexes for Case Studies & Biographical Sketches Chapter 10 11 12 13 14 15 16 Case Study Biographical Sketch Top Films of All Time 1, 34 World’s Richest People 36, 91 The Beatles’ Song Length 93, 154 Texas Hold’em 156, 222 Aces Wild on the Sixth at Oak Hill 223, 261 Chest Sizes of Scottish Militiamen 262, 306 The Chesapeake and Ohio Freight Study 307, 329 Bank Robberies: A Statistical Analysis 331, 366 Gender and Sense of Direction 367, 437 Dexamethasone Therapy and IQ 438, 511 Speaker Woofer Driver Manufacturing 513, 543 Arrested Youths 544, 575 Eye and Hair Color 576, 617 Healthcare: Spending and Outcomes 618, 656 Shoe Size and Height 657, 696 Self-Perception and Physical Activity 698, 741 Florence Nightingale 34 Adolphe Quetelet 92 John Tukey 154 Andrei Kolmogorov 222 James Bernoulli 261 Carl Friedrich Gauss 306 Pierre-Simon Laplace 329 William Gosset 366 Jerzy Neyman 437 Gertrude Cox 511 W Edwards Deming 543 Abraham de Moivre 575 Karl Pearson 617 Adrien Legendre 656 Sir Francis Galton 697 Sir Ronald Fisher 741 Index Adjacent values, 153 Alternative hypothesis, 390 choice of, 391 Analysis of residuals, 684 Analysis of variance, 720 one way, 723 ANOVA, see Analysis of variance Approximately normally distributed, 288 Assessing normality, 313 Associated variables, 612 Association, 611, 612 and causation, 624 hypothesis test for, 622 At least, 190 At most, 190 At random, 180 Back-to-back stem-and-leaf diagram, 494 Bar chart, 67 by computer, 71 procedure for constructing, 68 Bar graph segmented, 612 Basic counting rule, 230, 231 Basic principle of counting, see Basic counting rule Bayes’s rule, 223, 226 Bayes, Thomas, 223 Bell-shaped distribution, 99 Bernoulli trials, 261 and binomial coefficients, 263 Bernoulli, James biographical sketch, 283 Bias nonresponse, 39 response, 39 in sample surveys, 35 in samples, 39 undercoverage, 39 Biased estimator, 341, 355 Bimodal distribution, 98 Binomial coefficients, 260 and Bernoulli trials, 263 Binomial distribution, 261, 264, 319 as an approximation to the hypergeometric distribution, 268 by computer, 268 normal approximation to, 318 Poisson approximation to, 276 procedure for approximating by a normal distribution, 321 shape of, 266 Binomial probability formula, 264 procedure for finding, 264 Binomial probability tables, 266 Binomial random variable, 264 mean of, 267 standard deviation of, 267 Bins, 74 Bivariate data, 96, 201, 609 quantitative, 646 Bivariate quantitative data, 646 Bootstrap confidence intervals for one population mean, 384 Bootstrap distribution, 384 Box-and-whisker diagram, 153 Boxplot, 153 by computer, 157 Categorical variable, 59 Categories, 74 Cells of a contingency table, 202, 610 Census, 31 Census data, 100 Central limit theorem, 343 Certain event, 182 Chebyshev’s rule, 139 use in estimating relative standing, 171 χα2 , 537, 599 Chi-square curve, 536, 599 Chi-square curves basic properties of, 536, 599 Chi-square distribution, 536, 599 for a goodness-of-fit test, 602 for a homogeneity test, 629 for an independence test, 621 Chi-square goodness-of-fit test, 600, 603 by computer, 605 Chi-square homogeneity test, 628, 630 by computer, 624 Chi-square independence test, 619, 622 by computer, 624 concerning the assumptions for, 624 distribution of test statistic for, 621 χ -interval procedure for one population standard deviation, 543 Chi-square procedures, 598 Chi-square table use of, 537, 599 χ -test for one population standard deviation, 540 CI, 356 Class limits, 75 Class mark, 76 Class midpoint, 77 Class width, 76, 77 Classes, 74 choosing, 78, 95 cutpoint grouping, 76 limit grouping, 75 single-value, 74 Cluster sampling, 40 procedure for implementing, 40 Cochran, W G., 532, 534, 603, 622 Coefficient of determination, 661 by computer, 664 interpretation of, 661 relation to linear correlation coefficient, 670 Combination, 234 Combinations rule, 235 Complement, 188 Complementation rule, 196 Completely randomized design, 49 Conditional distribution, 611, 680, 681 by computer, 614 Conditional mean, 680, 681 Conditional mean t-interval procedure, 702 Conditional probability, 207 definition of, 207 rule for, 210 Conditional probability distribution, 214 Conditional probability rule, 210 Conditional standard deviation, 681 Confidence interval, 356 length