Introduction to business statistics (7th edition) by m weiers Introduction to business statistics (7th edition) by m weiers Introduction to business statistics (7th edition) by m weiers Introduction to business statistics (7th edition) by m weiers Introduction to business statistics (7th edition) by m weiers Introduction to business statistics (7th edition) by m weiers Introduction to business statistics (7th edition) by m weiers Introduction to business statistics (7th edition) by m weiers Introduction to business statistics (7th edition) by m weiers
a = right-tail area (e.g., for a right-tail area of 0.025 and d.f = 15, the t value is 2.131.) ␣: d.f ϭ 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 The t-Distribution t 0.10 0.05 0.025 0.01 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.309 1.309 1.308 1.307 1.306 1.306 1.305 1.304 1.304 1.303 1.303 1.302 1.302 1.301 1.301 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.696 1.694 1.692 1.691 1.690 1.688 1.687 1.686 1.685 1.684 1.683 1.682 1.681 1.680 1.679 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.040 2.037 2.035 2.032 2.030 2.028 2.026 2.024 2.023 2.021 2.020 2.018 2.017 2.015 2.014 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.453 2.449 2.445 2.441 2.438 2.435 2.431 2.429 2.426 2.423 2.421 2.418 2.416 2.414 2.412 0.005 63.657 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.744 2.738 2.733 2.728 2.724 2.719 2.715 2.712 2.708 2.704 2.701 2.698 2.695 2.692 2.690 ␣: 0.10 0.05 0.025 0.01 0.005 d.f ϭ 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ϱ 1.300 1.300 1.299 1.299 1.299 1.298 1.298 1.298 1.297 1.297 1.297 1.297 1.296 1.296 1.296 1.296 1.295 1.295 1.295 1.295 1.295 1.294 1.294 1.294 1.294 1.294 1.293 1.293 1.293 1.293 1.293 1.293 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.292 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.291 1.290 1.290 1.290 1.290 1.290 1.282 1.679 1.678 1.677 1.677 1.676 1.675 1.675 1.674 1.674 1.673 1.673 1.672 1.672 1.671 1.671 1.670 1.670 1.669 1.669 1.669 1.668 1.668 1.668 1.667 1.667 1.667 1.666 1.666 1.666 1.665 1.665 1.665 1.665 1.664 1.664 1.664 1.664 1.663 1.663 1.663 1.663 1.663 1.662 1.662 1.662 1.662 1.662 1.661 1.661 1.661 1.661 1.661 1.661 1.660 1.660 1.645 2.013 2.012 2.011 2.010 2.009 2.008 2.007 2.006 2.005 2.004 2.003 2.002 2.002 2.001 2.000 2.000 1.999 1.998 1.998 1.997 1.997 1.996 1.995 1.995 1.994 1.994 1.993 1.993 1.993 1.992 1.992 1.991 1.991 1.990 1.990 1.990 1.989 1.989 1.989 1.988 1.988 1.988 1.987 1.987 1.987 1.986 1.986 1.986 1.986 1.985 1.985 1.985 1.984 1.984 1.984 1.960 2.410 2.408 2.407 2.405 2.403 2.402 2.400 2.399 2.397 2.396 2.395 2.394 2.392 2.391 2.390 2.389 2.388 2.387 2.386 2.385 2.384 2.383 2.382 2.382 2.381 2.380 2.379 2.379 2.378 2.377 2.376 2.376 2.375 2.375 2.374 2.373 2.373 2.372 2.372 2.371 2.371 2.370 2.369 2.369 2.369 2.368 2.368 2.367 2.367 2.366 2.366 2.365 2.365 2.365 2.364 2.326 2.687 2.685 2.682 2.680 2.678 2.676 2.674 2.672 2.670 2.668 2.667 2.665 2.663 2.662 2.660 2.659 2.658 2.656 2.655 2.654 2.652 2.651 2.650 2.649 2.648 2.647 2.646 2.645 2.644 2.643 2.642 2.641 2.640 2.640 2.639 2.638 2.637 2.636 2.636 2.635 2.634 2.634 2.633 2.632 2.632 2.631 2.630 2.630 2.629 2.629 2.628 2.627 2.627 2.626 2.626 2.576 Source: t-values generated by Minitab, then rounded to three decimal places Computer Printouts and Instructions Solutions for Excel and Minitab Visual Description 2.1 The Histogram 2.2 The Stem-And-Leaf Display* 2.3 The Dotplot 2.4 The Bar Chart 2.5 The Line Chart 2.6 The Pie Chart 2.7 The Scatter Diagram 2.8 The Cross-Tabulation 2.9 Cross-Tabulation with Cell Summary Information Statistical Description 3.1 Descriptive Statistics: Central Tendency 3.2 Descriptive Statistics: Dispersion 3.3 The Box Plot* 3.4 Standardizing the Data 3.5 Coefficient of Correlation Sampling 4.1 Simple Random Sampling Discrete Probability Distributions 6.1 Binomial Probabilities 6.2 Hypergeometric Probabilities 6.3 Poisson Probabilities 6.4 Simulating Observations From a Discrete Probability Distribution Continuous Probability Distributions 7.1 Normal Probabilities 7.2 Inverse Normal Probabilities 7.3 Exponential Probabilities 7.4 Inverse Exponential Probabilities 7.5 Simulating Observations From a Continuous Probability Distribution Sampling Distributions 8.1 Sampling Distributions and Computer Simulation Confidence Intervals 9.1 Confidence Interval For Population Mean, Known* 9.2 Confidence Interval For Population Mean, Unknown* 9.3 Confidence Interval For Population Proportion* 9.4 Sample Size Determination Hypothesis Tests: One Sample 10.1 Hypothesis Test For Population Mean, Known* 10.2 Hypothesis Test For Population Mean, Unknown* Page 21 26 27 29 30 32 40 45 46 65 75 77 81 88 122 180 185 191 195 219 220 230 232 234 260 279 286 290 297 Computer Printouts and Instructions Solutions for Excel and Minitab Page 10.3 Hypothesis Test For Population Proportion* 342 10.4 The Power Curve For A Hypothesis Test 352 Hypothesis Tests: Comparing Two Samples 11.1 Pooled-Variances t-Test for (1 Ϫ 2), Population Variances Unknown but Assumed Equal 11.2 Unequal-Variances t-Test for (1 Ϫ 2), Population Variances Unknown and Not Equal 11.3 The z-Test for (1 Ϫ 2) 11.4 Comparing the Means of Dependent Samples 11.5 The z-Test for Comparing Two Sample Proportions* 11.6 Testing for the Equality of Population Variances Analysis of Variance 12.1 One-Way Analysis of Variance 12.2 Randomized Block Analysis of Variance 12.3 Two-Way Analysis of Variance Chi-Square Applications 13.1 Chi-Square Test for Goodness of Fit 13.2 Chi-Square Goodness-of-Fit Test for Normality* 13.3 Chi-Square Test for Independence of Variables* 13.4 Chi-Square Test Comparing Proportions From Independent Samples* 13.5 Confidence Interval for a Population Variance 13.6 Hypothesis Test for a Population Variance Nonparametric Methods 14.1 Wilcoxon Signed Rank Test for One Sample* 14.2 Wilcoxon Signed Rank Test for Comparing Paired Samples* 14.3 Wilcoxon Rank Sum Test for Two Independent Samples* 14.4 Kruskal-Wallis Test for Comparing More Than Two Independent Samples* 14.5 Friedman Test for the Randomized Block Design* 14.6 Sign Test for Comparing Paired Samples* 14.7 Runs Test for Randomness 14.8 Kolmogorov-Smirnov Test for Normality 14.9 Spearman Coefficient of Rank Correlation* 371 377 383 388 393 399 424 438 453 475 477 483 488 494 495 512 515 520 524 529 534 538 541 543 326 335 Simple Linear Regression 15.1 Simple Linear Regression 558 Computer Printouts and Instructions Solutions for Excel and Minitab 15.2 Interval Estimation in Simple Linear Regression* 15.3 Coefficient of Correlation 15.4 Residual Analysis Multiple Regression 16.1 Multiple Regression 16.2 Interval Estimation in Multiple Regression* 16.3 Residual Analysis in Multiple Regression Model Building 17.1 Fitting a Polynomial Regression Equation, One Predictor Variable 17.2 Fitting a Polynomial Regression Equation, Two Predictor Variables 17.3 Multiple Regression With Qualitative