EIGHTH EDITION Statistics for Business and Economics Global Edition Paul Newbold University of Nottingham William L Carlson St Olaf College Betty M Thorne Stetson University Boston Amsterdam Delhi Columbus Cape Town Mexico City Indianapolis Dubai São Paulo New York London Sydney Madrid San Francisco Milan Hong Kong Munich Seoul Upper Saddle River Paris Montréal Toronto Singapore Taipei Tokyo Editorial Director: Sally Yagan Editor in Chief: Donna Battista Senior Acquisitions Editor: Chuck Synovec Senior Acquisitions Editor, Global Edition: Steven Jackson Editor, Global Edition: Leandra Paoli Senior Editorial Project Manager: Mary Kate Murray Editorial Assistant: Ashlee Bradbury Director of Marketing: Maggie Moylan Executive Marketing Manager: Anne Fahlgren Marketing Manager, International: Dean Erasmus Senior Managing Editor: Judy Leale Production Project Manager: Jacqueline A Martin Senior Operations Supervisor: Arnold Vila Operations Specialist: Cathleen Petersen Art Director: Steve Frim Cover Designer: Jodi Notowitz Cover Art: © Zoe - Fotolia.com Media Project Manager: John Cassar Associate Media Project Manager: Sarah Peterson Full-Service Project Management: PreMediaGlobal, Inc 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.pearson.com/uk © Pearson Education Limited 2013 The rights of Paul Newbold, William L Carlson and Betty Thorne to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988 Authorised adaptation from the United States edition, entitled Statistics for Business and Economics, 8th Edition, ISBN: 978-0-13-274565-9 by Paul Newbold, William L Carlson and Betty Thorne, published by Pearson Education, Inc., © 2013 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, 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and/or the program(s) described herein at any time Partial screen shots may be viewed in full within the software version specified Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on the appropriate page within the text ISBN 13: 978-0-273-76706-0 ISBN 10: 0-273-76706-2 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library 10 16 15 14 13 12 Typeset in Palatino LT Std by PreMediaGlobal, Inc Printed and bound by Courier Kendallville in The United States of America The publisher’s policy is to use paper manufactured from sustainable forests I dedicate this book to Sgt Lawrence Martin Carlson, who gave his life in service to his country on November 19, 2006, and to his mother, Charlotte Carlson, to his sister and brother, Andrea and Douglas, to his children, Savannah, and Ezra, and to his nieces, Helana, Anna, Eva Rose, and Emily William L Carlson I dedicate this book to my husband, Jim, and to our family, Jennie, Ann, Renee, Jon, Chris, Jon, Hannah, Leah, Christina, Jim, Wendy, Marius, Mihaela, Cezara, Anda, and Mara Iulia Betty M Thorne ABOUT THE AUTHORS Dr Bill Carlson is professor emeritus of economics at St Olaf College, where he taught for 31 years, serving several times as department chair and in various administrative functions, including director of academic computing He has also held leave assignments with the U.S government and the University of Minnesota in addition to lecturing at many different universities He was elected an honorary member of Phi Beta Kappa In addition, he spent 10 years in private industry and contract research prior to beginning his career at St Olaf His education includes engineering degrees from Michigan Technological University (BS) and from the Illinois Institute of Technology (MS) and a PhD in quantitative management from the Rackham Graduate School at the University of Michigan Numerous research projects related to management, highway safety, and statistical education have produced more than 50 publications He received the Metropolitan Insurance Award of Merit for Safety Research He has previously published two statistics textbooks An important goal of this book is to help students understand the forest and not be lost in the trees Hiking the Lake Superior trail in Northern Minnesota helps in developing this goal Professor Carlson led a number of study-abroad programs, ranging from to months, for study in various countries around the world He was the executive director of the Cannon Valley Elder Collegium and a regular volunteer for a number of community activities He is a member of both the Methodist and Lutheran disaster-relief teams and a regular participant in the local Habitat for Humanity building team He enjoys his grandchildren, woodworking, travel, reading, and being on assignment on the North Shore of Lake Superior Dr Betty M Thorne, author, researcher, and award-winning teacher, is professor of statistics and director of undergraduate studies in the School of Business Administration at Stetson University in DeLand, Florida Winner of Stetson University’s McEniry Award for Excellence in Teaching, the highest honor given to a Stetson University faculty member, Dr Thorne is also the recipient of the Outstanding Teacher of the Year Award and Professor of the Year Award in the School of Business Administration at Stetson Dr Thorne teaches in Stetson University’s undergradaute business program in DeLand, Florida, and also in Stetson’s summer program in Innsbruck, Austria; Stetson University’s College of Law; Stetson University’s Executive MBA program; and Stetson University’s Executive Passport program Dr Thorne has received various teaching awards in the JD/MBA program at Stetson’s College of Law in Gulfport, Florida She received her BS degree from Geneva College and MA and PhD degrees from Indiana University She has co-authored statistics textbooks which have been translated into several languages and adopted by universities, nationally and internationally She serves on key school and university committees Dr Thorne, whose research has been published in various refereed journals, is a member of the American Statistical Association, the Decision Science Institute, Beta Alpha Psi, Beta Gamma Sigma, and the Academy of International Business She and her husband, Jim, have four children They travel extensively, attend theological conferences and seminars, participate in international organizations dedicated to helping disadvantaged children, and missionary work in Romania BRIEF CONTENTS Preface 13 Data File Index 19 CHAPTER Using Graphs to Describe Data CHAPTER Using Numerical Measures to Describe Data CHAPTER Elements of Chance: Probability Methods CHAPTER Discrete Probability Distributions CHAPTER Continuous Probability Distributions CHAPTER Distributions of Sample Statistics CHAPTER Confidence Interval Estimation: One Population CHAPTER Confidence Interval Estimation: Further Topics CHAPTER Hypothesis Tests of a Single Population 21 59 93 146 197 244 284 328 346 CHAPTER 10 Two Population Hypothesis Tests 385 CHAPTER 11 Two Variable Regression Analysis 417 CHAPTER 12 Multiple Variable Regression Analysis CHAPTER 13 Additional Topics in Regression Analysis 551 CHAPTER 14 Introduction to Nonparametric Statistics 602 CHAPTER 15 Analysis of Variance CHAPTER 16 Forecasting with Time-Series Models CHAPTER 17 Sampling: Stratified, Cluster, and Other Sampling Methods Appendix Tables 473 645 684 716 738 Index 783 This page intentionally left blank www.downloadslide.net CONTENTS Preface 13 Data File Index CHAPTER 1.1 1.2 1.3 1.4 1.5 1.6 19 Using Graphs to Describe Data 21 Decision Making in an Uncertain Environment Random and Systematic Sampling 22 Sampling and Nonsampling Errors 24 Classification of Variables 25 Categorical and Numerical Variables 25 Measurement Levels 26 Graphs to Describe Categorical Variables 28 Tables and Charts 28 Cross Tables 29 Pie Charts 31 Pareto Diagrams 32 Graphs to Describe Time-Series Data 35 Graphs to Describe Numerical Variables 40 Frequency Distributions 40 Histograms and Ogives 44 Shape of a Distribution 44 Stem-and-Leaf Displays 46 Scatter Plots 