of, 364 relation to hypothesis testing, 417, 475 Confidence interval for a conditional mean in regression, 702 Confidence interval for the difference between two population means by computer for independent samples, and normal populations or large samples, 485 by computer for independent samples, normal populations or large samples, and equal but unknown standard deviations, 475 by computer for a paired sample, and normal differences or a large sample, 514 I-1 I-2 INDEX Confidence interval for the difference between two population means (cont.) independent samples, and normal populations or large samples, 484 independent samples, normal populations or large samples, and equal but unknown standard deviations, 474 nonpooled t-interval procedure, 484 in one-way analysis of variance, 742 paired sample, and normal differences or large sample, 513 paired t-interval procedure, 513 pooled t-interval procedure, 474 Confidence interval for the difference between two population proportions, 588 by computer for large and independent samples, 590 two-proportions plus-four z-interval procedure, 589 Confidence interval for one population mean by computer in regression, 706 by computer when σ is known, 368 by computer when σ is unknown, 380 in one-way analysis of variance, 742 in regression, 702 σ known, 361 σ unknown, 377 Confidence interval for one population proportion, 570 by computer, 573 one-proportion plus-four z-interval procedure, 573, 578 Confidence interval for one population standard deviation, 543 by computer, 544 Confidence interval for the ratio of two population standard deviations, 555 by computer, 557 Confidence interval for the slope of a population regression line, 696 by computer, 697 Confidence intervals relation to hypotheses tests, 417 Confidence level, 356, 365 and accuracy, 365 family, 742 individual, 742 and margin of error, 365 Confidence-interval estimate, 355, 356 Contingency table, 96, 201, 609 by computer, 613 Continuous data, 60 Continuous variable, 59, 60 Control, 48 Control group, 48 Correction for continuity, 321 Correlation, 640 of events, 214 rank, 675 Correlation t-test, 710, 711 Count of a class, 64 Counting rules, 230 application to probability, 236 basic counting rule, 230, 231 combinations rule, 235 permutations rule, 233 special permutations rule, 234 Cox, Gertrude Mary biographical sketch, 533 Critical values, 400 obtaining, 401 use as a decision criterion in a hypothesis test, 400 Critical-value approach to hypothesis testing, 398 Cumulative frequency, 96 Cumulative probability, 266, 307 inverse, 308 Cumulative relative frequency, 96 Curves density, 285 Curvilinear regression, 654 Cutpoint grouping, 76 terms used in, 77 Data, 60 bivariate, 96, 201, 609 continuous, 60 discrete, 60 grouping of, 74 population, 100 qualitative, 60 quantitative, 60 sample, 100 univariate, 96, 201, 609 Data analysis a fundamental principle of, 362 Data classification and the choice of a statistical method, 61 Data set, 60 Deciles, 147 Degrees of freedom, 375 for an F-curve, 549, 721 Degrees of freedom for the denominator, 549, 721 Degrees of freedom for the numerator, 549, 721 Deming, W Edwards biographical sketch, 565 de Moivre, Abraham, 318 biographical sketch, 597 Density curves, 285 basic properties of, 285 Dependent events, 218 Descriptive measure resistant, 119 Descriptive measures, 115 of center, 116 of central tendency, 116 of spread, 127 of variation, 127 Descriptive statistics, 24, 25 Designed experiment, 27 Deviations from the mean, 128 Discrete data, 60 Discrete random variable, 246 mean of, 254 probability distribution of, 247 standard deviation of, 256 variance of, 256 Discrete random variables independence of, 259 Discrete variable, 59, 60 Distribution bell shaped, 98 bimodal, 98 conditional, 611, 680, 681 of a data set, 97 of the difference between the observed and predicted values of a response variable, 703 left skewed, 99 marginal, 612 mean, 681 multimodal, 98 normal, 284 of a population, 100 of the predicted value of a response variable, 701 rectangular, 98 reverse J shaped, 99 right skewed, 99 of a sample, 100 standard deviation, 681 symmetric, 98 triangular, 98 uniform, 98 unimodal, 98 of a variable, 100 Dotplot, 81 by computer, 87 procedure for constructing, 81 Double