Predictor Variables 17.4 Transformation of the Multiplicative Model Page 565 570 580 606 613 627 649 656 661 665 Computer Printouts and Instructions Solutions for Excel and Minitab 17.5 The Correlation Matrix 17.6 Stepwise Regression* Page 668 671 Models for Time Series and Forecasting 18.1 Fitting a Linear or Quadratic Trend Equation 18.2 Centered Moving Average For Smoothing a Time Series 18.3 Excel Centered Moving Average Based On Even Number of Periods 18.4 Exponentially Smoothing a Time Series 18.5 Determining Seasonal Indexes* 18.6 Forecasting With Exponential Smoothing 18.7 Durbin-Watson Test for Autocorrelation* 18.8 Autoregressive Forecasting 696 699 706 710 720 723 Statistical Process Control 20.1 Mean Chart* 20.2 Range Chart* 20.3 p-Chart* 20.4 c-Chart 780 781 789 792 691 694 * Data Analysis Plus™ 7.0 add-in Seeing Statistics Applets Applet 10 11 12 13 14 15 16 17 18 19 20 21 Key Item Title Influence of a Single Observation on the Median Scatter Diagrams and Correlation Sampling Size and Shape of Normal Distribution Normal Distribution Areas Normal Approximation to Binomial Distribution Distribution of Means—Fair Dice Distribution of Means—Loaded Dice Confidence Interval Size Comparing the Normal and Student t Distributions Student t Distribution Areas z-Interval and Hypothesis Testing Statistical Power of a Test Distribution of Difference Between Sample Means F Distribution Interaction Graph in Two-Way ANOVA Chi-Square Distribution Regression: Point Estimate for y Point-Insertion Scatter Diagram and Correlation Regression Error Components Mean Control Chart Text Section 3.2 3.6 4.6 7.2 7.3 7.4 8.3 8.3 9.4 9.5 9.5 10.4 10.7 11.4 12.3 12.5 13.2 15.2 15.4 15.4 20.7 Applet Page 99 100 132 241 242 243 268 269 309 310 310 362 363 410 464 465 504 597 598 599 805 Location Computer setup and notes Follows preface t-table Precedes z-table z-table Inside rear cover Other printed tables Appendix A Selected odd answers Appendix B Seeing Statistics applets, Thorndike video units, case and exercise data sets, Excel worksheet templates, and Data Analysis PlusTM 7.0 Excel add-in software with accompanying workbooks, including Test Statistics and Estimators, Online Chapter 21, appendices, and additional support http://www.cengage.com/bstatistics/weiers INTRODUCTION TO ST A S T S I E STIC N I S S BU 7E Ronald M Weiers Eberly College of Business and Information Technology Indiana University of Pennsylvania and H John Heinz III College Carnegie Mellon University WITH BUSINESS CASES BY J Brian Gray University of Alabama Lawrence H Peters Texas Christian University Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States Introduction to Business Statistics, Seventh Edition Ronald M Weiers Vice President of Editorial, Business: Jack W Calhoun Publisher: Joe Sabatino Sr Acquisitions Editor: Charles McCormick, Jr Developmental Editor: Elizabeth Lowry and Suzanna Bainbridge Editorial Assistant: Nora Heink Sr Marketing Communications Manager: Jim Overly Content Project Manager: Kelly Hillerich © 2011, © 2008 South-Western, 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 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 Media Editor: Chris Valentine Frontlist Buyer, Manufacturing: Miranda Klapper Compositor: MPS Limited, A Macmillan Company Sr Art Director: Stacy Shirley Internal/Cover Designer: Craig Ramsdell Cover Image: © Getty Images Photo Acquisition Manager: Don Schlotman ExamView® is a registered trademark of eInstruction Corp Windows is a registered trademark of the Microsoft Corporation used herein under license Macintosh and Power Macintosh are registered trademarks of Apple Computer, Inc used herein under license © 2008 Cengage Learning All Rights Reserved Cengage Learning WebTutor™ is a trademark of Cengage Learning Library of Congress Control Number: 2009943073 ISBN-13: 978-0-538-45217-5 ISBN-10: 0-538-45217-X South-Western Cengage Learning 5191 Natorp Boulevard Mason, OH 45040 USA 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 Printed in the United States of America 13 12 11 10 To Connor, Madeleine, Hugh, Christina, Aidan, Mitchell, Owen, Emmett, Mr Barney Jim, and With loving memories of our wonderful son, Bob, who is swimming with the dolphins off Ocracoke Island This page intentionally left blank CONTENT F E I S BR Part 1: Business Statistics: Introduction and Background A Preview of Business Statistics Visual Description of Data 15 Statistical Description of Data 57 Data Collection and Sampling Methods 101 Part 2: Probability Probability: Review of Basic Concepts 133 Discrete Probability Distributions 167 Continuous Probability Distributions 205 Part 3: Sampling Distributions and Estimation Sampling Distributions 244 Estimation from Sample Data 270 Part 4: Hypothesis Testing 10 Hypothesis Tests Involving a Sample Mean or Proportion 311 11 Hypothesis Tests Involving Two Sample Means or Proportions 364 12 Analysis of Variance Tests 411 13 Chi-Square Applications 467 14 Nonparametric Methods 505 Part 5: Regression, Model Building, and Time Series 15 Simple Linear Regression and Correlation 551 16 Multiple Regression and Correlation 600 17 Model Building 644 18 Models for Time Series and Forecasting 687 Part 6: Special Topics 19 Decision Theory 737 20 Total Quality Management 758 21 Ethics in Statistical Analysis and Reporting (Online Chapter) Appendices A Statistical Tables A-1 B Selected Answers B-1 Index/Glossary I-1 v TABLE A.6 (continued) a = 0.025 F(a, n 1, n 2) F v2 ؍df, denominator 1 647.8 38.51 17.44 12.22 10.01 8.81 8.07 7.57 7.21 10 6.94 11 6.72 12 6.55 13 6.41 14 6.30 15 6.20 16 6.12 17 6.04 18 5.98 19 5.92 20 5.87 21 5.83 22 5.79 23 5.75 24 5.72 25 5.69 26 5.66 27 5.63 28 5.61 29 5.59 30 5.57 40 5.42 60 5.29 120 5.15 ؕ 5.02 v1 ؍df, numerator 10 12 15 20 24 30 40 60 120 ؕ 799.5 864.2 899.6 921.8 937.1 948.2 956.7 963.3 968.6 976.7 984.9 993.1 997.2 1001 1006 1010 1014 1018 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.41 39.43 39.45 39.46 39.46 39.47 39.48 39.49 39.50 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 14.42 14.34 14.25 14.17 14.12 14.08 14.04 13.99 13.95 13.90 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 8.84 8.75 8.66 8.56 8.51 8.46 8.41 8.36 8.31 8.26 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.52 6.43 6.33 6.28 6.23 6.18 6.12 6.07 6.02 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.37 5.27 5.17 5.12 5.07 5.01 4.96 4.90 4.85 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.67 4.57 4.47 4.42 4.36 4.31 4.25 4.20 4.14 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.30 4.20 4.10 4.00 3.95 3.89 3.84 3.78 3.73 3.67 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03 3.96 3.87 3.77 3.67 3.61 3.56 3.51 3.45 3.39 3.33 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.62 3.52 3.42 3.37 3.31 3.26 3.20 3.14 3.08 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.53 3.43 3.33 3.23 3.17 3.12 3.06 3.00 2.94 2.88 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.28 3.18 3.07 