47 Data Presentation Errors 51 Misleading Histograms 51 Misleading Time-Series Plots 53 22 Using Numerical Measures to Describe Data 2.1 Measures of Central Tendency and Location 59 Mean, Median, and Mode 60 Shape of a Distribution 62 Geometric Mean 63 Percentiles and Quartiles 64 Measures of Variability 68 Range and Interquartile Range 69 Box-and-Whisker Plots 69 Variance and Standard Deviation 71 Coefficient of Variation 75 Chebyshev’s Theorem and the Empirical Rule 75 z-Score 77 Weighted Mean and Measures of Grouped Data 80 Measures of Relationships Between Variables 84 Case Study: Mortgage Portfolio 91 CHAPTER 2.2 2.3 2.4 59 CHAPTER 3.1 3.2 3.3 3.4 3.5 CHAPTER 4.1 4.2 4.3 4.4 4.5 4.6 4.7 CHAPTER 5.1 5.2 5.3 5.4 5.5 5.6 Contents Elements of Chance: Probability Methods 93 Random Experiment, Outcomes, and Events 94 Probability and Its Postulates 101 Classical Probability 101 Permutations and Combinations 102 Relative Frequency 106 Subjective Probability 107 Probability Rules 111 Conditional Probability 113 Statistical Independence 116 Bivariate Probabilities 122 Odds 126 Overinvolvement Ratios 126 Bayes’ Theorem 132 Subjective Probabilities in Management Decision Making Discrete Probability Distributions 138 146 Random Variables 147 Probability Distributions for Discrete Random Variables 148 Properties of Discrete Random Variables 152 Expected Value of a Discrete Random Variable 152 Variance of a Discrete Random Variable 153 Mean and Variance of Linear Functions of a Random Variable 155 Binomial Distribution 159 Developing the Binomial Distribution 160 Poisson Distribution 167 Poisson Approximation to the Binomial Distribution 171 Comparison of the Poisson and Binomial Distributions 172 Hypergeometric Distribution 173 Jointly Distributed Discrete Random Variables 176 Conditional Mean and Variance 180 Computer Applications 180 Linear Functions of Random Variables 180 Covariance 181 Correlation 182 Portfolio Analysis 186 Continuous Probability Distributions 197 Continuous Random Variables 198 The Uniform Distribution 201 Expectations for Continuous Random Variables 203 The Normal Distribution 206 Normal Probability Plots 215 Normal Distribution Approximation for Binomial Distribution Proportion Random Variable 223 The Exponential Distribution 225 Jointly Distributed Continuous Random Variables 228 Linear Combinations of Random Variables 232 Financial Investment Portfolios 232 Cautions Concerning Finance Models 236 219 CHAPTER 6.1 6.2 6.3 6.4 CHAPTER 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 CHAPTER 8.1 8.2 8.3 Distributions of Sample Statistics 244 Sampling from a Population 245 Development of a Sampling Distribution 246 Sampling Distributions of Sample Means 249 Central Limit Theorem 254 Monte Carlo Simulations: Central Limit Theorem 254 Acceptance Intervals 260 Sampling Distributions of Sample Proportions 265 Sampling Distributions of Sample Variances 270 Confidence Interval Estimation: One Population 284 Properties of Point Estimators 285 Unbiased 286 Most Efficient 287 Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known 291 Intervals Based on the Normal Distribution 292 Reducing Margin of Error 295 Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown 297 Student’s t Distribution 297 Intervals Based on the Student’s t Distribution 299 Confidence Interval Estimation for Population Proportion (Large Samples) 303 Confidence Interval Estimation for the Variance of a Normal Distribution 306 Confidence Interval Estimation: Finite Populations 309 Population Mean and Population Total 309 Population Proportion 312 Sample-Size Determination: Large Populations 315 Mean of a Normally Distributed Population, Known Population Variance 315 Population Proportion 317 Sample-Size Determination: Finite Populations 319 Sample Sizes for Simple Random Sampling: Estimation of the Population Mean or Total 320 Sample Sizes for Simple Random Sampling: Estimation of Population Proportion 321 Confidence Interval Estimation: Further Topics 328 Confidence Interval Estimation of the Difference Between Two Normal Population Means: Dependent Samples 329 Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples 333 Two Means, Independent Samples, and Known Population Variances 333 Two Means, Independent Samples, and Unknown Population Variances Assumed to Be Equal 335 Two Means, Independent Samples, and Unknown Population Variances Not Assumed to Be Equal 337 Confidence Interval Estimation of the Difference Between Two Population Proportions (Large Samples) 340 Contents www.downloadslide.net Table 12 Cutoff Points for the Distribution of the Durbin-Watson Test Statistic (Continued ) a = 0.05 n K dL dU dL dU dL dU dL dU dL dU 15 0.81 1.07 0.70 1.25 0.59 1.46 0.49 1.70 0.39 1.96 16 0.84 1.09 0.74 1.25 0.63 1.44 0.53 1.66 0.44 1.90 17 0.87 1.10 0.77 1.25 0.67 1.43 0.57 1.63 0.48 1.85 18 0.90 1.12 0.80 1.26 0.71 1.42 0.61 1.60 0.52 1.80 19 0.93 1.13 0.83 1.26 0.74 1.41 0.65 1.58 0.56 1.77 20 0.95 1.15 0.86 1.27 0.77 1.41 0.68 1.57 0.60 1.74 21 0.97 1.16 0.89 1.27 0.80 1.41 0.72 1.55 0.63 1.71 22 1.00 1.17 0.91 1.28 0.83 1.40 0.75 1.54 0.66 1.69 23 1.02 1.19 0.94 1.29 0.86 1.40 0.77 1.53 0.70 1.67 24 1.04 1.20 0.96 1.30 0.88 1.41 0.80 1.53 0.72 1.66 25 1.05 1.21 0.98 1.30 0.90 1.41 0.83 1.52 0.75 1.65 26 1.07 1.22 1.00 1.31 0.93 1.41 0.85 1.52 0.78 1.64 27 1.09 1.23 1.02 1.32 0.95 1.41 0.88 1.51 0.81 1.63 28 1.10 1.24 1.04 1.32 0.97 1.41 0.90 1.51 0.83 1.62 29 1.12 1.25 1.05 1.33 0.99 1.42 0.92 1.51 0.85 1.61 30 1.13 1.26 1.07 1.34 1.01 1.42 0.94 1.51 0.88 1.61 31 1.15 1.27 1.08 1.34 1.02 1.42 0.96 1.51 0.90 1.60 32 1.16 1.28 1.10 1.35 1.04 1.43 0.98 1.51 0.92 1.60 33 1.17 1.29 1.11 1.36 1.05 1.43 1.00 1.51 0.94 1.59 34 1.18 1.30 1.13 1.36 1.07 1.43 1.01 1.51 0.95 1.59 35 1.19 1.31 1.14 1.37 1.08 1.44 1.03 1.51 0.97 1.59 36 1.21 1.32 1.15 1.38 1.10 1.44 1.04 1.51 0.99 1.59 37 1.22 1.32 1.16 1.38 1.11 1.45 1.06 1.51 1.00 1.59 38 1.23 1.33 1.18 1.39 1.12 1.45 1.07 1.52 1.02 1.58 39 1.24 1.34 1.19 1.39 1.14 1.45 1.09 1.52 1.03 1.58 40 1.25 1.34 1.20 1.40 1.15 1.46 1.10 1.52 1.05 1.58 45 1.29 1.38 1.24 1.42 1.20 1.48 1.16 1.53 1.11 1.58 50 1.32 1.40 1.28 1.45 1.24 1.49 1.20 1.54 1.16 1.59 55 1.36 1.43 1.32 1.47 1.28 1.51 1.25 1.55 1.21 1.59 60 1.38 1.45 1.35 1.48 1.32 1.52 1.28 1.56 1.25 1.60 65 1.41 1.47 1.38 1.50 1.35 1.53 1.31 1.57 1.28 1.61 70 1.43 1.49 1.40 1.52 1.37 1.55 1.34 1.58 1.31 1.61 75 1.45 1.50 1.42 1.53 1.39 1.56 1.37 1.59 1.34 1.62 80 1.47 1.52 1.44 1.54 1.42 1.57 1.39 1.60 1.36 1.62 85 1.48 1.53 1.46 1.55 1.43 1.58 1.41 1.60 1.39 1.63 90 1.50 1.54 1.47 1.56 1.45 1.59 1.43 1.61 1.41 1.64 95 1.51 1.55 1.49 1.57 1.47 1.60 1.45 1.62 1.42 1.64 100 1.52 1.56 1.50 1.58 1.48 1.60 1.46 1.63 1.44 1.65 Computed from TSP 4.5 based on R W Farebrother, “A Remark on Algorithms AS106, AS153, and AS155: The Distribution of a Linear Combination of Chi-Square Random Variables”, Journal of the Royal Statistical Society, Series C (Applied Statistics), 1984, 29, pp 323–333 778 Appendix Tables www.downloadslide.net Table 13 Critical Values of Studentized Range Q a = 0.05 The Studentized Range Upper Quantiles Q(k, df; 0.05) df k-> 17.969 26.976 32.819 37.082 40.408 10 11 12 13 14 43.119 45.397 47.357 49.071 50.592 51.957 53.194 54.323 13.988 14.389 14.749 15.076 15.375 6.085 8.331 9.798 10.881 11.734 12.435 13.027 13.539 4.501 5.910 6.825 7.502 8.037 8.478 8.852 9.177 9.462 9.717 9.946 10.155 10.346 3.926 5.040 5.757 6.287 6.706 7.053 7.347 7.602 7.826 8.027 8.208 8.373 8.524 15 16 55.361 56.320 17 18 19 20 57.212 58.044 58.824 59.558 15.650 15.905 16.143 16.365 16.573 16.769 10.522 10.686 10.838 10.980 11.114 11.240 8.914 9.027 9.133 9.233 8.664 8.793 3.635 4.602 5.218 5.673 6.033 6.330 6.582 6.801 6.995 7.167 7.323 7.466 7.596 7.716 7.828 7.932 8.030 8.122 8.208 3.460 4.339 4.896 5.305 5.628 5.895 6.122 6.319 6.493 6.649 6.789 6.917 7.034 7.143 7.244 7.338 7.426 7.508 7.586 