blinding, 53 Empirical rule, 140 for variables, 304 Equal-likelihood model, 182 Error, 648, 725 Error mean square, 725 Error sum of squares, 661 by computer, 664 computing formula for in regression, 663 in one-way analysis of variance, 725 in regression, 661 Estimator biased, 341, 355 unbiased, 341, 355 Event, 180, 186, 188 (A & B), 188 (A or B), 188 certain, 182 complement of, 188 given, 207 impossible, 182 (not E), 188 occurrence of, 187 INDEX Events, 186 correlation of, 214 dependent, 218 exhaustive, 223 independent, 214, 217, 218, 222 mutually exclusive, 191 negatively correlated, 214 notation and graphical display for, 188 positively correlated, 214 relationships among, 188 Excel, 35 Exhaustive events, 223 Expectation, 254 Expected frequencies, 601 for a chi-square goodness-of-fit test, 602 for a chi-square homogeneity test, 629 for a chi-square independence test, 621 Expected utility, 258 Expected value, 254 Experiment, 180 Experimental design, 47 principles of, 48 Experimental units, 48 Experimentation, 31 Explanatory variable, 652 Exploratory data analysis, 58, 177 Exponential distribution, 348 Exponentially distributed variable, 348 Extrapolation, 652 Factor, 48, 723 Factorials, 232, 260 Failure, 261 Fα , 549, 722 Family confidence level, 742 F-curve basic properties of, 549, 721 F-distribution, 549, 552, 721 Finite-population correction factor, 341 F-interval procedure for two population standard deviations, 555 First quartile, 147, 148 Fisher, Ronald, 27, 549, 721 biographical sketch, 763 Five-number summary, 151 f /N rule, 180 Focus database, 56 Frequency, 64 cumulative, 96 Frequency distribution of qualitative data, 64 procedure for constructing, 64 Frequency histogram, 78 Frequentist interpretation of probability, 182 F-statistic, 725 for comparing two population standard deviations, 552 in one-way analysis of variance, 729 F-table use of, 549, 722 F-test for two population standard deviations, 553 by computer, 557 Functions utility, 258 Fundamental counting rule, see Basic counting rule Galton, Francis, 639 biographical sketch, 719 Gauss, Carl Friedrich, 678 biographical sketch, 328 General addition rule, 197 General multiplication rule, 215 Geometric distribution, 273 Given event, 207 Goodness of fit chi-square test for, 603 Gosset, William Sealy, 375 biographical sketch, 388 Graph improper scaling of, 107 truncated, 106 Grouped data formulas for the sample mean and sample standard deviation, 138 Grouping choosing the method, 77 by computer, 85 guidelines for, 74 single-value, 74 Heteroscedasticity, 681 Histogram, 78 by computer, 86 frequency, 78 percent, 78 probability, 247 procedure for constructing, 78 relative frequency, 78 Homogeneous, 628 Homoscedasticity, 681 Hypergeometric distribution, 268, 272 binomial approximation to, 268 Hypothesis, 390 Hypothesis test, 389, 390 choosing the hypotheses, 390 logic of, 392 possible conclusions for, 396 relation to confidence interval, 417, 475 Hypothesis test for association of two variables of a population, 622 Hypothesis test for one population mean by computer for σ known, 417 by computer for σ unknown, 426 σ known, 410 σ unknown, 424 Wilcoxon signed-rank test, 434 Hypothesis test for one population proportion, 579 by computer, 581 I-3 Hypothesis test for one population standard deviation, 541 by computer, 544 non-robustness of, 540 Hypothesis test for a population linear correlation coefficient, 711 by computer, 713 Hypothesis test for several population means Kruskal–Wallis test, 753 one-way ANOVA test, 731, 732 Hypothesis test for the slope of a population regression line, 694 by computer, 697 Hypothesis test for two population means by computer for independent samples, and normal populations or large samples, 485 by computer for independent samples, normal populations or large samples, and equal but unknown standard deviations, 475 by computer for a paired sample, and normal differences or a large sample, 514 independent samples, and normal populations or large samples, 481 independent samples, normal populations or large samples, and equal but unknown standard deviations, 470 Mann–Whitney test, 497 nonpooled t-test, 481 paired sample, and normal differences or a large sample, 510 paired t-test, 510 paired Wilcoxon signed-rank test, 