3.02 2.96 2.91 2.85 2.79 2.72 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.25 3.15 3.05 2.95 2.89 2.84 2.78 2.72 2.66 2.60 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21 3.15 3.05 2.95 2.84 2.79 2.73 2.67 2.61 2.55 2.49 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.06 2.96 2.86 2.76 2.70 2.64 2.59 2.52 2.46 2.40 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 2.89 2.79 2.68 2.63 2.57 2.51 2.45 2.38 2.32 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.82 2.72 2.62 2.56 2.50 2.44 2.38 2.32 2.25 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 2.77 2.67 2.56 2.50 2.44 2.38 2.32 2.26 2.19 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.72 2.62 2.51 2.45 2.39 2.33 2.27 2.20 2.13 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 2.68 2.57 2.46 2.41 2.35 2.29 2.22 2.16 2.09 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80 2.73 2.64 2.53 2.42 2.37 2.31 2.25 2.18 2.11 2.04 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.60 2.50 2.39 2.33 2.27 2.21 2.14 2.08 2.00 4.35 3.75 3.41 3.18 3.02 2.90 2.81 2.73 2.67 2.57 2.47 2.36 2.30 2.24 2.18 2.11 2.04 1.97 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.54 2.44 2.33 2.27 2.21 2.15 2.08 2.01 1.94 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68 2.61 2.51 2.41 2.30 2.24 2.18 2.12 2.05 1.98 1.91 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 2.49 2.39 2.28 2.22 2.16 2.09 2.03 1.95 1.88 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63 2.57 2.47 2.36 2.25 2.19 2.13 2.07 2.00 1.93 1.85 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 2.45 2.34 2.23 2.17 2.11 2.05 1.98 1.91 1.83 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59 2.53 2.43 2.32 2.21 2.15 2.09 2.03 1.96 1.89 1.81 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.41 2.31 2.20 2.14 2.07 2.01 1.94 1.87 1.79 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.39 2.29 2.18 2.07 2.01 1.94 1.88 1.80 1.72 1.64 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33 2.27 2.17 2.06 1.94 1.88 1.82 1.74 1.67 1.58 1.48 3.80 3.23 2.89 2.67 2.52 2.39 2.30 2.22 2.16 2.05 1.94 1.82 1.76 1.69 1.61 1.53 1.43 1.31 3.69 3.12 2.79 2.57 2.41 2.29 2.19 2.11 2.05 1.94 1.83 1.71 1.64 1.57 1.48 1.39 1.27 1.00 TABLE A.6 (continued) v2 ؍df, denominator a = 0.01 F(a, n 1, n 2) F v1 ؍df, numerator 10 12 15 20 24 30 40 60 120 ؕ 4052 4999.5 5403 5625 5764 5859 5928 5982 6022 6056 6106 6157 6209 6235 6261 6287 6313 6339 6366 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39 99.40 99.42 99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.50 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23 27.05 26.87 26.69 26.60 26.50 26.41 26.32 26.22 26.13 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55 14.37 14.20 14.02 13.93 13.84 13.75 13.65 13.56 13.46 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05 9.89 9.72 9.55 9.47 9.38 9.29 9.20 9.11 9.02 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87 7.72 7.56 7.40 7.31 7.23 7.14 7.06 6.97 6.88 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62 6.47 6.31 6.16 6.07 5.99 5.91 5.82 5.74 5.65 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81 5.67 5.52 5.36 5.28 5.20 5.12 5.03 4.95 4.86 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26 5.11 4.96 4.81 4.73 4.65 4.57 4.48 4.40 4.31 10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85 4.71 4.56 4.41 4.33 4.25 4.17 4.08 4.00 3.91 11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54 4.40 4.25 4.10 4.02 3.94 3.86 3.78 3.69 3.60 12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30 4.16 4.01 3.86 3.78 3.70 3.62 3.54 3.45 3.36 13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10 3.96 3.82 3.66 3.59 3.51 3.43 3.34 3.25 3.17 14 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.94 3.80 3.66 3.51 3.43 3.35 3.27 3.18 3.09 3.00 15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.80 3.67 3.52 3.37 3.29 3.21 3.13 3.05 2.96 2.87 16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 3.55 3.41 3.26 3.18 3.10 3.02 2.93 2.84 2.75 17 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 3.46 3.31 3.16 3.08 3.00 2.92 2.83 2.75 2.65 18 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 3.37 3.23 3.08 3.00 2.92 2.84 2.75 2.66 2.57 19 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 3.30 3.15 3.00 2.92 2.84 2.76 2.67 2.58 2.49 20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 3.23 3.09 2.94 2.86 2.78 2.69 2.61 2.52 2.42 21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 3.17 3.03 2.88 2.80 2.72 2.64 2.55 2.46 2.36 22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 3.12 2.98 2.83 2.75 2.67 2.58 2.50 2.40 2.31 23 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 3.07 2.93 2.78 2.70 2.62 2.54 2.45 2.35 2.26 24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 3.03 2.89 2.74 2.66 2.58 2.49 2.40 2.31 2.21 25 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 2.99 2.85 2.70 2.62 2.54 2.45 2.36 2.27 2.17 26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 2.96 2.81 2.66 2.58 2.50 2.42 2.33 2.23 2.13 27 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 2.93 2.78 2.63 2.55 2.47 2.38 2.29 2.20 2.10 28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 2.90 2.75 2.60 2.52 2.44 2.35 2.26 2.17 2.06 29 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 2.87 2.73 2.57 2.49 2.41 2.33 2.23 2.14 2.03 30 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 2.84 2.70 2.55 2.47 2.39 2.30 2.21 2.11 2.01 40 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 2.66 2.52 2.37 2.29 2.20 2.11 2.02 1.92 1.80 60 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 2.50 2.35 2.20 2.12 2.03 1.94 1.84 1.73 1.60 120 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47 2.34 2.19 2.03 1.95 1.86 1.76 1.66 1.53 1.38 ؕ 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41 2.32 2.18 2.04 1.88 1.79 1.70 1.59 1.47 1.32 1.00 Source: Standard Mathematical Tables, 26th ed., William H Beyer (ed.), CRC Press, Inc., Boca Raton, FL, 1983 A-28 Appendix A: Statistical Tables TABLE A.7 The Chi-Square Distribution e.g., for a right-tail test with a = 0.01 and d.f = 4, chi-square is 13.277 x2 For ␣ Right-Tail Area of d.f 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 50 60 70 80 90 100 0.99 0.00016 0.0201 0.115 0.297 0.554 0.872 1.239 1.646 2.088 2.558 3.053 3.571 4.107 4.660 5.229 5.812 6.408 7.015 7.633 8.260 8.897 9.542 10.916 10.856 11.524 12.198 12.879 13.565 14.256 14.953 22.164 29.707 37.485 45.442 53.540 61.754 70.065 0.975 0.00098 0.0506 0.216 0.484 0.831 1.237 1.690 2.180 2.700 3.247 3.816 4.404 5.009 5.629 6.262 6.908 7.564 8.231 8.907 9.591 10.283 10.982 11.689 12.401 13.120 13.844 14.573 15.308 16.047 16.791 24.433 32.357 40.482 48.758 57.153 65.647 74.222 0.95 0.00039 0.103 0.352 0.711 1.145 1.635 2.167 2.733 3.325 3.940 4.575 5.226 5.892 6.571 7.261 7.962 8.672 9.390 10.117 10.851 11.591 12.338 13.091 13.848 14.611 15.379 16.151 16.928 17.708 18.493 26.509 34.764 43.188 51.739 60.391 69.126 77.930 0.90 0.0158 0.211 0.584 1.064 1.610 2.204 2.833 