3.344 4.165 4.681 5.060 5.359 5.606 5.815 5.997 6.158 6.302 6.431 6.550 6.658 6.759 6.852 6.939 7.020 7.097 7.169 3.261 4.041 4.529 4.886 5.167 5.399 5.596 5.767 5.918 6.053 6.175 6.287 6.389 6.483 6.571 6.653 6.729 6.801 6.869 3.199 3.948 4.415 4.755 5.024 5.244 5.432 5.595 5.738 5.867 5.983 6.089 6.186 6.276 6.359 6.437 6.510 6.579 6.643 10 3.151 3.877 4.327 4.654 4.912 5.124 5.304 5.460 5.598 5.722 5.833 5.935 6.028 6.114 6.194 6.269 6.339 6.405 6.467 11 3.113 3.820 4.256 4.574 4.823 5.028 5.202 5.353 5.486 5.605 5.713 5.811 5.901 5.984 6.062 6.134 6.202 6.265 6.325 12 3.081 3.773 4.199 4.508 4.750 4.950 5.119 5.265 5.395 5.510 5.615 5.710 5.797 5.878 5.953 6.023 6.089 6.151 6.209 13 3.055 3.734 4.151 4.453 4.690 4.884 5.049 5.192 5.318 5.431 5.533 5.625 5.711 5.789 5.862 5.931 5.995 6.055 6.112 14 3.033 3.701 4.111 4.407 4.639 4.829 4.990 5.130 5.253 5.364 5.463 5.554 5.637 5.714 5.785 5.852 5.915 5.973 6.029 15 3.014 3.673 4.076 4.367 4.595 4.782 4.940 5.077 5.198 5.306 5.403 5.492 5.574 5.649 5.719 5.785 5.846 5.904 5.958 16 2.998 3.649 4.046 4.333 4.557 4.741 4.896 5.031 5.150 5.256 5.352 5.439 5.519 5.593 5.662 5.726 5.786 5.843 5.896 17 2.984 3.628 4.020 4.303 4.524 4.705 4.858 4.991 5.108 5.212 5.306 5.392 5.471 5.544 5.612 5.675 5.734 5.790 5.842 18 2.971 3.609 3.997 4.276 4.494 4.673 4.824 4.955 5.071 5.173 5.266 5.351 5.429 5.501 5.567 5.629 5.688 5.743 5.794 19 2.960 3.593 3.977 4.253 4.468 4.645 4.794 4.924 5.037 5.139 5.231 5.314 5.391 5.462 5.528 5.589 5.647 5.701 5.752 20 2.950 3.578 3.958 4.232 4.445 4.620 4.768 4.895 5.008 5.108 5.199 5.282 5.357 5.427 5.492 5.553 5.610 5.663 5.714 21 2.941 3.565 3.942 4.213 4.424 4.597 4.743 4.870 4.981 5.081 5.170 5.252 5.327 5.396 5.460 5.520 5.576 5.629 5.679 22 2.933 3.553 3.927 4.196 4.405 4.577 4.722 4.847 4.957 5.056 5.144 5.225 5.299 5.368 5.431 5.491 5.546 5.599 5.648 23 2.926 3.542 3.914 4.180 4.388 4.558 4.702 4.826 4.935 5.033 5.121 5.201 5.274 5.342 5.405 5.464 5.519 5.571 5.620 24 2.919 3.532 3.901 4.166 4.373 4.541 4.684 4.807 4.915 5.012 5.099 5.179 5.251 5.319 5.381 5.439 5.494 5.545 5.594 25 2.913 3.523 3.890 4.153 4.358 4.526 4.667 4.789 4.897 4.993 5.079 5.158 5.230 5.297 5.359 5.417 5.471 5.522 5.570 26 2.907 3.514 3.880 4.141 4.345 4.511 4.652 4.773 4.880 4.975 5.061 5.139 5.211 5.277 5.339 5.396 5.450 5.500 5.548 27 2.902 3.506 3.870 4.130 4.333 4.498 4.638 4.758 4.864 4.959 5.044 5.122 5.193 5.259 5.320 5.377 5.430 5.480 5.528 28 2.897 3.499 3.861 4.120 4.322 4.486 4.625 4.745 4.850 4.944 5.029 5.106 5.177 5.242 5.302 5.359 5.412 5.462 5.509 29 2.892 3.493 3.853 4.111 4.311 4.475 4.613 4.732 4.837 4.930 5.014 5.091 5.161 5.226 5.286 5.342 5.395 5.445 5.491 30 2.888 3.486 3.845 4.102 4.301 4.464 4.601 4.720 4.824 4.917 5.001 5.077 5.147 5.211 5.271 5.327 5.379 5.429 5.475 779 (continued) www.downloadslide.net 780 Table 13 df k-> Critical Values of Studentized Range Q a = 0.05 (Continued) 10 11 12 13 14 15 16 17 18 19 20 31 2.884 3.481 3.838 4.094 4.292 4.454 4.591 4.709 4.812 4.905 4.988 5.064 5.134 5.198 5.257 5.313 5.365 5.414 5.460 32 2.881 3.475 3.832 4.086 4.284 4.445 4.581 4.698 4.802 4.894 4.976 5.052 5.121 5.185 5.244 5.299 5.351 5.400 5.445 33 2.877 3.470 3.825 4.079 4.276 4.436 4.572 4.689 4.791 4.883 4.965 5.040 5.109 5.173 5.232 5.287 5.338 5.386 5.432 34 2.874 3.465 3.820 4.072 4.268 4.428 4.563 4.680 4.782 4.873 4.955 5.030 5.098 5.161 5.220 5.275 5.326 5.374 5.420 35 2.871 3.461 3.814 4.066 4.261 4.421 4.555 4.671 4.773 4.863 4.945 5.020 5.088 5.151 5.209 5.264 5.315 5.362 5.408 36 2.868 3.457 3.809 4.060 4.255 4.414 4.547 4.663 4.764 4.855 4.936 5.010 5.078 5.141 5.199 5.253 5.304 5.352 5.397 37 2.865 3.453 3.804 4.054 4.249 4.407 4.540 4.655 4.756 4.846 4.927 5.001 5.069 5.131 5.189 5.243 5.294 5.341 5.386 38 2.863 3.449 3.799 4.049 4.243 4.400 4.533 4.648 4.749 4.838 4.919 4.993 5.060 5.122 5.180 5.234 5.284 5.331 5.376 39 2.861 3.445 3.795 4.044 4.237 4.394 4.527 4.641 4.741 4.831 4.911 4.985 5.052 5.114 5.171 5.225 5.275 5.322 5.367 40 2.858 3.442 3.791 4.039 4.232 4.388 4.521 4.634 4.735 4.824 4.904 4.977 5.044 5.106 5.163 5.216 5.266 5.313 5.358 48 2.843 3.420 3.764 4.008 4.197 4.351 4.481 4.592 4.690 4.777 4.856 4.927 4.993 5.053 5.109 5.161 5.210 5.256 5.299 60 2.829 3.399 3.737 3.977 4.163 4.314 4.441 4.550 4.646 4.732 4.808 4.878 4.942 5.001 5.056 5.107 5.154 5.199 5.241 80 2.814 3.377 3.711 3.947 4.129 4.277 4.402 4.509 4.603 4.686 4.761 4.829 4.892 4.949 5.003 5.052 5.099 5.142 5.183 120 2.800 3.356 3.685 3.917 4.096 4.241 4.363 4.468 4.560 4.641 4.714 4.781 4.842 4.898 4.950 4.998 5.043 5.086 5.126 240 2.786 3.335 3.659 3.887 4.063 4.205 4.324 4.427 4.517 4.596 4.668 4.733 4.792 4.847 4.897 4.944 4.988 5.030 5.069 Inf 2.772 3.314 3.633 3.858 4.030 4.170 4.286 4.387 4.474 4.552 4.622 4.685 4.743 4.796 4.845 4.891 4.934 4.974 5.012 10 11 12 13 14 15 16 17 18 19 20 The Studentized Range Upper Quantiles Q(k, df; 0.01) df k-> 90.024 135.041 164.258 185.575 202.210 215.769 227.166 236.966 245.542 253.151 259.979 266.165 271.812 277.003 281.803 286.263 290.426 294.328 297.997 14.036 19.019 22.294 24.717 26.629 10.619 12.170 13.324 14.241 8.260 6.511 8.120 9.173 9.958 10.583 5.702 6.976 7.804 8.421 8.913 28.201 29.530 30.679 31.689 32.589 33.398 34.134 34.806 35.426 36.000 36.534 37.034 37.502 37.943 14.998 15.641 16.199 16.691 17.130 17.526 17.887 18.217 18.522 18.805 19.068 19.315 19.546 19.765 11.101 11.542 11.925 12.264 12.567 12.840 13.090 13.318 13.530 13.726 13.909 14.081 14.242 14.394 9.321 9.669 9.971 10.239 10.479 10.696 10.894 11.076 11.244 11.400 11.545 11.682 11.811 11.932 5.243 6.331 7.033 7.556 7.972 8.318 8.612 8.869 9.097 9.300 9.485 9.653 9.808 9.951 10.084 10.208 10.325 10.434 10.538 4.949 5.919 6.542 7.005 7.373 7.678 7.939 8.166 8.367 8.548 8.711 8.860 8.997 9.124 9.242 9.353 9.456 9.553 9.645 4.745 5.635 6.204 6.625 6.959 7.237 7.474 7.680 7.863 8.027 8.176 8.311 8.436 8.552 8.659 8.760 8.854 8.943 9.027 4.596 5.428 5.957 6.347 6.657 6.915 7.134 7.325 7.494 7.646 7.784 7.910 8.025 8.132 8.232 8.325 8.412 8.495 8.573 10 4.482 5.270 5.769 6.136 6.428 6.669 6.875 7.054 7.213 7.356 7.485 7.603 7.712 7.812 7.906 7.993 8.075 8.153 8.226 11 4.392 5.146 5.621 5.970 6.247 6.476 6.671 6.841 6.992 7.127 7.250 7.362 7.464 7.560 7.648 7.731 7.809 7.883 7.952 12 4.320 5.046 5.502 5.836 6.101 6.320 6.507 6.670 6.814 6.943 7.060 7.166 7.265 7.356 7.441 7.520 7.594 7.664 7.730 13 4.260 4.964 5.404 5.726 5.981 6.192 6.372 6.528 6.666 6.791 6.903 7.006 7.100 7.188 7.269 7.345 7.417 7.484 7.548 14 4.210 4.895 5.322 5.634 5.881 6.085 6.258 6.409 6.543 6.663 6.772 6.871 6.962 7.047 7.125 7.199 7.268 7.333 7.394 www.downloadslide.net 15 4.167 4.836 5.252 5.556 5.796 5.994 6.162 6.309 6.438 6.555 6.660 6.756 6.845 6.927 7.003 7.074 7.141 7.204 7.264 16 4.131 4.786 5.192 5.489 5.722 5.915 6.079 6.222 6.348 6.461 6.564 6.658 6.744 6.823 6.897 6.967 7.032 7.093 7.151 17 4.099 4.742 5.140 5.430 5.659 5.847 6.007 6.147 6.270 6.380 6.480 6.572 6.656 6.733 6.806 6.873 6.937 6.997 7.053 18 4.071 4.703 5.094 5.379 5.603 5.787 5.944 6.081 6.201 6.309 6.407 6.496 6.579 6.655 6.725 6.791 6.854 6.912 6.967 19 4.046 4.669 5.054 5.334 5.553 5.735 5.889 6.022 6.141 6.246 6.342 6.430 6.510 6.585 6.654 6.719 6.780 6.837 6.891 20 4.024 4.639 5.018 5.293 5.510 5.688 5.839 5.970 6.086 6.190 6.285 6.370 6.449 6.523 6.591 6.654 6.714 6.770 6.823 21 4.004 4.612 4.986 5.257 5.470 5.646 5.794 5.924 6.038 6.140 6.233 6.317 6.395 6.467 6.534 6.596 6.655 6.710 6.762 22 3.986 4.588 4.957 5.225 5.435 5.608 5.754 5.882 5.994 6.095 6.186 6.269 6.346 6.417 6.482 6.544 6.602 6.656 6.707 23 3.970 4.566 4.931 5.195 5.403 5.573 5.718 5.844 5.955 6.054 6.144 6.226 6.301 6.371 6.436 6.497 6.553 6.607 6.658 24 3.955 4.546 4.907 5.168 5.373 5.542 5.685 5.809 5.919 6.017 6.105 6.186 6.261 6.330 6.394 6.453 6.510 6.562 6.612 25 3.942 4.527 4.885 5.144 5.347 5.513 5.655 5.778 5.886 5.983 6.070 6.150 6.224 