521 pooled t-test, 470 Hypothesis test for two population proportions, 586 by computer for large and independent samples, 590 Hypothesis test for two population standard deviations, 553 by computer, 557 non-robustness of, 554 Hypothesis test for the utility of a regression, 694 Hypothesis testing critical-value approach to, 398 P-value approach to, 403 relation to confidence intervals, 417 Hypothesis tests critical-value approach to, 402 P-value approach to, 408 relation to confidence intervals, 417 Impossible event, 182 Improper scaling, 107 Inclusive, 190 Independence, 217 for three events, 222 Independent, 217, 218 Independent events, 217, 218, 222 special multiplication rule for, 218 versus mutually exclusive events, 219 I-4 INDEX Independent random variables, 259 Independent samples, 461 Independent samples t-interval procedure, 484 Independent samples t-test, 481 pooled, 469 Independent simple random samples, 461 Indices, 120 Individual confidence level, 742 Inferences for two population means choosing between a pooled and a nonpooled t-procedure, 485 Inferential statistics, 24, 25 Influential observation, 652 Intercept, 643 Interquartile range, 150 Inverse cumulative probability, 308 IQR, 150 Joint percentage distribution, 206 Joint probability, 203 Joint probability distribution, 204 Kolmogorov, A N biographical sketch, 244 Kruskal–Wallis test, 750 alternate version of, 755 comparison with the one-way ANOVA test, 755 by computer, 755 method for dealing with ties, 750 procedure for, 753 test statistic for, 751 K -statistic, 751 Laplace, Pierre-Simon, 318 biographical sketch, 351 Law of averages, 255 Law of large numbers, 255 Leaf, 82 Least-squares criterion, 647, 648 Left-skewed distribution, 99 Left-tailed test, 391 rejection region for, 400 Legendre, Adrien-Marie biographical sketch, 678 Levels, 48, 723 Limit grouping, 75 terms used in, 76 Line, 641 Linear correlation coefficient, 667 and causation, 671 by computer, 672 computing formula for, 669 relation to coefficient of determination, 670 warning on the use of, 671 Linear equation with one independent variable, 641 Linear regression, 640 by computer, 654 warning on the use of, 654 Linearly correlated variables, 710 Linearly uncorrelated variables, 710 Lower class cutpoint, 76, 77 Lower class limit, 75, 76 Lower cutpoint of a class, 76, 77 Lower limit, 152 of a class, 75, 76 Mα , 494 Mann–Whitney table using, 494 Mann–Whitney test, 493, 497 alternate version of, 501 comparison with the pooled t-test, 500 by computer, 501 determining critical values for, 494 method for dealing with ties, 496 procedure for, 497 using a normal approximation, 506 Mann–Whitney–Wilcoxon test, 493 Margin of error, 357, 363–344 and confidence level, 365 for the estimate of μ, 364 for the estimate of p, 571 for the estimate of p1 − p2 , 594 for a one-mean t-interval, 380 and sample size, 366 Marginal distribution, 612 by computer, 614 Marginal probability, 203 Mark of a class, 76 Maximum error of the estimate, 370 Mean, 116 of a binomial random variable, 267 by computer, 121 conditional, 680 deviations from, 128 of a discrete random variable, 254 interpretation for random variables, 255 of a Poisson random variable, 275 of a population, see Population mean of a sample, see Sample mean trimmed, 119, 127 ¯ 336 of x, Mean of a random variable, 254 properties of, 259 Mean of a variable, 162 Measures of center, 116 comparison of, 118 Measures of central tendency, 116 Measures of spread, 127 Measures of variation, 127 Median, 117 by computer, 121 Minitab, 35 Modality, 98 Mode, 118 Modified boxplot, 153 Multimodal distributions, 98 Multiple comparisons Tukey method, 742 Multiple regression, 705 Multiplication rule, see Basic counting rule Multistage sampling, 45 Mutually exclusive events, 191 and the special addition rule, 195 versus independent events, 219 Negatively linearly correlated variables, 668, 710 Neyman, Jerzy biographical sketch, 459 Nightingale, Florence biographical sketch, 56 Nonhomogeneous, 628 Nonparametric methods, 379, 430 Nonpooled t-interval procedure, 484 Nonpooled t-test, 481 Nonrejection region, 400 Nonresponse, 39 Normal curve, 288 equation of, 288 parameters of, 288 standard, 291 Normal differences, 509 Normal distribution, 284, 288 approximate, 