3.490 4.168 4.865 5.578 6.304 7.042 7.790 8.547 9.312 10.085 10.865 11.651 12.443 13.240 14.042 14.848 15.659 16.473 17.292 18.114 18.939 19.768 20.599 29.051 37.689 46.459 55.329 64.278 73.291 82.358 Source: Chi-square values generated by Minitab, then rounded as shown 0.10 0.05 2.706 4.605 6.251 7.779 9.236 10.645 12.017 13.362 14.684 15.987 17.275 18.549 19.812 21.064 22.307 23.542 24.769 25.989 27.204 28.412 29.615 30.813 32.007 33.196 34.382 35.563 36.741 37.916 39.087 40.256 51.805 63.167 74.397 85.527 96.578 107.57 118.50 3.841 5.991 7.815 9.488 11.070 12.592 14.067 15.507 16.919 18.307 19.675 21.026 22.362 23.685 24.996 26.296 27.587 28.869 30.144 31.410 32.671 33.924 35.172 36.415 37.652 38.885 40.113 41.337 42.557 43.773 55.759 67.505 79.082 90.531 101.88 113.15 124.34 0.025 5.024 7.378 9.348 11.143 12.833 14.449 16.013 17.535 19.023 20.483 21.920 23.337 24.736 26.119 27.488 28.845 30.191 31.526 32.852 34.170 35.479 36.781 38.076 39.364 40.647 41.923 43.195 44.461 45.722 46.979 59.342 71.420 83.298 95.023 106.63 118.14 129.56 0.01 6.635 9.210 11.345 13.277 15.086 16.812 18.475 20.090 21.666 23.209 24.725 26.217 27.688 29.141 30.578 32.000 33.409 34.805 36.191 37.566 38.932 40.290 41.638 42.980 44.314 45.642 46.963 48.278 49.588 50.892 63.691 76.154 88.381 100.42 112.33 124.12 135.81 Appendix A: Statistical Tables A-29 TABLE A.8 Wilcoxon Signed Rank Test, Lower and Upper Critical Values Two-Tail Test: One-Tail Test: n؍4 10 11 12 13 14 15 16 17 18 19 20 ␣ 0.20 ␣ 0.10 ␣ 0.10 ␣ 0.05 1, 3, 12 4, 17 6, 22 9, 27 11, 34 15, 40 18, 48 22, 56 27, 64 32, 73 37, 83 43, 93 49, 104 56, 115 63, 127 70, 140 0, 1, 3, 4, 6, 9, 11, 14, 18, 22, 26, 31, 36, 42, 48, 54, 61, 10 14 18 24 30 36 44 52 60 69 79 89 100 111 123 136 149 ␣ 0.05 ␣ 0.025 0, 10 0, 15 1, 20 3, 25 4, 32 6, 39 9, 46 11, 55 14, 64 18, 73 22, 83 26, 94 30, 106 35, 118 41, 130 47, 143 53, 157 ␣ 0.02 ␣ 0.01 ␣ 0.01 ␣ 0.005 0, 0, 0, 1, 2, 4, 6, 8, 10, 13, 16, 20, 24, 28, 33, 38, 44, 0, 0, 0, 0, 1, 2, 4, 6, 8, 10, 13, 16, 20, 24, 28, 33, 38, 10 15 21 27 34 41 49 58 68 78 89 100 112 125 138 152 166 10 15 21 28 35 43 51 60 70 81 92 104 116 129 143 157 172 Source: Adapted from Roger C Pfaffenberger and James H Patterson, Statistical Methods for Business and Economics (Homewood, Ill.: Richard D Irwin, Inc., 1987), p 110, and R L McCornack, “Extended Tables of the Wilcoxon Matched Pairs Signed Rank Statistics,” Journal of the American Statistical Association 60 (1965), 864–871 A-30 Appendix A: Statistical Tables TABLE A.9 Wilcoxon Rank Sum Test, Lower and Upper Critical Values ␣ 0.025 (one-tail) or ␣ 0.05 (two-tail) n1: n2: 10 5, 6, 6, 7, 7, 8, 8, 9, 16 18 21 23 26 28 31 33 6, 11, 12, 12, 13, 14, 15, 16, 18 25 28 32 35 38 41 44 6, 12, 18, 19, 20, 21, 22, 24, 21 28 37 41 45 49 53 56 7, 12, 19, 26, 28, 29, 31, 32, 23 32 41 52 56 61 65 70 7, 13, 20, 28, 37, 39, 41, 43, 26 35 45 56 68 73 78 83 8, 14, 21, 29, 39, 49, 51, 54, 28 38 49 61 73 87 93 98 8, 15, 22, 31, 41, 51, 63, 66, 31 41 53 65 78 93 108 114 10 9, 16, 24, 32, 43, 54, 66, 79, 33 44 56 70 83 98 114 131 (Note: n1 is the smaller of the two samples—i.e., n1 # n2.) ␣ 0.05 (one-tail) or ␣ 0.10 (two-tail) n1: n 2: 10 6, 7, 7, 8, 9, 9, 10, 11, 15 17 20 22 24 27 29 31 7, 12, 13, 14, 15, 16, 17, 18, 17 24 27 30 33 36 39 42 7, 13, 19, 20, 22, 24, 25, 26, 20 27 36 40 43 46 50 54 8, 14, 20, 28, 30, 32, 33, 35, 22 30 40 50 54 58 63 67 9, 15, 22, 30, 39, 41, 43, 46, 24 33 43 54 66 71 76 80 9, 16, 24, 32, 41, 52, 54, 57, 27 36 46 58 71 84 90 95 10, 17, 25, 33, 43, 54, 66, 69, 29 39 50 63 76 90 105 111 (Note: n1 is the smaller of the two samples—i.e., n1 # n2.) Source: F Wilcoxon and R A Wilcox, Some Approximate Statistical Procedures (New York: American Cyanamid Company, 1964), pp 20–23 10 11, 18, 26, 35, 46, 57, 69, 83, 31 42 54 67 80 95 111 127 Appendix A: Statistical Tables A-31 TABLE A.10 Critical Values of D for the Kolmogorov–Smirnov Test of Normality Significance Level ␣ Sample Size n 10 11 12 13 14 15 16 17 18 19 20 25 30 Over 30 0.20 0.15 0.10 0.05 0.01 300 285 265 247 233 223 215 206 199 190 183 177 173 169 166 163 160 142 131 736 √n 319 299 277 258 244 233 224 217 212 202 194 187 182 177 173 169 166 147 136 768 √n 352 315 294 276 261 249 239 230 223 214 207 201 195 189 184 179 174 158 144 805 √n 381 337 319 300 285 271 258 249 242 234 227 220 213 206 200 195 190 173 161 886 √n 417 405 364 348 331 311 294 284 275 268 261 257 250 245 239 235 231 200 187 1.031 √n Source: From H W Lilliefors, “On the Kolmogorov–Smirnov Test for Normality with Mean and Variance Unknown,” Journal of the American Statistical Association, 62 (1967), pp 399–402 As adapted by Conover, Practical Nonparametric Statistics (New York: John Wiley, 1971), p 398 A-32 Appendix A: Statistical Tables TABLE A.11 Critical Values of Spearman’s Rank Correlation Coefficient, rs, One-Tail Test (For a two-tail test, the listed values correspond to the 2␣ level of significance.) n ␣ 0.05 ␣ 0.025 ␣ 0.01 ␣ 0.005 10 0.900 0.829 0.714 0.643 0.600 0.564 — 0.886 0.786 0.738 0.683 0.648 — 0.943 0.893 0.833 0.783 0.745 — — — 0.881 0.833 0.794 11 12 13 14 15 0.523 0.497 0.475 0.457 0.441 0.623 0.591 0.566 0.545 0.525 0.736 0.703 0.673 0.646 0.623 0.818 0.780 0.745 0.716 0.689 16 17 18 19 20 0.425 0.412 0.399 0.388 0.377 0.507 0.490 0.476 0.462 0.450 0.601 0.582 0.564 0.549 0.534 0.666 0.645 0.625 0.608 0.591 21 22 23 24 25 0.368 0.359 0.351 0.343 0.336 0.438 0.428 0.418 0.409 0.400 0.521 0.508 0.496 0.485 0.475 0.576 0.562 0.549 0.537 0.526 26 27 28 29 30 0.329 0.323 0.317 0.311 0.305 0.392 0.385 0.377 0.370 0.364 0.465 0.456 0.448 0.440 0.432 0.515 0.505 0.496 0.487 0.478 Source: E G Olds, “Distribution of Sums of Squares of Rank Differences for Small Samples,” Annals of Mathematical Statistics (1938) Appendix A: Statistical Tables A-33 TABLE A.12 Values of dL and dU for the Durbin–Watson Test for ␣ 0.05 n ؍number of observations k number of independent variables k؍1 n 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100 k؍2 k؍3 k؍4 k؍5 dL dU dL dU dL dU dL dU dL dU 1.08 1.10 1.13 1.16 1.18 1.20 1.22 1.24 1.26 1.27 1.29 1.30 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.43 1.44 1.48 1.50 1.53 1.55 1.57 1.58 1.60 1.61 1.62 1.63 1.64 1.65 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.45 1.46 1.47 1.48 1.48 1.49 1.50 1.50 1.51 1.51 1.52 1.52 1.53 1.54 1.54 1.54 1.57 1.59 1.60 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.69 0.95 0.98 1.02 1.05 1.08 1.10 1.13 1.15 1.17 1.19 1.21 1.22 1.24 1.26 1.27 1.28 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.43 1.46 1.49 1.51 1.54 1.55 1.57 1.59 1.60 1.61 1.62 1.63 1.54 1.54 1.54 1.53 1.53 1.54 1.54 1.54 1.54 1.55 1.55 1.55 1.56 1.56 1.56 1.57 1.57 1.57 1.58 1.58 1.58 1.59 1.59 1.59 1.60 1.60 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.70 1.71 1.72 0.82 0.86 0.90 0.93 0.97 1.00 1.03 1.05 1.08 1.10 1.12 1.14 1.16 1.18 1.20 1.21 1.23 1.24 1.26 1.27 1.28 1.29 1.31 1.32 1.33 1.34 1.38 1.42 1.45 1.48 1.50 1.52 1.54 1.56 1.57 1.59 1.60 1.61 1.75 