6.292 6.355 6.414 6.469 6.522 6.571 26 3.930 4.510 4.865 5.121 5.322 5.487 5.627 5.749 5.856 5.951 6.038 6.117 6.190 6.257 6.319 6.378 6.432 6.484 6.533 27 3.918 4.495 4.847 5.101 5.300 5.463 5.602 5.722 5.828 5.923 6.008 6.087 6.158 6.225 6.287 6.344 6.399 6.450 6.498 28 3.908 4.481 4.830 5.082 5.279 5.441 5.578 5.697 5.802 5.896 5.981 6.058 6.129 6.195 6.256 6.314 6.367 6.418 6.465 29 3.898 4.467 4.814 5.064 5.260 5.420 5.556 5.674 5.778 5.871 5.955 6.032 6.103 6.168 6.228 6.285 6.338 6.388 6.435 30 3.889 4.455 4.799 5.048 5.242 5.401 5.536 5.653 5.756 5.848 5.932 6.008 6.078 6.142 6.202 6.258 6.311 6.361 6.407 31 3.881 4.443 4.786 5.032 5.225 5.383 5.517 5.633 5.736 5.827 5.910 5.985 6.055 6.119 6.178 6.234 6.286 6.335 6.381 32 3.873 4.433 4.773 5.018 5.210 5.367 5.500 5.615 5.716 5.807 5.889 5.964 6.033 6.096 6.155 6.211 6.262 6.311 6.357 33 3.865 4.423 4.761 5.005 5.195 5.351 5.483 5.598 5.698 5.789 5.870 5.944 6.013 6.076 6.134 6.189 6.240 6.289 6.334 34 3.859 4.413 4.750 4.992 5.181 5.336 5.468 5.581 5.682 5.771 5.852 5.926 5.994 6.056 6.114 6.169 6.220 6.268 6.313 35 3.852 4.404 4.739 4.980 5.169 5.323 5.453 5.566 5.666 5.755 5.835 5.908 5.976 6.038 6.096 6.150 6.200 6.248 6.293 36 3.846 4.396 4.729 4.969 5.156 5.310 5.439 5.552 5.651 5.739 5.819 5.892 5.959 6.021 6.078 6.132 6.182 6.229 6.274 37 3.840 4.388 4.720 4.959 5.145 5.298 5.427 5.538 5.637 5.725 5.804 5.876 5.943 6.004 6.061 6.115 6.165 6.212 6.256 38 3.835 4.381 4.711 4.949 5.134 5.286 5.414 5.526 5.623 5.711 5.790 5.862 5.928 5.989 6.046 6.099 6.148 6.195 6.239 39 3.830 4.374 4.703 4.940 5.124 5.275 5.403 5.513 5.611 5.698 5.776 5.848 5.914 5.974 6.031 6.084 6.133 6.179 6.223 40 3.825 4.367 4.695 4.931 5.114 5.265 5.392 5.502 5.599 5.685 5.764 5.835 5.900 5.961 6.017 6.069 6.118 6.165 6.208 48 3.793 4.324 4.644 4.874 5.052 5.198 5.322 5.428 5.522 5.606 5.681 5.750 5.814 5.872 5.926 5.977 6.024 6.069 6.111 60 3.762 4.282 4.594 4.818 4.991 5.133 5.253 5.356 5.447 5.528 5.601 5.667 5.728 5.784 5.837 5.886 5.931 5.974 6.015 80 3.732 4.241 4.545 4.763 4.931 5.069 5.185 5.284 5.372 5.451 5.521 5.585 5.644 5.698 5.749 5.796 5.840 5.881 5.920 120 3.702 4.200 4.497 4.709 4.872 5.005 5.118 5.214 5.299 5.375 5.443 5.505 5.561 5.614 5.662 5.708 5.750 5.790 5.827 240 3.672 4.160 4.450 4.655 4.814 4.943 5.052 5.145 5.227 5.300 5.366 5.426 5.480 5.530 5.577 5.621 5.661 5.699 5.735 Inf 3.643 4.120 4.403 4.603 4.757 4.882 4.987 5.078 5.157 5.227 5.290 5.348 5.400 5.448 5.493 5.535 5.574 5.611 5.645 Source: cse.niaes.affrc.go.jp/miwa/probcalc/s-range/srng_tbl.html 781 www.downloadslide.net 782 Table 14 Cumulative Distribution Function of the Runs Test Statistic For a given number n of observations, the table shows the probability, for a random time series, that the number of runs will not exceed K n K 6 100 300 700 900 1.000 029 114 371 629 886 971 1.000 10 11 12 10 008 040 167 357 643 833 960 992 1.000 12 002 013 067 175 392 608 825 933 987 998 1.000 14 001 004 025 078 209 383 617 791 922 975 996 13 14 999 1.000 15 16 17 18 16 000 001 009 032 100 214 405 595 786 900 968 991 999 1.000 1.000 18 000 000 003 012 044 109 238 399 601 762 891 956 988 997 1.000 1.000 1.000 20 000 000 001 004 019 051 128 242 414 586 758 872 949 981 996 999 1.000 19 20 1.000 1.000 Reproduced with permission from F Swed and C Eisenhart, “Tables for testing randomness of grouping in a sequence of alternatives,” Annals of Mathematical Statistics 14 (1943) www.downloadslide.net I NDEX A Acceptance intervals, 260–262 Addition rule of probabilities, 112–113 Adjusted coefficient of determination R2, 492 Allocation proportional, 717 of sample effort among strata, 723–725 Alternative hypothesis, 347, 351, 356–359, 376, 406, 408 See also Hypothesis tests/testing Analysis of variance (ANOVA) comparison of several population means, 645–647 introduction to, 645 Kruskal-Wallis test and, 658–660 one-way, 647–656 for regression, 432–433 two-way, more than one observation per cell, 670–676 two-way, one observation per cell, randomized blocks, 661–667 Analysis of variance tables, two-way, 666–667 Approximate mean, 81–82 ARIMA (autoregressive integrated moving average) models, 713–714 Arithmetic mean, 60 Association test, 615–618 Asymmetric distribution, 62–63 Autocorrelated errors Durbin-Watson test and, 584–586 estimation of regressions with, 586–590 explanation of, 582–584 with lagged dependent variables, 590–591 Autocorrelation, 708–709 Autoregressive integrated moving average (ARIMA) models, 713–714 Autoregressive models estimation and, 709 example of, 709–710 explanation of, 708 first-order, 708 forecasting from, 709–712 second-order, 708 B Bar charts, 28–30, 52–53 Basic outcomes, 95 Bayes, Thomas, 132 Bayes’ theorem, 132–139 alternative statement, 135 examples, 132–138 explanation of, 132 management decision making, 138 solution steps for, 134 Bernoulli distribution, 159–161 Bernoulli random variable, 160 Beta coefficients, 456–458 Beta measure, of financial risk, 456–458 Between-groups mean square (MSG), 682–683 Between-groups variability, 649 Bias explanation of, 287 specification, 571–573 Biased estimators, 287 Binomial distribution, 159–165 compared with normal distribution, 221 compared with Poisson distribution, 172 derived mean and variance of, 160, 195–196 examples of, 162–165 explanation of, 162 normal distribution approximation for, 219–224 Poisson approximation to, 171–172 probability function table, 739–743 Binomial probabilities, cumulative, 744–748 Bivariate probabilities, 122–132 Blocking variables, 559–560, 661 Block means, 671 Box-and-whisker plots, 69–71 C Categorical data analysis contingency tables and, 614–618 goodness-of-fit tests, population parameters unknown, 609–613 goodness-of-fit tests, specified probabilities, 603–608 nonparametric tests for independent random samples, 628–632, 636–639 nonparametric tests for paired or matched samples, 619–626 Spearman rank correlation and, 634–635 Categorical variables, 25 graphs to describe, 28–35 Cell means, 671–672 Central limit theorem, 254–260 from linear sum of random variables, 280 Central tendency, measures of, 59–68 Chebychev’s theorem, 75–77 Chi-square distribution, 306–308 lower critical values table, 769 population variance, 271–272 upper critical values table, 768 variance of normal distribution, 375 Chi-square random variable, 605 for contingency tables, 615 Chi-square test examples of, 606–608 of variance of a normal distribution, 375–376 Classical probability, 101–102, 105 Cluster bar charts, 30, 52–53 Cluster sampling estimators for, 729–732 explanation of, 729 Cobb-Douglas production function, 519 Coefficient estimation, 553–554 Coefficient estimators derivation of, 553–554 least squares, 427–430, 439 variance, 437, 505–506 Coefficient of determination R2 adjusted, 492 explanation of, 433–437 regression models and, 492 sum of squares decomposition and, 489–490 Coefficient of multiple correlation, 492 Coefficient of multiple regression, 481–487 783 www.downloadslide.net Coefficient of standard errors, 495 Coefficient of variation (CV), 75 Collectively exhaustive events, 98 Combinations formula for determining number of, 104–105 number of, 102–103 Complement rule, 111–112, 118–119 Complements, 98–100 Component bar charts, 30 Composite hypothesis, 351, 356–359 Computer applications See also Excel for jointly distributed discrete random variables, 180 of regression coefficient, 429–430 Conditional coefficients, 486 Conditional mean, 180 Conditional probability, 113–114 Conditional probability distribution, 178 Conditional variance, 180 Confidence interval estimator, 291 Confidence intervals based on normal distribution, 292 for difference between two normal population means, dependent samples, 329–332 for difference between two normal population means, independent samples, 333–339 for difference between two population proportions, 340–341 examples of, 294, 300–302, 