288 as an approximation to the binomial distribution, 318 assessing using normal probability plots, 313 by computer, 307 standard, 291 Normal population, 362 Normal probability plots, 313 use in detecting outliers, 314 Normal scores, 312 Normally distributed population, 288 Normally distributed variable, 288 procedure for finding a range, 306 procedure for finding percentages for, 302 68-95-99.7 rule for, 304 standardized version of, 291 Not statistically significant, 396 Null hypothesis, 390 choice of, 390 Number of failures, 568 Number of successes, 568 Observation, 60 Observational study, 27 Observed frequencies, 601 Observed significance level, 406 Occurrence of an event, 187 Odds, 186 Ogive, 96 One-mean t-interval procedure, 377 INDEX One-mean t-test, 421 procedure for, 424 One-mean z-interval procedure, 361 One-mean z-test, 409, 410 obtaining critical values for, 401 obtaining the P-value for, 406 One-median sign test, 443 One-proportion plus-four z-interval procedure, 573 One-proportion z-interval procedure, 569 One-proportion z-test, 579 One-sample sign test, 443 One-sample t-interval procedure, 377 One-sample t-test, 421, 424 One-sample Wilcoxon confidence-interval procedure, 379 One-sample Wilcoxon signed-rank test, 429 One-sample z-interval procedure, 361 for a population proportion, 570 One-sample z-interval procedure for a population proportion, 569 One-sample z-test, 409 for a population proportion, 579 One-sample z-test for a population proportion, 579 One-standard-deviation χ -interval procedure, 543 One-standard-deviation χ -test, 540 One-tailed test, 391 One-variable proportion interval procedure, 569 One-variable proportion test, 579 One-variable sign test, 443 One-variable t-interval procedure, 377 One-variable t-test, 421 One-variable Wilcoxon signed-rank test, 429 One-variable z-interval procedure, 361 One-variable z-test, 409 One-way analysis of variance, 723 assumptions for, 723 by computer, 736 distribution of test statistic for, 729 procedure for, 732 One-way ANOVA identity, 730 One-way ANOVA table, 730 One-way ANOVA test, 731, 732 comparison with the Kruskal–Wallis test, 755 Ordinal data, 63 measures of center for, 126 Outlier, 126, 151 detection of with normal probability plots, 314 effect on the standard deviation, 138 identification of, 152 in regression, 652 Paired difference, 508 Paired samples, 507 Paired sign test, 529 Paired t-interval procedure, 512, 513 Paired t-test, 510 comparison with the paired Wilcoxon signed-rank test, 524 Paired Wilcoxon signed-rank test, 521 comparison with the paired t-test, 524 procedure for, 521 Parameter, 165 Parameters of a normal curve, 288 Parametric methods, 379, 430 Pearson product moment correlation coefficient, see Linear correlation coefficient Pearson, Karl, 27, 719 biographical sketch, 639 Percent histogram, 78 Percentage and probability, 180 and relative frequency, 65 Percentage distribution joint, 206 Percentiles, 147 of a normally distributed variable, 312 Permutation, 232 Permutation distribution, 480 Permutation test for comparing two means, 479 Permutations rule, 233 special, 234 Pictogram, 107 Pie chart, 67 by computer, 69 procedure for constructing, 67 Plus-four confidence interval procedures, 573, 589 Point estimate, 354, 355 Poisson distribution, 273, 274 as an approximation to the binomial distribution, 276 by computer, 277 Poisson probability formula, 274 Poisson random variable, 274 mean of, 275 standard deviation of, 275 Poisson, Simeon, 273, 352 Pool, 469 Pooled independent samples t-interval procedure, 473 Pooled independent samples t-test, 469 Pooled sample proportion, 586 Pooled sample standard deviation, 469 Pooled t-interval procedure, 473, 474 Pooled t-test, 469, 470 comparison with the Mann–Whitney test, 500 Pooled two-variable t-interval procedure, 473 Pooled two-variable t-test, 469 Population, 25 distribution of, 100 normally distributed, 288 I-5 Population data, 100 Population distribution, 100 Population linear correlation coefficient, 710 Population mean, 162 Population median notation for, 168 Population proportion, 566–546 Population regression equation, 681 Population regression line, 681 Population standard deviation, 164 computing formula for, 164 confidence interval for, 543 hypothesis test for, 