1.73 1.71 1.69 1.68 1.68 1.67 1.66 1.66 1.66 1.66 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.66 1.66 1.66 1.66 1.67 1.67 1.68 1.69 1.70 1.70 1.71 1.72 1.72 1.73 1.73 1.74 0.69 0.74 0.78 0.82 0.86 0.90 0.93 0.96 0.99 1.01 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.19 1.21 1.22 1.24 1.25 1.26 1.27 1.29 1.34 1.38 1.41 1.44 1.47 1.49 1.51 1.53 1.55 1.57 1.58 1.59 1.97 1.93 1.90 1.87 1.85 1.83 1.81 1.80 1.79 1.78 1.77 1.76 1.76 1.75 1.74 1.74 1.74 1.73 1.73 1.73 1.73 1.73 1.72 1.72 1.72 1.72 1.72 1.72 1.72 1.73 1.73 1.74 1.74 1.74 1.75 1.75 1.75 1.76 0.56 0.62 0.67 0.71 0.75 0.79 0.83 0.86 0.90 0.93 0.95 0.98 1.01 1.03 1.05 1.07 1.09 1.11 1.13 1.15 1.16 1.18 1.19 1.21 1.22 1.23 1.29 1.34 1.38 1.41 1.44 1.46 1.49 1.51 1.52 1.54 1.56 1.57 2.21 2.15 2.10 2.06 2.02 1.99 1.96 1.94 1.92 1.90 1.89 1.88 1.86 1.85 1.84 1.83 1.83 1.82 1.81 1.81 1.80 1.80 1.80 1.79 1.79 1.79 1.78 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.77 1.78 1.78 1.78 Source: From J Durbin and G.S Watson, “Testing for Serial Correlation in Least Squares Regression,” Biometrika, 38 June, 1951 A-34 Appendix A: Statistical Tables TABLE A.12 (continued) Values of dL and dU for the Durbin–Watson Test for ␣ 0.025 n ؍number of observations k number of indep endent variables k؍1 n 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100 k؍2 k؍3 k؍4 k؍5 dL dU dL dU dL dU dL dU dL 0.95 0.98 1.01 1.03 1.06 1.08 1.10 1.12 1.14 1.16 1.18 1.19 1.21 1.22 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.39 1.42 1.45 1.47 1.49 1.51 1.53 1.54 1.56 1.57 1.58 1.59 1.23 1.24 1.25 1.26 1.28 1.28 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.38 1.39 1.40 1.41 1.41 1.42 1.43 1.43 1.44 1.44 1.45 1.48 1.50 1.52 1.54 1.55 1.57 1.58 1.59 1.60 1.61 1.62 1.63 0.83 0.86 0.90 0.93 0.96 0.99 1.01 1.04 1.06 1.08 1.10 1.12 1.13 1.15 1.17 1.18 1.20 1.21 1.22 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.34 1.38 1.41 1.44 1.46 1.48 1.50 1.52 1.53 1.55 1.56 1.57 1.40 1.40 1.40 1.40 1.41 1.41 1.41 1.42 1.42 1.43 1.43 1.44 1.44 1.45 1.45 1.46 1.47 1.47 1.48 1.48 1.48 1.49 1.49 1.50 1.50 1.51 1.53 1.54 1.56 1.57 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.65 0.71 0.75 0.79 0.82 0.86 0.89 0.92 0.95 0.97 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.13 1.15 1.16 1.17 1.19 1.20 1.21 1.23 1.24 1.25 1.30 1.34 1.37 1.40 1.43 1.45 1.47 1.49 1.51 1.53 1.54 1.55 1.61 1.59 1.58 1.56 1.55 1.55 1.54 1.54 1.54 1.54 1.54 1.54 1.54 1.54 1.54 1.54 1.55 1.55 1.55 1.55 1.55 1.56 1.56 1.56 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.65 1.66 1.67 1.67 0.59 0.64 0.68 0.72 0.76 0.79 0.83 0.86 0.89 0.91 0.94 0.96 0.99 1.01 1.03 1.05 1.07 1.08 1.10 1.12 1.13 1.15 1.16 1.17 1.19 1.20 1.25 1.30 1.33 1.37 1.40 1.42 1.45 1.47 1.49 1.50 1.52 1.53 1.84 1.80 1.77 1.74 1.72 1.70 1.69 1.68 1.67 1.66 1.65 1.65 1.64 1.64 1.63 1.63 1.63 1.63 1.63 1.63 1.63 1.63 1.62 1.62 1.63 1.63 1.63 1.64 1.64 1.65 1.66 1.66 1.67 1.67 1.68 1.69 1.69 1.70 0.48 0.53 0.57 0.62 0.66 0.70 0.73 0.77 0.80 0.83 0.86 0.88 0.91 0.93 0.96 0.98 1.00 1.02 1.04 1.06 1.07 1.09 1.10 1.12 1.13 1.15 1.21 1.26 1.30 1.33 1.36 1.39 1.42 1.44 1.46 1.48 1.50 1.51 dU 2.09 2.03 1.98 1.93 1.90 1.87 1.84 1.82 1.80 1.79 1.77 1.76 1.75 1.74 1.73 1.73 1.72 1.71 1.71 1.70 1.70 1.70 1.70 1.70 1.69 1.69 1.69 1.69 1.69 1.69 1.69 1.70 1.70 1.70 1.71 1.71 1.71 1.72 Appendix A: Statistical Tables A-35 TABLE A.12 (continued) Values of dL and dU for the Durbin–Watson Test for ␣ 0.01 n ؍number of observations k number of independent variables k؍1 n 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 45 50 55 60 65 70 75 80 85 90 95 100 k؍2 k؍3 k؍4 k؍5 dL dU dL dU dL dU dL dU dL dU 0.81 0.84 0.87 0.90 0.93 0.95 0.97 1.00 1.02 1.04 1.05 1.07 1.09 1.10 1.12 1.13 1.15 1.16 1.17 1.18 1.19 1.21 1.22 1.23 1.24 1.25 1.29 1.32 1.36 1.38 1.41 1.43 1.45 1.47 1.48 1.50 1.51 1.52 1.07 1.09 1.10 1.12 1.13 1.15 1.16 1.17 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.32 1.33 1.34 1.34 1.38 1.40 1.43 1.45 1.47 1.49 1.50 1.52 1.53 1.54 1.55 1.56 0.70 0.74 0.77 0.80 0.83 0.86 0.89 0.91 0.94 0.96 0.98 1.00 1.02 1.04 1.05 1.07 1.08 1.10 1.11 1.13 1.14 1.15 1.16 1.18 1.19 1.20 1.24 1.28 1.32 1.35 1.38 1.40 1.42 1.44 1.46 1.47 1.49 1.50 1.25 1.25 1.25 1.26 1.26 1.27 1.27 1.28 1.29 1.30 1.30 1.31 1.32 1.32 1.33 1.34 1.34 1.35 1.36 1.36 1.37 1.38 1.38 1.39 1.39 1.40 1.42 1.45 1.47 1.48 1.50 1.52 1.53 1.54 1.55 1.56 1.57 1.58 0.59 0.63 0.67 0.71 0.74 0.77 0.80 0.83 0.86 0.88 0.90 0.93 0.95 0.97 0.99 1.01 1.02 1.04 1.05 1.07 1.08 1.10 1.11 1.12 1.14 1.15 1.20 1.24 1.28 1.32 1.35 1.37 1.39 1.42 1.43 1.45 1.47 1.48 1.46 1.44 1.43 1.42 1.41 1.41 1.41 1.40 1.40 1.41 1.41 1.41 1.41 1.41 1.42 1.42 1.42 1.43 1.43 1.43 1.44 1.44 1.45 1.45 1.45 1.46 1.48 1.49 1.51 1.52 1.53 1.55 1.56 1.57 1.58 1.59 1.60 1.60 0.49 0.53 0.57 0.61 0.65 0.68 0.72 0.75 0.77 0.80 0.83 0.85 0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.01 1.03 1.04 1.06 1.07 1.09 1.10 1.16 1.20 1.25 1.28 1.31 1.34 1.37 1.39 1.41 1.43 1.45 1.46 1.70 1.66 1.63 1.60 1.58 1.57 1.55 1.54 1.53 1.53 1.52 1.52 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.51 1.52 1.52 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.60 1.61 1.62 1.63 0.39 0.44 0.48 0.52 0.56 0.60 0.63 0.66 0.70 0.72 0.75 0.78 0.81 0.83 0.85 0.88 0.90 0.92 0.94 0.95 0.97 0.99 1.00 1.02 1.03 1.05 1.11 1.16 1.21 1.25 1.28 1.31 1.34 1.36 1.39 1.41 1.42 1.44 1.96 1.90 1.85 1.80 1.77 1.74 1.71 1.69 1.67 1.66 1.65 1.64 1.63 1.62 1.61 1.61 1.60 1.60 1.59 1.59 1.59 1.59 1.59 1.58 1.58 1.58 1.58 1.59 1.59 1.60 1.61 1.61 1.62 1.62 1.63 1.64 1.64 1.65 A-36 Appendix A: Statistical Tables TABLE A.13 Factors for Determining 3-Sigma Control Limits, Mean and Range Control Charts Number of Observations in Each Sample Factor for Determining Control Limits, Control Chart for the Mean Factors for Determining Control Limits, Control Chart for the Range n A2 D3 D4 1.880 1.023 0.729 0.577 0 0 3.267 2.575 2.282 2.115 10 0.483 0.419 0.373 0.337 0.308 0.076 0.136 0.184 0.223 2.004 1.924 1.864 1.816 1.777 11 12 13 14 15 0.285 0.266 0.249 0.235 0.223 0.256 0.284 0.308 0.329 0.348 1.744 1.716 1.692 1.671 1.652 Source: From E S Pearson, “The Percentage Limits for the Distribution of Range in Samples from a Normal Population,” Biometrika 24 (1932): 416 A P P E N D I X S TED C E EL Answers to Selected Odd-Numbered Exercises 2.3 a 45.59 million b lower limit is 35, upper limit is under 45 c 10 years d 40 years 2.5 a 183.53 thousand b lower limit is 45, upper limit is under 55 c 10 years d. 50 years 2.45 a y ϭ 323.53 ϩ 0.8112x b yes, direct 2.55 a 1342 cities b 2815 cities c 253 cities; 8.77% d 175,000 2.67 a yes b lawjudge ϭ 0.788 ϩ 0.840*acad 2.69 a yes b Canada ϭ 1.089 ϩ 1.754*U.S 2.71 c highest: mechanical and electrical 1; lowest: mechanical and electrical 3.1 x ϭ $20.449, median ϭ $20.495 3.3 x ϭ 57.05 visitors, median ϭ 57.50, mode ϭ 63 3.5 x ϭ 6.93, median ϭ 7.095 3.7 x ϭ 38.1, median ϭ 36.5 3.9 83.2 3.11 a mean b median 3.13 x ϭ 398.86, median ϭ 396.75 3.15 females: ANSWE