304–305, 308, 310–313 explanation of, 293 finite populations, 309–313 forecast, and prediction intervals, 447–448 for mean of normal distribution, population variance known, 291–296 for mean of normal distribution, population variance unknown, 297–302 for population mean, 291–302, 309–312 for population proportion, 303–305, 312–313 for population regression slope, 440–441 for population total, 309–312 for predictions, 447–448 reducing margin of error of, 295–296 for regression coefficients, 438–445, 495 784 Index sample size determination, large populations, 340–341 Student’s t distribution and, 297–302 of two means, dependent samples, 329 of two means, unknown population variances that are assumed to be equal, 335–337 of two means, unknown population variances that are not assumed to be equal, 337–339 for variance of normal distribution, 306–309 Confidence level, 292 Consistent estimators, 326 Contingency tables, 52 See also cross tables chi-square random variable for, 615 explanation of, 614–615 test of association in, 615–618 Continuous numerical variables, 26 Continuous random variables, 147–148, 197–205 covariance of, 229 (See also Jointly distributed continuous random variables) expectations for, 203–205 jointly distributed, 228–236 probability density functions and, 199–201 uniform distribution, 201 Control charts, 261–262 Control intervals, 261–262 Correlation applications of, 452 coefficient of determination R2 and, 436 coefficient of multiple correlation, 492 hypothesis test for, 452–453 of random variables, 182, 229 zero population, 453–454 Correlation analysis, 452–454 Correlation coefficient analysis, 87–88 Correlation coefficients, 84–88 defined, 84 example using, 85–88 of random variables, 182–183, 229 scatter plots and, 85 Spearman rank, 634–635 statistical independence and, 184 Counterfactual argument, 351 Covariance (Cov), 84, 181–182 computing using Excel, 87 continuous random variables, 229 statistical independence, 184 Critical value, 353 Cross-sectional data, 35 Cross tables, 29–30 Cumulative binomial probabilities, 744–748 Cumulative distribution function, 198–199, 202 of normal distribution, 208 Cumulative line graphs, 44 Cumulative probability function, 150–151 Cyclical component, of time series, 685 D Data cross-sectional, 35 interval, 26 measurement levels, 26–27 nominal, 26 ordinal, 26 presentation errors, 51–55 qualitative, 26 quantitative, 26 ratio, 27 time-series, 35–39 Data files descriptions, 470–471, 548–550 Davies, O L., 558 Decision making sampling and, 22–23 in uncertain environment, 22–25 Decision rules, guidelines for choosing, 382–383 Degrees of freedom, 273, 440 Dependent samples, 329–332, 387–390 Dependent variables, 47 lagged, as regressors, 567–570 Descriptive statistics, 25 Differences, of random variables, 184, 230 Discrete numerical variables, 25 Discrete random variables, 147 expected value of, 152–153 expected value of functions, 155 jointly distributed, 176–188 probability distributions for, 148–151 joint probability functions of, 178 properties of, 152–157 standard deviation of, 153–155 variance of, 153–155, 194 www.downloadslide.net Distribution shape, 62–63 See also specific distributions Diversifiable risk, 456–458 Dummy variables, 522–526, 554–565 experimental design models, 558–563 public sector applications, 563–565 for regression models, 522–526, 558–565 Durbin-Watson test, 584–586 cut-off points, 777–778 E Efficient estimators, 288 Empirical rule, 76–77 Equality, 403–405 of variances between two normally distributed populations, 403–405 Errors, 51–54, 495, 577–581 data presentation, 51–55 nonsampling, 24–25 reducing margin of, 295–296 sampling, 24, 293, 349 standard error, estimate, 490 Type I, 349–351, 407 Type II, 349–351, 369–373, 407 Error sum of squares, 427–428, 432–433, 489, 652 Error variance, estimation of, 490 Estimated regression model, 424 Estimates, 285 confidence interval, 291 explanation of, 285 point, 286 standard error, 490 Estimation See also Confidence intervals of beta coefficients, 456–458 coefficient, 553–554 of error variance, 490 least squares, 469–470, 483 of model error variance, 437 of multiple regression coefficients, 481–487 of population proportion, 313 of regressions with autocorrelated errors, 586–590 Estimators, 285 biased, 287 confidence interval, 291 consistent, 326 efficient, 288 examples of, 288 explanation of, 285 least squares, 469–470 least squares coefficient, 427–430, 439 least squares derivation of, 546–547 point, 285–289 of population mean, 725 unbiased, 286–287, 289 Events, 96–100 collectively exhaustive, 98 complements, 98–100 independent, 125–126 intersection of, 96–100, 144–145 mutually exclusive, 96–97, 117 union, 97–100, 144–145 Excel, 87 See also Minitab confidence intervals using, 301–302, 331–332 covariance and correlation using, 183 jointly distributed discrete random variables, 180 regression analysis using, 429 shape of a distribution, 62 Expected value of continuous random variables, 203–205 of discrete random variables, 152–153 of functions of random variables, 155, 181, 184 of sample mean, 250 Experimental design models, 558–563 Exploratory data analysis (EDA), 46 Exponential distribution, 225–227 Exponential model transformations, 518–520 Exponential smoothing, 697–707 Extreme points, 459, 461, 464 F Failure to reject, 349–351 F distribution, 403, 771–774 Financial investment portfolios, 232–236 Financial risk, beta measure of, 456–458 Finite population correction factor, 251, 309 Finite populations, confidence interval estimation for, 309–313 First-order autoregressive models, 708–709 First quartile, 64–65 Fisher, R A., 558 Five-number summary, 65 Forecasting from autoregressive models, 709–712 regression models and, 446–450 seasonal time series, 704–707 simple exponential smoothing and, 697–707 trends and, 686 F probability distribution hypothesis test for population slope coefficient using, 443–445 Frequency distributions, 28, 40 class width, 41 construction of, 41 cumulative, 42 inclusive and nonoverlapping classes, 41–42 interval width, 41 number of classes for, 41 for numerical data, 40–43 relative, 28, 42 F tests for simple regression coefficient, 444–445 t tests vs., 508–509 Functions, of random variables, 155–157 G Geometric mean, 63–64 Geometric mean rate of return, 63 Goodness-of-fit tests explanations of, 603 population parameters unknown, 609–613 specified probabilities, 603–608 Gosset, William Sealy, 297, 326 Graphical analysis, 458–464 Graphs for categorical variables, 28–35 data presentation errors, 51–55 to describe relationships between variables, 47–49 distribution shape, 44–46 histograms, 44 of multiple regression model, 480 for numerical variables, 40–50 ogives, 44 scatter plots, 47–49 stem-and-leaf displays, 46–47 for time-series data, 35–40 Grouped data, measures of, 81–82 Group means, 671 Index 785 www.downloadslide.net H Heteroscedasticity explanation of, 577–579 graphical techniques for detecting, 578–579 test for, 579–580 Histograms, 44 misleading, 51–53 Holt-Winters exponential smoothing forecasting model, 700–707 example of, 701–703 nonseasonal series, 701–703 seasonal series, 704–707 Hypergeometric distribution, 173–175 Hypothesis alternative, 351, 352, 356–359, 376 composite, 351, 356–359 null, 347–351, 376 one-sided composite alternative, 351 simple, 351 two-sided composite alternative, 351, 360–361 Hypothesis test decisions, 351 Hypothesis tests/testing, 346–347 assessing power of, 368–373 comments on, 406–408 concepts of, 347–351 confidence intervals, 438–445 control chart, 408 for correlation, 452–454 for difference between two normal population means, dependent samples, 387–390 for difference between two normal population means, independent samples, 391–398 for difference between two population proportions, 399–402 of equality of variances between two normally distributed populations, 403–405 flow chart