541 Population standard deviations confidence interval for the ratio of two, 556 hypothesis test for comparing, 553 Population variance, 164 Positively linearly correlated variables, 668, 710 Posterior probability, 227 Potential outliers, 152 Power, 448 and sample size, 453 Power curve, 449 procedure for, 449 Practical significance versus statistical significance, 416 Predicted value t-interval procedure, 704 Prediction interval, 703 by computer, 706 procedure for, 704 relation to confidence interval, 703 Predictor variable, 652 Prior probability, 227 Probability application of counting rules to, 236 basic properties of, 182 conditional, 207 cumulative, 266, 307 equally-likely outcomes, 180 frequentist interpretation of, 182 inverse cumulative, 308 joint, 203 marginal, 203 model of, 182 notation for, 195 posterior, 227 prior, 227 rules of, 195 Probability distribution binomial, 264 conditional, 214 of a discrete random variable, 247 geometric, 273 hypergeometric, 268, 272 interpretation of, 250 joint, 204 Poisson, 273, 274 Probability histogram, 247 Probability model, 182 Probability sampling, 32 Probability theory, 178 I-6 INDEX Proportion population, see Population proportion sample, see Sample proportion sampling distribution of, 568, 569 Proportional allocation, 43 P-value, 405 as the observed significance level, 406 determining, 406 general procedure for obtaining, 409 use in assessing the evidence against the null hypothesis, 408 use as a decision criterion in a hypothesis test, 406 qα , 742 q-curve, 742 q-distribution, 742 Qualitative data, 60 bar chart of, 67 frequency distribution of, 64 pie chart of, 67 relative-frequency distribution of, 65 Qualitative variable, 59, 60 Quantitative data, 60 bivariate, 646 choosing classes for, 95 dotplot of, 81 histogram of, 78 organizing, 74 stem-and-leaf diagram of, 82 using technology to organize, 85 Quantitative variable, 59, 60 Quartile first, 147, 148 second, 147, 148 third, 147, 148 Quartiles, 147, 148 of a normally distributed variable, 312 Quetelet, Adolphe biographical sketch, 114 Quintiles, 147 Random sample simple, 32 Random sampling, 32 with replacement, 32 without replacement, 32 simple, 33 systematic, 39 Random variable, 246 binomial, 264 discrete, see Discrete random variable interpretation of mean of, 255 notation for, 247 Poisson, 274 Random variables independence of, 259 Random-number generator, 35 Random-number table, 33 Randomization, 48 Randomized block design, 50 Range, 128 Rank correlation, 675 Rectangular distribution, 99 Regression multiple, 641, 705 simple linear, 705 Regression equation definition of, 649 determination of using the sample covariance, 660 formula for, 649 Regression identity, 662 Regression inferences assumptions for in simple linear regression, 681 Regression line, 649 criterion for finding, 654 definition of, 649 Regression model, 681 Regression sum of squares, 661 by computer, 664 computing formula for, 663 Regression t-interval procedure, 696 Regression t-test, 694 Rejection region, 400 Relative frequency, 65 cumulative, 96 and percentage, 65 Relative-frequency distribution procedure for constructing, 66 of qualitative data, 65 Relative-frequency histogram, 78 Relative-frequency polygon, 96 Relative standing and Chebyshev’s rule, 171 estimating, 171 Replication, 48 Representative sample, 32 Research hypothesis, 390 Residual, 684 in ANOVA, 723 Residual analysis in ANOVA, 723 Residual plot, 685 Residual standard deviation, 684 Resistant measure, 119 Response bias, 39 Response variable, 48, 735 in regression, 652 Reverse-J-shaped distribution, 99 Right skewed, 99 property of a χ -curve, 536, 599 property of an F-curve, 549, 721 Right-skewed distribution, 99 Right-tailed test, 391 rejection region for, 400 Robust, 362 Robust procedure, 362 Rounding error, 77 Roundoff error, 77 Rule of total probability, 223, 224 Rule of 24, 723 Same shape, 492 Same-shape populations, 496 Sample, 25 distribution of, 100 representative, 32 simple random, 32 size of, 121 stratified, 43 Sample covariance, 660 Sample data, 100 Sample distribution, 100 Sample mean, 121 as an estimate for a population mean, 163 formula for grouped data, 138 sampling distribution of, 331 standard error of, 339 Sample proportion, 567, 568 formula for, 568 