RS Chapter Chapter Chapter B x ϭ 40.62, median ϭ 39.00; males: x ϭ 41.08, median ϭ 41.50 3.17 range ϭ 39, MAD ϭ 10.35 visitors, s ϭ 12.40, s2 ϭ 153.84 3.19 a ϭ 29.11 million, median ϭ 22.4 million, range ϭ 44.5 million, midrange ϭ 39.45 million b MAD ϭ 12.99 million c ϭ 15.44 million, 2 ϭ 238.396 3.21 a x ϭ 27.2 mpg, median ϭ 28 mpg, range ϭ 30 mpg, midrange ϭ 25 mpg b MAD ϭ 5.6 mpg c s ϭ 8.052, s2 ϭ 64.84 3.23 Q1 ϭ 7, Q2 ϭ 18, Q3 ϭ 30, interquartile range ϭ 23, quartile deviation ϭ 11.5 3.25 a x ϭ 23.35, median ϭ 22.86, range ϭ 26.13, midrange ϭ 26.465 b MAD ϭ 4.316 c s ϭ 5.49, s2 ϭ 30.14 3.27 a x ϭ 90.771, median ϭ 91.4, range ϭ 40.4, midrange ϭ 92.0 b MAD ϭ 6.70 c s ϭ 8.36, s2 ϭ 69.90 3.29 a 84% b 88.89% c 96% 3.31 90%, yes 3.33 a 68% b 2.5% c 84% d 13.5% 3.35 Barnsboro 3.39 a approximately 7.00 and 1.504 3.41 approximately 21.75 and 15.65 3.43 r ϭ Ϫ0.8 3.45 lawjudge ϭ 0.7880 ϩ 0.8404*acad, r2 ϭ 0.9344, r ϭ 0.967 3.47 generic ϭ Ϫ3.5238 ϩ 0.377*brand, r2 ϭ 0.7447, r ϭ 0.863 3.49 $4.69 3.51 x ϭ 117.75, median ϭ 117.5, no 3.53 no, positively skewed 3.55 a x becomes 3.1 lbs., s remains 0.5 lbs b 4.1 lbs 3.57 a x ϭ 2.099, median ϭ 2.115, range ϭ 0.46, midrange ϭ 2.08 b MAD ϭ 0.137 c s ϭ 0.156, s2 ϭ 0.02446 3.59 120, 116, 124, 20, symmetrical 3.61 greater variation for data in exercise 3.60 Chapter 4.3 a secondary b secondary 4.11 response error 4.13 telephone 4.39 systematic 4.43 a sample b sample c sample d census 4.69 a 54 b 146 B-1 5.1 subjective 5.7 decrease for men, increase for women 5.9 0.36 5.13 a b 196 c 147 d 372 5.19 0.945, 0.035 5.21 0.35, 0.65 5.23 0.797 5.25 b 0.13 c 0.30 d 0.89 5.27 0.91 5.29 a 0.947 b 0.710 c 0.351 d 0.992 5.31 no, no 5.33 a 0.16 b 0.31 c 0.12 d 0.41 5.35 0.851 5.37 a 0.025 b 0.709 c 0.266 5.39 0.175 5.43 0.154 5.45 a 0.51 b 0.85 c 0.77 5.47 a 0.5 b 0.455 5.49 a 0.1 b 0.233 5.51 256 5.53 36 5.57 20 5.59 7.9019*1027 5.61 a 0.000000005 b 0.0625 c 0.062500005 d 5.63 a 0.001 b classical c yes 5.65 a b c 5.67 a 0.005 b 0.855 c 0.14 d 0.995 5.69 a 0.85 b 0.278 c 0.046 5.71 a 0.7 b 0.9 c 0.667 5.73 a 0.973 b 4.741*10Ϫ12 c 10 5.75 22 5.77 0.296, 0.963 5.79 a 0.9 b 0.429 5.81 120 5.83 1320 5.85 10,000 Chapter 6.3 a discrete b continuous c discrete d continuous 6.5 ϭ 7.2, ϭ 2.18, 2 ϭ 4.76 6.7 ϭ 1.9, ϭ 1.14, 2 ϭ 1.29 6.9 $10 6.11 E(x) ϭ 3.1 6.13 $0.50 6.15 $37.9 million, $41.9 million, $40.3 million, minor 6.19 a 3.6 b 1.59 c 0.2397 d 0.9133 e 0.5075 6.21 a 0.0102 b 0.2304 c 0.3456 d 0.0778 6.23 a 0.9703 b 0.0294 c 0.0003 d 0.0000 6.25 a 0.9375 b 0.6875 6.27 0.1250, 0.1250, 0.3750 6.29 0.3439 6.31 a 0.0014 b 0.0139 c yes 6.35 a 0.1000 b 0.6000 c 0.3000 6.37 0.9000 6.39 a 0.1353 b 0.2707 c 0.8571 d 0.5940 6.41 a 4.9 b 0.1460 c 0.1753 d 0.9382 e 0.8547 6.43 a 1.8 b 0.2975 c 0.0723 d 0.9974 e 0.5268 6.45 0.0047, should consider slight decrease 6.47 a 10.0 b 0.0901 c 0.1251 d 0.7916 e 0.7311 6.49 0.2275, $45,000 6.51 not merely a coincidence 6.55 0.9098 6.57 no 6.61 87.95% 6.63 0.3684 6.65 0.1837 6.67 0.6065 6.69 0.3125 6.71 0.1904 6.73 0.0839 6.75 0.9872 6.77 0.7748 6.79 0.0012, not believable Chapter 7.9 a 0.5 b approx 0.683 c approx 0.8415 d e approx 0.4775 f approx 0.9775 7.11 a 0.5 b approx 0.955 c approx 0.683 d approx 0.9985 7.13 a approx 0.1585 b approx 0.683 c approx 0.0225 d approx 0.819 7.15 a approx 0.0015 b approx 0.1585 7.17 a Ϫ0.67, 0.67 b Ϫ1.28, 1.28 c Ϫ0.74, 0.74 7.19 a Ϫ2.00 b Ϫ0.80 c 0.00 d 3.40 e 4.60 7.21 a 0.3643 b 0.1357 c 0.9115 7.23 a 0.8730 b 0.2272 c 0.1091 7.25 a 0.52 b Ϫ1.28 c 0.10 d 0.52 7.27 a 0.0874 b 0.8790 B-2 c 0.8413 7.29 a 0.4207 b 0.3050 c 0.3446 7.31 $409,350 7.33 a 0.4207 b $9545 7.35 3.22 minutes 7.37 70,500 7.41 a 10.0, 2.739 b 0.1098, 0.2823, 0.3900, 0.1003 7.43 a 12.0, 1.549 b 0.2501 c 0.2510 d 0.9463 7.45 0.4350 7.47 0.4191 7.53 a 0.5488 b 0.4493 c 0.3679 d 0.3012 7.55 0.2865 7.57 0.619, 0.383, 8779.7 hours 7.61 11.51% 7.63 0.3911 7.65 no 7.67 0.0668, 0.0228 7.69 0.1587 7.71 0.8023 7.73 not credible 7.75 0.6604 7.77 0.4584, 0.2101 7.79 0.4307 7.81 0.0918, 0.0446 7.83 20.615 7.85 a 0.4628 b 0.7772 c 12,900 7.87 0.4724 Chapter 8.3 0.18, 0.15, 1000 8.7 a 25 b 10 c d 3.162 8.9 a 0.8413 b 0.6853 c 0.9938 8.11 0.8849, 0.8823 8.13 concern is justified 8.15 0.1056 8.17 0.1949 8.19 0.9976 8.21 ϭ 0.46, p # 0.0895 8.23 a 0.9616 b 0.5222 c 0.9616 8.25 a 0.40 b 0.35 c 0.035 d 0.9236 8.27 0.9938 8.29 0.0000; district’s claim is much more credible 8.35 0.1170 8.37 0.8023 8.43 a 0.0183 b not credible 8.45 b 0.0446 8.47 a 2.40 b 0.0082 c no 8.51 a 0.10 b 0.0062 c no 8.53 0.0643 8.55 0.0000 8.57 0.0228 Chapter 9.7 a 2.625 b 4.554 9.11 a 0.45 b (0.419, 0.481) c 95%, 0.95 9.15 90%: (236.997, 243.003); 95%: (236.422, 243.578) 9.17 90%: (82.92, 87.08); 95%: (82.52, 87.48) 9.19 (149.006, 150.994) 9.23 (99.897, 100.027); yes 9.27 1.313 9.29 a 1.292 b Ϫ1.988 c 2.371 9.31 95%: (46.338, 54.362); 99%: (44.865, 55.835) 9.33 a (22.16, 27.84) b yes 9.35 (28.556, 29.707) 9.37 (1520.96, 1549.04) 9.39 (17.43, 21.97); no 9.41 (14.646, 15.354); yes 9.43 (0.429, 0.491) 9.45 (0.153, 0.247); not credible 9.47 (0.449, 0.511) 9.49 (0.579, 0.625) 9.51 a (0.527, 0.613) 9.53 (0.649, 0.711) 9.55 (0.566, 0.634); no; may not succeed 9.57 (0.311, 0.489) 9.61 92 9.63 1068 9.65 863 9.67 601 9.71 95%: (0.522, 0.578); 99%: (0.513, 0.587) 9.73 458 9.75 92 9.77 462 9.79 1226 9.81 0.01 9.83 (135.211, 138.789) 9.85 246 9.87 90%: (44.91, 49.96); 95%: (44.39, 50.47) 9.89 411 9.91 $1200 9.93 95%: (0.347, 0.433); 99%: (0.334, 0.446) 9.95 4161 9.97 722 9.99 1068 9.101 1110 9.103 3736 9.105 90%: (0.375, 0.425); 95%: (0.370, 0.430) 9.107 (0.018, 0.062) 9.109 ($95.56, $98.45) 9.111 (64.719, 68.301); funds are not endangered Chapter 10 10.3 a no b yes c yes d no e yes f no 10.5 type I 10.7 type II 10.13 type I 10.17 a numerically high b numerically low 10.23 no; not reject H0 10.25 a 0.0618 b 0.1515 c 0.0672 10.27 reject H0; p-value ϭ 0.021 10.29 not reject H0; p-value ϭ 0.035 10.31 no; not reject H0; p-value ϭ 0.052 10.33 p-value ϭ 0.316; not reject H0 10.35 a not reject H0 b reject H0 c not reject H0 d reject H0 10.37 (1.995, 2.055); not reject H0; same 10.41 not reject H0 10.43 no; not reject H0 10.45 no; reject H0 10.47 yes; reject H0 10.49 not reject H0 10.51 yes; reject H0 10.53 (86.29, 92.71); no; yes Appendix B: Selected Answers 10.55 (35.657, 37.943); no; yes 10.57 0.03; reject H0 10.61 reject H0 10.63 reject H0 10.65 no; reject H0; 0.003 10.67 yes; reject H0; p-value ϭ 0.005 10.69 reject H0; p-value ϭ 0.014 10.71 yes; p-value ϭ 0.220 10.73 no; not reject H0; p-value ϭ 0.079 10.75 (0.735, 0.805); yes; yes 10.77 (0.402, 0.518); yes; yes 10.81 alpha unchanged, beta decreases 10.83 0.9871 10.87 a 2.33 b 0.036 10.93 reject H0, has increased 10.95 a 0.05 level: reject H0 b 95% CI: (236,279; 255,321) 10.97 yes 10.99 reject H0 10.101 reject H0; statement not credible 10.103 not reject H0; claim is credible 10.105 a 0.9505 b 0.8212 c 0.5753 d 0.2946 e 0.1020 10.107 b e.g., 0.005 c e.g., 0.02 d 0.024 10.109 yes; reject H0; p-value ϭ 0.015 10.111 no; not reject H0; p-value