for selecting, 413–414 introduction to, 352–353 for mean of a normal distribution, population variance known, 352–361, 369–371 for mean of normal distribution, population variance unknown, 362–364 for one-way analysis of variance, 651–653 of population proportion, 366–367 786 Index for population slope coefficient using F distribution, 443–445 power of, 351 for regression coefficients, 497–502, 505–509 for regression models, 438–445 for two-way analysis of variance, 666–667 for variance of a normal distribution, 375–377 for zero population correlation, 453–454 I Income distribution, 63 Independent events, 117, 125–126 Independent random samples, nonparametric tests for, 628–632 Independent samples, 333–339, 391–398 Independent variables, 47 jointly distributed, 178 Indicator variables, 522–526 See also Dummy variables Inference about population regression, 495 model interpretation and, 554 Inferential statistics, 25 Integral calculus, 242–243 Interaction, as source of variability, 670 Intercept, 419 Interquartile range (IQR), 69 Intersection of events, 96–97, 99–100, 151 Interval data, 26 Intervals acceptance, 260–262 control, 261–262 for frequency distribution, 44 Interval scales, 26 Investment portfolios beta measure of financial risk, 456–458 portfolio analysis, 232–236 returns on, 234–236 Irregular component of time series, 685 moving averages to smooth, 689–691 J Jarque-Bera test for normality, 611–613 Joint cumulative distribution function, 228–229 Jointly distributed continuous random variables, 176–188, 228–236 See also Continuous random variables; Random variables examples of, 230–231 financial investment portfolios, 232–236 linear combinations of, 232 Jointly distributed discrete random variables, 176–190 See also Discrete random variables; Random variables computer applications, 180 conditional mean and variance, 180 correlation, 182–183 covariance, 182 examples of, 176–177, 179–180, 183 expected value of functions of, 181 independence of, 178 portfolio analysis, 185–188 Joint probability, 96, 114–115, 117, 123–125 Joint probability distribution, 177–178 Joint probability function, 177 properties of, 178 K Knowledge, 25 Kruskal-Wallis test, 658–660 Kurtosis, 611, 613 L Lagged dependent variables, 567–570 autocorrelation errors in models with, 590–591 Law of large numbers, 254 Least squares algorithm, 514–515 Least squares coefficient estimators, 427–430, 439 Least squares derivation of estimators, 546–547 Least squares derived coefficient estimators, 428–429 Least squares estimation, sample multiple regression and, 483 Least squares estimators, derivation of, 469–470 Least squares procedure, 427–428, 482–487 Least squares regression, 419–420 Least squares regression line, 419, 446 www.downloadslide.net Leverage, 459 Linear combinations, of random variables, 232 Linear functions, of random variables, 180–181, 205 Linear models, 418–420 Linear regression equation, 431–437 analysis of variance and, 433 coefficient of determination R2, 433–434 Linear regression model, 421–426 assumptions, 422–423 examples using, 425–426 outcomes, 424 population, 423 Linear regression population equation model, 423 Linear relationships, 418–419 Linear sum of random variables, 280 Line charts, 35–39 Logarithmic transformations, 517–518 Lower confidence limit, 293 Lower tail test, 620 M Mann-Whitney U statistic, 628–629 Mann-Whitney U test, 628–630 Marginal distributions, 229 Marginal probabilities, 123–125, 179–180 Marginal probability distribution, 177–178 Margin of error, 293, 299, 304 reducing, 295–296 Matched pairs, 387–388 Mathematical derivations, 546–548, 682–683 Matrix plots, 486–487 Mean, 60–64 approximate, 81–82 of Bernoulli random variable, 160 of binomial distribution, 162, 195–196 conditional, 180 of continuous random variables, 204 geometric, 63–64 of jointly distributed random variables, 196 of linear functions of a random variable, 155–157, 194–195 measures of variability from, 68–79 of normal distribution, population variance known, 315–316, 352–361, 369–371 of normal distribution, population variance unknown, 362–364 of Poisson probability distribution, 168 of sampling distribution of sample variances, 283 weighted, 80–83 Mean square regression (MSR), 505, 506 Mean squares between-groups, 651 within-groups, 651 Measurement levels, 26–27 Measures of central tendency, 59–68 geometric mean, 63–64 mean, median, mode, 60–62 shape of a distribution, 62–63 Median, 60–62, 63 Minimum variance unbiased estimator, 288 Minitab, 87 See also Excel autoregressive models, 709–712 confidence intervals using, 337, 338–339, 341 descriptive measures using, 87 Durbin-Watson test, 586 exponential model estimation, 519 hypothesis testing, 377, 389–390, 396 lagged dependent variables, 569 matrix plots, 486–487 Monte Carlo sampling simulations, 280–283 for probability distributions, 154, 164–165 regression analysis using, 429–430 Missing values, 27, 330–331 Mode, 60–62 Model error variance, estimation of, 437 Model specification, 529–531, 552–553 Monte Carlo sampling simulations, 254–260, 280–283 Minitab, 280–283 Most efficient estimator, 287–289 Moving averages explanation of, 689–691 extraction of seasonal component through, 692–697 simple centered (2m 1)-point, 691 Multicollinearity, 574–577 corrections for, 576–577 indicators for, 576 Multiple comparisons, 654–655 Multiple regression See also Regression analysis application procedure and, 529–537 applications of, 475–476 confidence intervals and hypothesis tests for individual regression coefficients, 493–502 estimation of coefficients and, 481–487 explanatory power of multiple regression equation and, 488–492 introduction to, 474 least squares procedure, 482–487 objectives, 476 prediction and, 511–513 tests on regression coefficients, 505–509 Multiple regression equation, 488–492 Multiple regression model, 474 assumptions, 482 development of, 477–480, 531–532 dummy variables for, 522–526 explanation of, 474–480 model specification, 474–476 objectives, 476–477 population, 479 residuals analysis and, 534–537 test on all coefficients of, 497 three-dimensional graphing of, 480 transformations for nonlinear, 514–520 Multiplication rule of probabilities, 114–116 Mutually exclusive events, 96–97, 117 N Nominal data, 26 Nondiversifiable risk, 456 Nonlinear regression models logarithmic transformations, 517–518 quadratic transformations, 515–517 transformations for, 514–520 Index 787 www.downloadslide.net Nonparametic tests for independent random samples, 628–632 Kruskal-Wallis test, 658–660 Mann-Whitney U test, 628–630 normal approximation to the sign test, 623–624 for paired or matched samples, 619–626 for randomness, 636–639 sign test, 619–621, 626 Spearman rank correlation, 634–635 Wilcoxon rank sum test, 631–632 Wilcoxon signed rank test, 622–623 Nonprobabilistic sampling methods, 734 Nonsampling errors, 24–25 Nonuniform variance, 577–578 Normal approximation Mann-Whitney U test, 629 to sign test, 623–624 to Wilcoxon signed rank test, 624–626 Normal distribution, 206–217 to approximate binomial distribution, 219–224 compared with binomial distribution, 221 confidence interval estimation for variance of, 306–309 confidence interval for mean of, 291–296 cumulative distribution function of, 208 examples of, 211–214 explanation of, 206–207 probability density function for, 207 properties of, 207 standard, 209–210 test for, 611–613 tests of mean of, population variance known, 352–361 tests of the variance of, 375–377 Normality, test for, 611 Normal probability plots, 215–217 Normal random variables, range probabilities for, 209 Null hypothesis, 347–351, 376 See also Hypothesis p-value, 360–361, 376 rejection of, 406–407 sign test, 619–621 specifying, 406–407 788 Index testing regression coefficients, 497 tests/testing goodness-of-fit tests, 603–608 Number of combinations, 102 formula for determining, 102 Numerical variables, 