pooled, 586 Sample size, 121 and accuracy, 366 for estimating the difference between two population proportions, 594 for estimating a population mean, 366 for estimating a population proportion, 572 and margin of error, 366 and power, 453 and sampling error, 334, 339 Sample space, 187, 188 Sample standard deviation, 128 computing formula for, 131, 132 defining formula for, 130, 131 as an estimate of a population standard deviation, 164 formula for grouped data, 138 pooled, 469 Sample variance, 130 Samples independent, 461 number possible, 236 paired, 507 Sampling, 31 cluster, 40 multistage, 45 with replacement, 268 without replacement, 268 simple random, 32 stratified, 43 systematic random, 39 Sampling distribution, 331 of the difference between two sample means, 466 of the difference between two sample proportions, 585 of the sample proportion, 568, 569 of the sample standard deviation, 540 of the slope of the regression line, 693 Sampling distribution of the sample mean, 331 for a normally distributed variable, 342 Sampling error, 330 and sample size, 334, 339 INDEX Scatter diagram, 646 Scatterplot, 646 by computer, 654 Second quartile, 147, 148 Segmented bar graph, 612 Sensitivity, 229 Sign test for one median, 443 for two medians, 529 Significance level, 395 Simple linear regression, 705 Simple random paired sample, 507 Simple random sample, 32 by computer, 35 Simple random samples independent, 461 Simple random sampling, 32 with replacement, 32 without replacement, 32 Single-value classes, 74 Single-value grouping, 74 histograms for, 78 68-95-99.7 rule, 141, 304 Skewness, 99 Slope, 643 graphical interpretation of, 644 Spearman rank correlation coefficient, 675 Spearman, Charles, 675 Special addition rule, 195 Special multiplication rule, 218 Special permutations rule, 234 Specificity, 229 Squared deviations sum of, 129 Standard deviation of a binomial random variable, 267 of a discrete random variable, 256 of a Poisson random variable, 275 of a population, see Population standard deviation of a sample, see Sample standard deviation sampling distribution of, 540 ¯ 338 of x, Standard deviation of a random variable, 256 computing formula for, 256 properties of, 259 Standard deviation of a variable, 164 Standard error, 339 Standard error of the estimate, 683, 684 by computer, 687 Standard error of the sample mean, 339 Standard normal curve, 291 areas under, 297 basic properties of, 296 finding the z-score(s) for a specified area, 299 Standard normal distribution, 291 Standard-normal table use of, 297 Standard score, 167 Standardized variable, 166 Standardized version of a variable, 166 ¯ 374 of x, Statistic, 165 sampling distribution of, 331 test, 393 Statistical independence, 217 see also Independence Statistical significance versus practical significance, 416 Statistically dependent variables, 612 Statistically independent variables, 612 Statistically significant, 396 Statistics descriptive, 24, 25 inferential, 24, 25 Stat plots turning off, 87 Stem, 82 Stem-and-leaf diagram, 82 back-to-back, 494 procedure for constructing, 83 using more than one line per stem, 84 Stemplot, 82 Straight line, 641 Strata, 43 Stratified sampling, 43 proportional allocation in, 43 Stratified sampling theorem, 224 Stratified sampling with proportional allocation, 43 procedure for implementing, 43 Student’s t-distribution, see t-distribution Studentized range distribution, 742 ¯ 374 Studentized version of x, distribution of, 421 Subject, 48 Subscripts, 120 Success, 261 Success probability, 261 Sum of squared deviations, 129 Summation notation, 120 Symmetric, 98 property of a t-curve, 376 property of the standard normal curve, 296 Symmetric distribution, 98 assumption for the Wilcoxon signed-rank test, 430 Symmetric population, 433 Symmetry, 98 Systematic random sampling, 39 procedure for implementing, 39 tα , 376 t-curve, 375 basic properties of, 376 t-distribution, 375, 421, 469, 480, 509, 693, 702, 704, 710 Technology Center, 35 Test statistic, 393 Third quartile, 147, 148 I-7 TI-83/84 Plus, 35 Time series, 660 t-interval procedure, 377 Total sum of squares, 660 by computer, 664 in one-way analysis of variance, 730 in regression, 661 Transformations, 506 Treatment, 48, 725 Treatment group, 48 Treatment mean square in