ϭ 0.059 10.113 not reject H0; p-value ϭ 0.282 Chapter 11 11.3 not reject H0, Ͼ 0.20 11.5 yes; reject H0 11.7 not reject H0; between 0.05 and 0.10; (Ϫ8.872, 0.472) 11.9 reject H0; between 0.10 and 0.05; 90% CI: (Ϫ1.318, Ϫ0.082) 11.11 claim could be valid; reject H0; between 0.01 and 0.025 11.13 yes; p-value ϭ 0.031 11.15 (Ϫ24.23, 1.03); yes; yes 11.17 (Ϫ3.33, 31.20); yes; yes 11.19 not reject H0 11.21 yes, not reject H0; Ͼ 0.20; 95% CI: (Ϫ23.43, 6.43) 11.23 not reject H0; 0.1400; (Ϫ117.18, 17.18); yes; yes 11.25 not reject H0; (Ϫ2.03, Ϫ1.37); yes; yes 11.27 reject H0; 0.000 11.29 reject H0; 0.006 11.33 reject H0 11.35 yes, not reject H0; 0.2538; 95% CI: (Ϫ23.10, 6.10) 11.37 not reject H0; 0.1967; (Ϫ7.77, 37.77) 11.39 reject H0; 0.0122 11.41 reject H0; 0.001 11.43 not reject H0; 0.12 11.45 dependent 11.47 reject H0 11.49 reject H0; between 0.005 and 0.01 11.51 not reject H0; 0.170; (Ϫ4.663, 1.774) 11.53 reject H0 11.55 no; not reject H0 11.57 not reject H0 11.59 yes; reject H0; 0.0607; (Ϫ0.150, Ϫ0.010) 11.61 reject H0; 0.0583 11.63 not reject H0; 0.057; (Ϫ0.031, 0.211) 11.65 not reject H0; 0.1866; (Ϫ0.055, 0.005) 11.67 not reject H0; no, no 11.69 yes; not reject H0; no 11.71 yes; reject H0 11.73 reject H0 11.75 suspicion confirmed; reject H0; between 0.025 and 0.05 11.77 not reject H0; (Ϫ505.32, 65.32) 11.79 reject H0; Ͻ 0.005 11.81 yes; reject H0; 0.0141 11.83 reject H0; table: Ͻ 0.01; computer: 0.0075; (0.13, 6.67) 11.85 not reject H0; (Ϫ1.13, 0.13) 11.87 yes; reject H0 11.89 no; not reject H0 11.91 yes; reject H0; Ͻ 0.005 11.93 yes; reject H0; 0.001 11.95 yes; not reject H0; no 11.97 not reject H0; 0.140; (Ϫ1.95, 12.96) 11.99 not supported; not reject H0; 0.135 11.101 not reject H0; 0.414; (Ϫ0.1204, 0.0404) Chapter 12 12.7 designed 12.21 not reject H0; Ͼ 0.05 12.23 not reject H0; Ͼ 0.05 12.25 not reject H0 12.27 b reject H0 12.29 b not reject H0 c 1: (48.914, 61.086); 2: (42.714, 54.886); 3: (39.514, 51.686) 12.35 1: (16.271, 19.009); 2: (13.901, 16.899); 3: (15.690, 18.060) 12.47 reject H0; between 0.025 and 0.05 12.49 not reject H0; not reject H0 12.51 not reject H0; not reject H0 12.53 reject H0 12.55 reject H0 12.59 yes; reject H0 12.69 Factor A, not reject H0; Factor B, reject H0; Interaction, reject H0 Appendix B: Selected Answers 12.71 Factor A, not reject H0; Factor B, reject H0; Interaction, not reject H0 12.73 Factor A, reject H0; Factor B, reject H0; Interaction, reject H0 12.75 Assembly, not reject H0; Music, reject H0; Interaction, reject H0; Method 1, (35.846, 41.654); Method 2, (34.096, 39.904); Classical, (29.096, 34.904); Rock, (40.846, 46.654) 12.77 Bag, not reject H0; Dress, reject H0; Interaction, reject H0; Carry, (24.798, 30.536); Don’t Carry, (27.298, 33.036); Sloppy, (41.736, 48.764); Casual, (17.736, 24.764); Dressy, (16.736, 23.764) 12.79 Keyboard, reject H0; Wordpack, not reject H0; Interaction, reject H0 12.83 randomized block 12.85 independent: faceplate design; dependent: time to complete task; designed 12.87 no, randomized block procedure should be used 12.89 reject H0 12.91 not reject H0 12.93 reject H0 12.95 not reject H0 12.97 reject H0 12.99 Style, not reject H0; Darkness, reject H0; Interaction, not reject H0; Style 1, (25.693, 30.307); Style 2, (23.693, 28.307); Light, (27.425, 33.075); Medium, (22.175, 27.825); Dark, (22.925, 28.575) 12.101 Position, reject H0; Display, not reject H0; Interaction, reject H0; Position 1, (42.684, 47.982); Position 2, (47.129, 52.427); Display 1, (42.089, 48.577); Display 2, (43.923, 50.411); Display 3, (46.923, 53.411) Chapter 13 13.7 a 3.490 b 13.362 c 2.733 d 15.507 e 17.535 f 2.180 13.9 a A ϭ 8.547, B ϭ 22.307 b A ϭ 7.261, B ϭ 24.996 c A ϭ 6.262, B ϭ 27.488 d A ϭ 5.229, B ϭ 30.578 13.13 13.15 a b 12.592 c not reject H0 13.17 yes; reject H0 13.19 not reject H0 13.21 not reject H0 13.23 not reject H0 13.25 reject H0 13.29 a b c 12 d e 12 f 13.31 a 12.833 b 15.507 c 16.812 d 7.779 13.33 no, reject H0; between 0.025 and 0.01 13.35 no; reject H0; between 0.05 and 0.025 13.37 no; reject H0; less than 0.01 13.39 yes; not reject H0 13.41 no; reject H0 13.43 not reject H0 13.45 not reject H0 13.47 reject H0 13.49 yes; not reject H0 13.53 (15.096, 43.011) 13.55 (2.620, 9.664) 13.57 (0.1346, 0.2791) 13.59 not reject H0 13.61 not reject H0 ; between 0.05 and 0.025 13.63 (0.0329, 0.0775) 13.65 not reject H0 13.67 reject H0 13.69 yes; not reject H0 13.71 not reject H0 ; between 0.10 and 0.05 13.73 no; not reject H0; between 0.10 and 0.05 13.75 (0.02001, 0.05694) 13.77 reject H0 13.79 not reject H0 13.81 reject H0 13.83 reject H0 13.85 not reject H0 13.87 probably not; reject H0 Chapter 14 14.7 reject H0; Ͻ 0.005 14.9 yes; reject H0; 0.017 14.11 not reject H0; 0.137 14.13 reject H0 14.15 yes, reject H0 14.17 not reject H0; between 0.05 and 0.10 14.19 no; not reject H0; 0.137 14.23 not reject H0 14.25 yes; not reject H0; 0.2443 14.29 reject H0 14.31 no; reject H0 14.33 no; reject H0; 0.058 14.37 yes; not reject H0; between 0.10 and 0.90 14.39 no; not reject H0; 0.393 14.43 not reject H0 14.45 reject H0 14.49 not reject H0 14.51 not reject H0 14.53 not reject H0 14.55 0.83, yes B-3 14.57 0.343, no 14.59 reject H0; 0.0287 14.61 no, 0.619 14.63 not reject H0 14.65 yes; reject H0; 0.0056 14.67 no; not reject H0; between 0.05 and 0.10 14.69 yes; not reject H0; between 0.025 and 0.05 14.71 yes; not reject H0; between 0.025 and 0.05 14.75 claim not credible, reject H0; between 0.05 and 0.025 14.77 0.868, yes 14.79 no; not reject H0; 0.343 14.81 not reject H0; 0.210 14.83 they can tell the difference; reject H0; 0.016 14.85 not reject H0; 0.486 Chapter 15 15.5 second 15.7 second 15.9 a Shares ϭ 44.3 ϩ38.756*Years b 431.9 15.11 totgross ϭ 110.02 ϩ 1.0485*2wks; $214.87 million 15.13 Acres ϭ 349,550 Ϫ 7851*Rain; 208,223 acres 15.21 a yˆ ϭ 21.701 Ϫ 1.354x b 3.617 c (8.107, 16.339) d (4.647, 14.383) e interval d is wider 15.23 a Rating ϭ 54.97 ϩ 7.166*TD% b 90.796 c 1.386 d (86.728, 94.863) e (88.833, 92.758) 15.25 91.48; (Ϫ33.9, 510.1) 15.27 Revenue ϭ Ϫ1.66*108 ϩ 64,076,803*Dealers; CI: (5.88*109, 6.60*109); PI: (4.92*109, 7.57*109) 15.29 CI: (89,209; 295,832); PI: (Ϫ155,578; 540,619) 15.33 0.81 15.37 a Coll ϭ 24.48 ϩ 0.955*Comp b 0.860, 0.740 c 110.44 15.39 a %Over ϭ Ϫ82.19 ϩ 0.04236*Cals b 0.931, 0.866 c 44.89% 15.41 r ϭ 0.800; r2 ϭ 0.640 15.43 Forgross ϭ Ϫ69.382 ϩ 1.5266*Domgross; r ϭ 0.7356; r2 ϭ 0.5411 15.45 no 15.47 Ͼ 0.10 15.49 a reject H0 b reject H0 c (0.556, 1.354) 15.51 a reject H0 b reject H0 c (0.392, 9.608) 15.53 61.2, 58.8 15.55 774.80, 536.01, 238.79; 0.692; not reject H0 15.57 Gallons ϭ 5,921,560.92 ϩ 10.44806*Hours; r ϭ 0.993; r2 ϭ 0.986; no; (8.746, 12.150) 15.59 NetIncome ϭ 59.8006 ϩ 0.0382*Revenue; r ϭ 0.7492; r2 ϭ 0.5612; no; (0.031, 0.045) 15.71 NetIncome ϭ 0.211 ϩ 0.0999*TotRev; $2.009 billion 15.73 a OneYr% ϭ Ϫ2.01 ϩ1.45*ThreeYr% b 5.264% c 8.172% 15.75 NetIncome ϭ 2.301 ϩ 0.116*OpRev; $5.789 billion 15.77 a Amount ϭ Ϫ2366.0 ϩ 623.93*Policies b r ϭ 0.99; r2 ϭ 0.984 c $16352 million 15.79 a Fuel ϭ 48.065 ϩ 0.042244*Miles b 0.992, 0.984 c 179.02 billion gallons 15.81 a RearFull ϭ 318 ϩ 2.612*RearCorner b 0.397, 0.157 c $2408 15.83 a Strength ϭ 60.02 ϩ 10.507*Temptime b 53.0% c 0.017 d 0.017 e (2.445, 18.569) 15.85 a Rolresis ϭ 9.450 Ϫ 0.08113*psi b 23.9% c 0.029 d 0.029 e (Ϫ0.15290, Ϫ0.00936) 15.87 CI: (8.26, 28.87); PI: (Ϫ6.66, 43.78) 15.89 CI: (49.710, 54.647); PI: (46.776, 57.581) 15.91 a GPA ϭ Ϫ0.6964 ϩ 0.0033282*SAT; 2.965 b 69.5% c CI: (2.527, 3.402); PI: (1.651, 4.278) 15.93 a Pay% ϭ 7.020 ϩ 1.516*Rate%; 19.148% b 98.0%; yes c CI: (18.9874, 19.3084); PI: (18.6159, 19.6799) 15.95 a Estp/e ϭ 52.56 Ϫ 0.0959*Revgrow%; 38.17 b 0.2%; no c CI: (Ϫ0.74, 77.07); PI: (Ϫ94.67, 171.01) Chapter 16 16.9 a 300, 7, 13 b 399 16.11 a yˆ ϭ 10.687 ϩ 2.157x1 ϩ 0.0416x2 c 24.59 16.13 a yˆ ϭ Ϫ127.19 ϩ 7.611x1 ϩ 0.3567x2 c Ϫ17.79 16.15 b 454.42 16.17 a 130.0 b 3.195 c (98.493, 101.507) d (93.259, 106.741) B-4 16.19 a CalcFin ϭ Ϫ26.6 ϩ 0.776*MathPro ϩ 0.0820*SATQ; 90% CI: (64.01, 73.46) b 90% PI: (59.59, 77.88) 16.21 a (81.588, 90.978) b (77.565, 95.002) 16.27 0.716 16.29 a yes b 1, reject H0; 2, not reject H0 d 1, (0.54, 3.77); 2, (Ϫ0.07, 0.15) 16.31 1, (0.0679, 0.4811); 2, (0.1928, 0.5596); 3, (0.1761, 0.4768) 16.33 a yes b each is significant 16.35 a yˆ ϭ Ϫ40,855,482 ϩ 44,281.6x1 ϩ 152,760.2x2 b yes c 1, reject H0; 2, not reject H0 d 1, (41,229.4, 47,333.8); 2, (Ϫ4,446,472, 4,751,992) 16.45 a yˆ ϭ Ϫ0.8271 ϩ 0.007163x1 ϩ 0.01224x2 b 1, (0.00615, 0.00818); 2, (0.00198, 0.02249); c 0.959 16.51 Speed ϭ 67.6 Ϫ 3.21*Occupants Ϫ 6.63*Seatbelt 16.53 a yˆ ϭ 99.865 ϩ 1.236x1 ϩ 0.822x2 b 125.816 lbs c (124.194, 127.438) d (124.439, 127.193) e 1, (0.92, 1.55); 2, (0.09, 1.56) 16.55 a gpa ϭ Ϫ1.984 ϩ 0.00372*sat ϩ 0.00658*rank b 2.634 c (1.594, 3.674) d (2.365, 2.904) e 1, (0.000345, 0.007093); 2, (Ϫ0.010745, 0.023915) 16.57 $137,289 Chapter 17 17.3 negative, negative 17.5 positive, negative, positive 17.7 $Avgrate ϭ 336.094 Ϫ 8.239*%Occup ϩ 0.07709*%Occup2; 49.1% 17.9 0to60 ϭ 26.8119 Ϫ 0.153866*hp ϩ 0.0003083*hp2; 8.396 seconds; yes 17.11 Forgross ϭ 860.8 Ϫ 4.152*Domgross ϩ 0.007689* Domgross2; $430.4 million; yes 17.13 second-order with interaction 17.15 $percall ϭ 61.2 ϩ 25.63*yrs ϩ 6.41*score Ϫ1.82*yrs2 Ϫ 0.058*score2 ϩ 0.29*yrs*score; R2 ϭ 0.949; yes 17.17 a oprev ϭ Ϫ231.2 ϩ 0.129*employs ϩ 0.00565*departs; yes b oprev ϭ 399.2 ϩ 0.0745*employs ϩ 0.00087*departs ϩ 0.00000014*employs*departs; R increases from 0.958 to 0.986 17.19 0to60 ϭ 25.4 Ϫ 0.161*hp Ϫ 0.00030*curbwt ϩ 0.000028*hp*curbwt; R2 ϭ 0.734; yes 17.23 two 17.25 600 customers 17.27 price ϭ Ϫ30.77 ϩ 4.975*gb ϩ 54.20*highrpm; $54.20 17.29 productivity ϭ 75.4 ϩ 1.59*yrsexp Ϫ 7.36*metha ϩ 9.73*methb; R2 ϭ 0.741 17.31 yˆ ϭ 0.66(1.38)x 17.33 yˆ ϭ 42.668371(1.0169419)x; R2 ϭ 0.496; $138.30 17.35 log revenue ϭ Ϫ0.1285 ϩ 1.0040 log employs Ϫ 0.1121 log departs; revenue ϭ 0.7439*employs1.0040*departsϪ0.1121; $546.2 million 17.41 yes 17.43 may be present 17.45 will not be a problem 17.49 a x5, x2, x9 b yˆ ϭ 106.85 Ϫ 0.35x5 Ϫ 0.33x2 c 0.05 level: x5, x2, x9; 0.02 level: x2 17.59 Pages ϭ Ϫ141.5 ϩ 422.5x Ϫ 61.01x2 ϩ 2.749x3; 3727 17.61 yˆ ϭ 10.705 ϩ 0.974x Ϫ 0.015x2; yes; 83.6% 17.63 Wchill ϭ Ϫ11.296 ϩ 1.320 Temp Ϫ 0.456 Wind; Wchill ϭ Ϫ11.296 ϩ 1.185 Temp Ϫ 0.456 Wind ϩ 0.00542 TempxWind; from 0.995 to 0.997 17.65 productivity ϭ 19.09 ϩ 0.211*backlog ϩ 0.577*female; R2 ϭ 0.676; yes 17.67 Log_AllLoans ϭ Ϫ1.0130 ϩ 2.0567Log_CredCard ϩ 0.0635Log_Resid; AllLoans ϭ 0.09705*CredCard2.0567*Resid0.0635; 1.76% 17.69 yes; OpCost/Hr ϭ 525.8 ϩ3.21*Gal/Hr Ϫ 0.68*Range; 90.68% 17.71 a yes, test b final ϭ 14.79 ϩ 0.885*test1; R2 ϭ 0.8568 17.73 Rating ϭ 2.225 ϩ 4.1793*YdsperAtt Ϫ 4.1763*Int_pct ϩ3.3231*TD_pct ϩ 0.8305*Comp_pct; 100.00% (rounded) Appendix B: Selected Answers Chapter 18 18.3 369,600 gallons 18.5 with x ϭ for 2004, Earnings ϭ 15.045 ϩ 0.582x; $20.865 18.7 a Subs ϭ 13.371 ϩ 19.357x; 361.8 million b Subs ϭ 29.993 ϩ 12.233x ϩ 0.54798x2; 427.7 million c quadratic 18.17 the 0.4 curve; the 0.7 curve 18.21 30% 18.23 b I , 74.72; II, 103.98; III, 123.76; IV, 97.54 18.25 a J, 100.50; F, 94.33; M, 103.16; A, 103.60; M, 98.06; J, 100.55; J, 98.17; A, 98.38; S, 96.86; O, 108.84; N, 93.20; D, 104.35 18.27 $192.0 thousand, $201.6 thousand 18.29 1213.2; 1541.2 18.31 $69.43 billion 18.33 39.655 quadrillion Btu 18.35 189,000 gallons 18.39 quadratic, quadratic 18.41 quadratic, quadratic 18.45 0.58, positive autocorrelation 18.47 a inconclusive b inconclusive 18.49 yt ϭ Ϫ1.51 ϩ 1.119ytϪ1; 288.5 18.51 yt ϭ 525.6 ϩ 0.812ytϪ1; 2895.5; MAD ϭ 100.5 18.53 100 18.55 best: leisure and hospitality; worst: construction 18.57 $114,364 18.59 Army ϭ 476.29 ϩ 5.4643x; 558.25 thousand 18.61 Restaurants ϭ Ϫ1408.0 ϩ 1206.50x Ϫ 9.92905x2; 25,851 restaurants 18.63 a AvgBill ϭ 31.4743 ϩ 1.62536x; $55.855 b AvgBill ϭ 31.0071 ϩ 1.93679x Ϫ 0.038929x2; $51.300 c quadratic, quadratic 18.67 I, 95.14; II, 89.69; III, 95.64; IV, 119.53 18.69 I, 192.88; II, 63.87; III, 30.14; IV, 113.11 18.71 I, 94.68; II, 93.54; III, 111.05; IV, 100.73 18.73 I, 72.50; II, 83.11; III, 111.16; IV, 132.77 18.75 I, 71; II, 91; III, 104; IV, 66 18.77 Cost ϭ 38.3268 ϩ 0.794341x ϩ 0.0538258x2; Cost ϭ 37.1427 ϩ 1.38642x; quadratic 18.83 DW statistic ϭ 0.48; positive autocorrelation 18.85 CPIt ϭ 2.0216 ϩ 1.01812*CPItϪ1; MAD ϭ 1.388; 213.08 18.87 6.36% increase Chapter 19 19.9 0, 2000, 2000 shirts 19.11 a maximax b maximax c maximin 19.13 purchase, not purchase, purchase 19.17 make claims, $600 19.19 design B, $7.6 million 19.21 direct, 31.5 minutes, 0.5 minutes 19.25 A or C, $12,800, $12,800 19.27 direct, 0.5 minutes; longer, 9.0 minutes 19.29 296 cod 19.31 3520 programs 19.33 units 19.35 current; Dennis; Dennis 19.37 DiskWorth; ComTranDat; ComTranDat Chapter 20 20.35 0.0026 20.39 in control 20.41 out of control 20.43 out of control 20.45 LCL ϭ 0, UCL ϭ 0.088 20.47 LCL ϭ 0, UCL ϭ 15.72 20.49 centerline ϭ 0.197; LCL ϭ 0.113; UCL ϭ 0.282; in control 20.51 centerline ϭ 4.450; LCL ϭ 0; UCL ϭ 10.779; out of control 20.53 in control 20.55 no 20.57 0.89; not capable 20.59 yes; mean chart failed test #1 at sample 20.61 yes; mean chart failed tests #1 and #5 at sample 20.63 a in control b yes, 0.65; not capable 20.69 c-chart 20.71 1.07; capable 20.73 centerline ϭ 0.05225; LCL ϭ 0.00504; UCL ϭ 0.09946; in control 20.75 in control 20.77 centerline ϭ 0.0988; LCL ϭ 0.0355; UCL ϭ 0.1621; in control 20.79 yes, 0.74; not capable ... www.cengage.com/permissions Further permissions questions can be emailed to permissionrequest@cengage.com Media Editor: Chris Valentine Frontlist Buyer, Manufacturing: Miranda Klapper Compositor: MPS Limited,... A Macmillan Company Sr Art Director: Stacy Shirley Internal/Cover Designer: Craig Ramsdell Cover Image: © Getty Images Photo Acquisition Manager: Don Schlotman ExamView® is a registered trademark... Model 676 17.9 Summary 677 Integrated Case: Thorndike Sports Equipment 681 Integrated Case: Fast-Growing Companies 681 Business Case: Westmore MBA Program 682 Business Case: Easton Realty Company