25–26 graphs to describe, 40–50 O Odds, 126 Ogives, 44 One-sided composite alternative hypothesis, 347, 351 One-way analysis of variance, 647–656 framework for, 648 hypothesis test for, 651–653 multiple comparisons between subgroup means, 654–655 population model for, 655–656 sum of squares decomposition for, 650–651 One-way analysis of variance tables, 652–653 Ordering, 103 Ordinal data, 26 Outcomes basic, 95 for bivariate events, 122 random experiments and, 95 Outliers, 47, 62, 461 effect of, 462–464 Overall mean, 672, 725–726 Overinvolvement ratios, 126–129 P Paired samples, Wilcoxon signed rank test for, 622–623 Parameters, 24, 60 Pareto, Vilfredo, 32 Pareto diagrams, 32–34 Pearson’s product-moment correlation coefficient, 84–86 Percent explained variability, 435 Percentile, 64–67 Permutations, 102–104 Pie charts, 31–32 Point estimates, 286 Point estimators, properties of, 285–289 Poisson, Simeon, 167 Poisson approximation to binomial distribution, 171–172 Poisson probability distribution, 167–172 approximation to binomial distribution, 171–172 assumptions of, 167 comparison to binomial distribution, 172 cumulative, table of, 759–767 examples of, 168–172 explanation of, 167 functions, mean, and variance, 168 individual, table of, 750–758 test for, 609–611 Pooled sample variance, 336 Population defined, 23 sampling errors, 24 sampling from, 245–249 Population covariance, 84 Population mean allocation overall, 724 comparison of several, 645–647 confidence interval estimation of difference between two, 329–339 confidence interval for, 309–311 estimation of, 718–719, 730 guidelines for choosing decision rule for, 382 tests of difference between, dependent samples, 387–390 tests of difference between, independent samples, 391–398 Population model linear regression, 423 for one-way analysis of variance, 655–656 Population multiple regression model, 479 Population proportions confidence interval estimation for, 303–305, 312–313 estimation of, 313, 340–341, 721–723, 730 guidelines for choosing decision rule for, 383 optimal allocation, 724 sample size for, 317–319 tests of, 366–367, 371–373 tests of difference between, 399–402 Population regression parameters, 495 Population regression slope basis for inference about, 440 confidence interval, 440–443 tests of, 442 Populations, examples of, 245 www.downloadslide.net Population slope coefficient, hypothesis test for, 443–445 Population total confidence interval for, 309–311 estimation of, stratified random sample, 720–721 Population variance, 71–72 chi-square distribution of, 271–272 confidence intervals and, 293–294, 335–339 independent samples and, 333–339 tests of difference with known, 391–393 tests of difference with unknown, 393–396 tests of mean of normal distribution with known, 333–334, 352–361, 369–371 tests of mean of normal distribution with unknown, 335–339, 362–364, 396–398 tests of normal distribution, 375–377 Portfolio analysis, 186–188, 232–236 Portfolio market value, 185–188 Power, 350–351 Power function, 370–371 Prediction multiple regression and, 511–513 regression models and, 446–450 Prediction intervals, 447–448 Predictor variables, bias from excluding significant, 571–573 Price-earnings ratios, 289 Probability, 93–94 addition rule of, 112–113 Bayes’ theorem, 132–138 bivariate, 122–132 classical, 101–102 complement rule, 111–112, 118–119 conditional, 113–114 examples, 105–106 joint, 114–115, 117, 123–125 marginal, 123–125, 179–180 multiplication rule of, 114–116 for normally distributed random variables, 212 overinvolvement ratios and, 126–129 permutations and combinations, 102–105 random experiments and, 94–95 of range using cumulative distribution function, 199 relative frequency, 106 rules, 111–122 statistical independence and, 116–119 subjective, 107–110 Probability density functions, 199–200, 252 areas under, 200–201 for chi-square distribution, 272 for exponential distribution, 226 for normal distribution, 207 properties of, 199–200 for sample means, 252 for sample proportions, 267 of standard normal and Student’s t distribution, 298 Probability distribution function, 149, 199 Probability distributions Bernoulli distribution, 159–161 binomial distribution, 159–165 chi-square distribution, 271–272 for discrete random variables, 148–151 exponential distribution, 225–227 hypergeometric distribution, 173–175 Poisson probability distribution, 167–172 Student’s t distribution, 326–327 uniform, 201 Probability functions binomial distribution table, 739–743 conditional, 178 joint probability function, 177, 178 marginal probability function, 177 Probability plots, normal, 215–217, 535 Probability postulates consequences of, 108–109 explanation of, 107–108 Probability value (p-value), 360–361 Problem definition, 25 Properties of cumulative probability distributions, 151 of joint probability functions, 178 of probability distribution functions, 150 Proportional allocation, 723 Proportion random variable, 223–224 Proportions, confidence interval estimation for, 303–305 Public sector research, 563 Public sector research and policy analysis, dummy variable regression in, 563–565 p-value, 354–359 for chi-square test for variance, 376 for sign test, 620 Q Quadratic transformations, 515–517 Qualitative data, 26 Quantitative data, 26 Quartiles, 64–65 Queuing problems, 169–171 Quota sampling, 734 R Random experiments, 94 outcomes of, 94–100 Randomized block design, 661–662 Random samples/sampling, 23 independent, 333–339 nonparametric tests for independent, 628–632 simple, 23, 245–246 Random variables, 147–148 continuous (See Continuous random variables) correlation of, 229 differences between, 184 differences between pairs of, 230 linear combinations of, 232 linear functions of, 180–181, 205 linear sums and differences of, 184 mean and variance of linear functions of, 155–157 proportion, 223–224 statistical independence and, 181, 184 sums of, 229–230 Range explanation of, 69 interquartile, 69 Ratio data, 27 Ratio of mean squares, 683 Ratios overinvolvement, 126–129 price-earnings, 289 Regression See also Least squares regression; Multiple regression; Simple regression analysis of variance and, 432–433 autocorrelated errors and, 582–591 dummy variables and experimental design, 554–565 heteroscedasticity, 577–581 lagged valued of dependent variables, 567–570 least squares regression, 419–420 Index 789 www.downloadslide.net Regression (continued) linear regression model and, 421–426 mean square, 490, 506 multicollinearity, 574–577 specification bias, 571–573 Regression coefficients computer computation of, 429–430 confidence intervals for, 495–497 hypothesis tests for, 493–495 subsets of, tests on, 506–507 tests on, 505–507 Regression models See also Multiple regression model; Nonlinear regression models coefficient estimation, 553–554 dummy variables, 522–526, 554– 558 interpretation and inference, 554 linear, 418–426, 431–437 methodology for building, 552–554 specification, 552–553 verification, 554 Regression sum of squares, 432, 433, 490 Reject, 351 Relative efficiency, 288 Relative frequency distribution, 28, 42 Relative frequency probability, 106 Reliability factor, 293 Repeated measurements, 329, 331–332 Residuals, analysis of, 534–537 Returns, on financial portfolios, 234–236 Risk, 233 diversifiable, 456–458 nondiversifiable, 456 Runs test, 636–639 S Sample covariance, 84 Sample means acceptance intervals, 260–262 central limit theorem, 254–260 expected value of, 250 explanation of, 249 sampling distributions of, 249–262 standard normal distribution for, 251–253 Sample proportions examples of, 267–268 explanation of, 265 sampling distributions of, 265–268 790 Index Sample sizes determining, 340–341 determining, for stratified random sampling, 725–726 finite populations, 319–322 large populations, 315–319 Sample space, 95 Samples/sampling See also Random samples/sampling cluster, 729–732 defined, 23 dependent, 329–332, 386–390 explanation of, 22–25 independent, 333–339, 386–390 Monte Carlo sampling simulations, 280–283 nonprobabilistic methods, 734 from population, 245–249 simple random, 23, 245–246 stratified, 716–726 systematic, 23 two-phase, 732–734 Sample standard deviation, 271 Sample variances, 73 chi-square distribution, 271–272 explanation of, 271 sampling distributions of, 270–275, 283 Sampling distributions explanation of, 246–249 of least squares coefficient estimator, 439 of sample means, 249–262 of sample proportions, 265–268 of sample variances, 270–275, 283 Sampling error, 24–25, 293, 349 Sampling without replacement, 173–174 Sampling with replacement, 174 Sarbanes-Oxley Act (SOX), 617–618 Scatter plot analysis, 459–464 Scatter plots, 47–49 for residuals analysis, 535–537 Seasonal component extraction of, through moving averages, 692–697 of time series, 686–687 Seasonal index method, 704–707 Seasonal time series, forecasting, 704–707 Second-order autoregressive models, 708 Second quartile, 64 Side-by-side bar chart, 30 Significance level, 349, 351 Sign test explanation of, 619 normal approximation to, 623–626 for paired or matched samples, 619–623 p-value for, 620 for single population median, 626 Simple exponential smoothing explanation of, 698 forecasting through, 698–700 Holt-Winters model and, 700–703 Simple hypothesis, 347, 351 Simple random samples/sampling, 23, 245 beta measure of financial risk, 456–458 correlation analysis and, 452–454 explanatory power of linear regression equation and, 431–437 graphical analysis and, 458–464 least squares coefficient estimators and, 427–430 prediction and, 446–450 sample sizes, 320–322 statistical inference and, 438–445 Simple regression See Regression Simple regression coefficient, F test for, 444–445 Skewed distribution, 45–46 Skewness, 45, 91–92, 611, 613 Slope, 419 differences in, 525 Spearman rank correlation, 634–635 cutoff points, 776 Specification bias, 571–573 SSE, 427–428, 432–433 SSR, 433–435 SST, 433–435 Stacked bar charts, 30 Standard deviation, 72–73, 74 of continuous random variables, 204 of discrete random variable, 153–155 sample, 271 Standard error of the estimate, 490 Standardized normal random variable, 251 Standardized residual, 461–464 Standard normal distribution, 209 cumulative distribution function table, 738 for sample means, 251–253 www.downloadslide.net Statistical independence, 116–119, 181, 184 covariance, 184 Statistical inference, 438–445 Statistical significance, 407 Statistical thinking, 22 Statistics, 22, 60 See also Nonparametic tests defined, 24 descriptive, 25 inferential, 25 Stem-and-leaf displays, 46–47 Stock market crash of 2008, 94 beta coefficients limitations, 457 cautions concerning financial models, 236 Stratified random sampling allocation of sample effort among strata and, 723–725 analysis of results from, 718–720 determining sample sizes for, 725–726 estimation of population mean, 718–719 estimation of population proportion, 721–723 estimation of population total, 720–721 examples of, 719–720 explanation of, 716–717 Student’s t distribution, 326–327 confidence intervals and, 297–302 hypothesis tests, 362–364 for two means with unknown population variances not assumed to be equal, 344 upper critical values table, 770 Subgroup means, multiple comparisons between, 654 Subjective probability, 107–110 Sum of squares, 433, 489, 649 Sum of squares decomposition coefficient of determination and, 489–490 one-way analysis of variance, 650–651 two-way analysis of variance, 665 Sums, of random variables, 184, 229–230 Survey responses missing values in, 330–331 sampling errors, 24 Symmetric distributions, 45 Systematic sampling, 23 T Tables for categorical variables, 28–29 cross tables, 29–30 to describe relationships between variables, 47–49 frequency distribution, 28–29 Test of association, 615–618 Tests See Hypothesis tests/testing Third quartile, 65 Time plots, autocorrelation and, 582–583 Time series autoregressive integrated moving average models, 713–714 autoregressive models, 708–712 components of, 685–689 explanation of, 684–685 exponential smoothing and, 697–707 forecasting seasonal, 704–707 moving averages, 689–697 Time-series component analysis, 688 Time-series data explanation of, 684–685 graphs to describe, 35–40 Time-series plots, 35–39 misleading, 53–54 Time-series regression model, 587–590 Total explained variability, 547–548 Total sum of squares, 433, 489, 682 Treatment variables, 559–560 Tree diagrams, 123–124 Trend component, of time series, 685–686 t tests, vs F tests, 508–509 Two-phase sampling, 732–734 Two-sided composite alternative hypothesis, 347, 351, 360–361 Two-tail test, 620 Two-way analysis of variance examples of, 675–676 hypothesis tests for, 666 more than one observation per cell, 670–676 one observation per cell, 661–667 several observations per cell, 670–676 sum of squares decomposition for, 665 table format, 666–667 tables, 666–667 Two-way analysis of variance tables, 666–667 Type I errors, 349–351, 353, 407 Type II errors, 349–351, 369–370, 407 determining probability of, 369–371 U Unbiased estimator, 286–287 Uncertainty, decision making under, 22–25 Uniform distribution, 201, 204 Uniform probability distribution, 198 Unions, 97–100, 151 Upper confidence limit, 293 V Variability between-groups, 649 interaction as source of, 670 total explained, 547–548 within-groups, 649 Variability, measures of, 68–79 Variables See also Continuous random variables bias from excluding significant predictor, 571–573 blocking, 559–560, 661 categorical, 25, 28–34 classification of, 25–26 correlation analysis and, 452–454 defined, 25 dependent, 47 dummy, 522–526, 554–565 effect of dropping statistically significant, 532–534 independent, 47 indicator, 522–526 lagged dependent, 567–570 of linear functions of a random variable, 188 measures of relationships between, 84–89 numerical, 25–26, 40–49 relationships between, 418–419 tables and graphs to describe relationships between, 47–49 treatment, 559–560 Variance, 71–74 See also Analysis of variance (ANOVA) of Bernoulli random variable, 160 of binomial distribution, 162, 195–196 conditional, 180 of continuous random variables, 204 Index 791 www.downloadslide.net Variance (continued) of discrete random variables, 153–155, 184, 194 for grouped data, 81–82 of jointly distributed random variables, 196 of linear functions of a random variable, 155–157, 194–195 nonuniform, 577–578 of normal distribution, confidence interval estimation for, 306–309 of normal distribution, tests for, 375–377 of Poisson probability distribution, 168 sampling distributions of sample, 270–275 792 Index between two normally distributed populations, tests of equality, 403–405 Variation, coefficient of, 75 Venn diagrams for addition rule, 112 for complement of event, 98 for intersection of events, 97, 100, 144–145 for union of events, 96–98, 144–145 Verifications, 194–196 W Waiting line problems, 169–171 Weighted mean, 80–83 Width, 293 Wilcoxon rank sum statistic T, 631 Wilcoxon rank sum test, 631–632 cutoff points for statistic, 775 Wilcoxon signed rank test, 622–626 normal approximation to, 624–626 Within-groups mean square (MSW), 682 Within-groups variability, 649 Y y-intercept, 419 Z Zero population correlation, 453–454 z-score, 77–78 ... United States edition, entitled Statistics for Business and Economics, 8th Edition, ISBN: 978-0-13-274565-9 by Paul Newbold, William L Carlson and Betty Thorne, published by Pearson Education, Inc.,... data sets and computer based analysis These examples emphasize business and economics examples for the following: • • • • MBA or undergraduate business programs that teach business statistics. .. descriptive statistics and inferential statistics Descriptive and Inferential Statistics Descriptive statistics focus on graphical and numerical procedures that are used to summarize and process