one-way analysis of variance, 725 Treatment sum of squares in one-way analysis of variance, 725 Tree diagram, 216 Trial, 260 Triangular distribution, 99 Trimmed mean, 119, 127 Truncated graph, 106 t-test, 421 comparison with the Wilcoxon signed-rank test, 438 Tukey multiple-comparison method by computer, 745 in one-way ANOVA, 742 procedure for, 743 Tukey, John, 153, 491 biographical sketch, 176 Tukey’s quick test, 492 Two-means z-interval procedure, 466 Two-means z-test, 466 Two-proportions plus-four z-interval procedure, 589 Two-proportions z-interval procedure, 588 Two-proportions z-test, 586 Two-sample F-interval procedure, 555 Two-sample F-test, 553 Two-sample t-interval procedure, 484 with equal variances assumed, 473 Two-sample t-test, 481 with equal variances assumed, 469 Two-sample z-interval procedure, 466 for two population proportions, 589 Two-sample z-test, 466 for two population proportions, 587 Two-standard-deviations F-interval procedure, 555 Two-standard-deviations F-test, 553 Two-tailed test, 391 Two-variable proportions interval procedure, 589 Two-variable proportions test, 587 Two-variable t-interval procedure, 484 pooled, 473 Two-variable t-test, 481 pooled, 469 Two-variable z-interval procedure, 466 Two-variable z-test, 466 Two-way table, 201, 609 Type I error, 393 probability of, 395 Type II error, 393 probability of, 395 I-8 INDEX Type II error probabilities calculation of, 444 procedure for, 447 Unbiased estimator, 341, 355 Undercoverage, 39 Uniform distribution, 99, 351 Uniformly distributed variable, 351 Unimodal distribution, 98 Univariate data, 96, 201, 609 Upper class cutpoint, 76, 77 Upper class limit, 75, 76 Upper cutpoint of a class, 76, 77 Upper limit, 152 of a class, 75, 76 Utility expected, 258 Utility functions, 258 Variable, 59, 60 approximately normally distributed, 288 assessing normality, 313 categorical, 59 continuous, 59, 60 discrete, 59, 60 distribution of, 100 exponentially distributed, 348 mean of, 162 normally distributed, 288 qualitative, 59, 60 quantitative, 59, 60 standard deviation of, 164 standardized, 166 standardized version of, 166 uniformly distributed, 351 variance of, 164 Variance of a discrete random variable, 256 of a population, see Population variance of a random variable, 256 of a sample, see Sample variance of a variable, 164 Venn diagrams, 188 Venn, John, 188 Wα , 432 WeissStats Resource Site, 35 WeissStats site, 35 Whiskers, 153 Wilcoxon rank-sum test, 493 Wilcoxon signed-rank table using the, 432 Wilcoxon signed-rank test, 429 comparison with the t-test, 438 by computer, 438 dealing with ties, 436 determining critical values for, 432 observations equal to the null mean, 436 for paired samples, 521 procedure for, 434 testing a median with, 438 using a normal approximation, 443 x¯ critical value, 445 XLSTAT, 35 Y = functions turning off, 87 y-intercept, 643 z α , 360 z-curve, 296 see also Standard normal curve z-interval procedure, 361 for a population proportion, 569 z-score, 167 as a measure of relative standing, 168 z-test, 409 for a population proportion, 579 This page intentionally left blank Photo Credits About the Author Chapter p 5, Carol Weiss p 353, Folio/Alamy p 388 (top), Folio/Alamy p 388 (bottom), Pearson Education Chapter p 23, United Archives GmbH/Alamy p 24, TSN/ZUMAPRESS/Newscom p 25, Bettmann/Corbis p 27, Sports Illustrated/Getty Images p 56 (top), United Archives GmbH/Alamy p 56 (bottom), Library of Congress Chapter Chapter p 460, Steve Lovegrove/Fotolia p 533 (top), Steve Lovegrove/Fotolia p 533 (bottom), North Carolina State University Archives p 58, Jason DeCrow/AP Images p 113, Jason DeCrow/AP Images p 114, Library of Congress Chapter p 115, Gamma/Gamma-Rapho/Getty Images p 176 (top), Gamma/Gamma-Rapho/Getty Images p 176 (bottom), Pearson Education Chapter p 178, Krastiu 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Copyright, Designs and Patents Act 1988 Authorized adaptation from the United States edition, Introductory Statistics, 10th edition, ISBN 9780321989178, by Neil A Weiss published by Pearson Education... Bemelmans Project Team Lead: Christina Lepre Acquisitions Editor, Global Edition: Sourabh Maheshwari Project Editor, Global Edition: Radhika Raheja Project Manager: Shannon Steed Senior Designer: