Table Of Content

Probability & Statistics for Engineers &; Scientists Probability & Statistics for Engineers & Scientists E I G H TH E D I T I ON Ronald E. Walpole Roanoke College Raymond H. Myers Virginia Polytechnic Institute and State University Sharon L. Myers Radford University Keying Ye University of Texas at San Antonio PEARSON Prentice Pearson Education International Hall If you purchased this book within the United States or Canada you should be aware that it has been wrongfully imported without the approval of the Publisher or Author. Editor in Chief: Sally Yagun Production Editor: Lynn Savino Wendel Senior Managing Editor: Linda Mihatov Belmms Assistant Managing Editor: Bayani Mendoza de Leon Executive Managing Editor: Kathleen Schiaparelli Manufacturing Buyer: Maura Zaldivar Manufacturing Manager: Alexis Heydt-Long Marketing Manager: Halee Dinsey Marketing Assistant: Jennifer de Leeuwcrk Director of Marketing: Patrice Jones Editorial Assistant/Print Supplements Editor: Jennifer Urban Art Editor: Thomas Benfatti Art Director: Heather Scott Creative Director: Juan R. Lopez Director of Creative Services: Paul Belfanti Cover Photo: Corbis Royalty Free Art Studio: Laser-words PEARSON © 2007, 2002, 1998. 1993, 1989, 1985, 1978, 1972 Pearson Education, Inc. Pearson Prentice Hall Prentice Pearson Education, Inc. Hall Upper Saddle River, N.I 07458 All rights reserved. No part, of tins book may be reproduced, in any form or by any means, without permission in writing from the publisher. Pearson Prentice Hall™ is a trademark of Pearson Education, Inc. 10 9 8 7 6 5 43 ISBN 0-13-204767-5 Pearson Education LTD., London Pearson Education Australia PTY. Limited, Sydney Pearson Education Singapore, Pte. Ltd. Pearson Education North Asia Ltd., Hong Kong Pearson Education Canada, Ltd.. Toronto Pearson Education de Mexico, S.A. de C.V. Pearson Education-Japan, Tokyo Pearson Education Malaysia, Pte. Ltd. Pearson Education, Upper Saddle River, New Jersey This book is dedicated to Billy and Julie R.H.M. and S.L.M. Limin K.Y. Contents Preface xv 1 Introduction to Statistics and Data Analysis 1 1.1 Overview: Statistical Inference, Samples, Populations and Exper imental Design 1 1.2 The Hole of Probability 4 1.3 Sampling Procedures; Collection of Data 7 1.4 Measures of Location: The Sample Mean and Median 11 Exercises 13 1.5 Measures of Variability 1 •! Exercises 17 1.0 Discrete and Continuous Data 17 1.7 Statistical Modeling, Scientific Inspection, and Graphical Diag nostics ]!) J .8 Graphical Methods and Data Description 20 1.9 General Types of Statistical Studies: Designed Experiment, Observational Study, and Retrospective Study 25 Exercises 28 2 Probability 31 2.1 Sample Space 31 2.2 Events 34 Exercises 38 '2.3 Counting Sample Points 40 Exercises 47 2.4 Probability of an Event 48 2.5 Additive Rules 52 Exercises 55 2.6 Conditional Probability 58 2.7 Multiplicative Rules 61 Exercises 65 Contents Vlll 2.8 Bayes' Rule 68 Exercises 72 Review Exercises 73 3 Random Variables and Probability Distributions 77 3.1 Concept of a Random Variable 77 3.2 Discrete Probability Distributions 80 3.3 Continuous Probability Distributions 84 Exercises 88 3.4 Joint Probability Distributions 91 Exercises 101 Review Exercises 103 3.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 106 4 Mathematical Expectation 107 4.1 Mean of a Random Variable 107 Exercises 113 4.2 Variance and Covariance of Random Variables 115 Exercises 122 4.3 Means and Variances of Linear Combinations of Random Variables 123 4.4 Chebyshov's Theorem 131 Exercises 134 Review Exercises 136 4.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 138 5 Some Discrete Probability Distributions 141 5.1 Introduction and Motivation 141 5.2 Discrete Uniform Distribution 141 5.3 Binomial and Multinomial Distributions 143 Exercises 150 5.4 Hypergeometric Distribution 152 Exercises 157 5.5 Negative Binomial and Geometric Distributions 158 5.6 Poisson Distribution and the Poisson Process 161 Exercises 165 Review Exercises 167 5.7 Potential Misconceptions and Hazards: Relationship to Material in Other Chapters 169 Contents IX 6 Some Continuous Probability Distributions 171 6.1 Continuous Uniform Distribution 171 6.2 Normal Distribution 172 6.3 Areas under the Normal Curve 176 6.4 Applications of the Normal Distribution 182 Exercises 185 6.5 Normal Approximation to the Binomial 187 Exercises 19;} 6.6 Gamma and Exponential Distributions 194 6.7 Applications of the Exponential and Gamma Distributions 197 6.8 Chi-Squared Distribution 200 6.9 Lognormal Distribution 201 6.10 VVeibull Distribution (Optional) 202 Exercises 205 Review Exercises 206 6.1 1 Potential Misconceptions and Hazards: Relationship to Material in Other Chapters 209 7 Functions of Random Variables (Optional).. 211 7.1 Introduction 211 7.2 Transformations of Variables 211 7.3 Moments and Moment-Generating Functions 219 Exercises 226 8 Fundamental Sampling Distributions and Data Descriptions 229 8.1 Random Sampling 229 8.2 Some Important Statistics 231 Exercises 23 1 8.3 Data Displays and Graphical Methods 236 8.4 Sampling Distributions 243 8.5 Sampling Distribution of Means 244 Exercises 251 8.6 Sampling Distribution of S 251 8.7 ^-Distribution 257 8.8 F-Distribution 261 Exercises 265 Review Exercises 266 8.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 268 Contents 9 One- and Two-Sample Estimation Problems 269 9.1 Introduction 269 9.2 Statistical Inference 269 9.3 Classical Methods of Estimation 270 9.4 Single Sample: Estimating the Mean 274 9.5 Standard Error of a Point Estimate 280 9.6 Prediction Intervals 281 9.7 Tolerance Limits 283 Exercises 285 9.8 Two Samples: Estimating the Difference between Two Means ... 288 9.9 Paired Observations 294 Exercises 297 9.10 Single Sample: Estimating a Proportion 299 9.11 Two Samples: Estimating the Difference between Two Proportions 302 Exercises 304 9.12 Single Sample: Estimating the Variance 306 9.13 Two Samples: Estimating the Ratio of Two Variances 308 Exercises 310 9.14 Maximum Likelihood Estimation (Optional) 310 Exercises 315 Review Exercises 315 9.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 319 10 One- and Two-Sample Tests of Hypotheses 321 10.1 Statistical Hypotheses: General Concepts 321 10.2 Testing a Statistical Hypothesis 323 10.3 One- and Two-Tailed Tests 332 10.4 The Use of P-Values for Decision Making in Testing Hypotheses. 334 Exercises 336 10.5 Single Sample: Tests Concerning a Single Mean (Variance Known) 338 10.6 Relationship to Confidence Interval Estimation 341 10.7 Single Sample: Tests on a Single Mean (Variance Unknown) 342 10.8 Two Samples: Tests on Two Means 345 10.9 Choice of Sample Size for Testing Means 350 10.10 Graphical Methods for Comparing Means 355 Exercises 357 10.11 One Sample: Test on a Single Proportion 361 10.12 Two Samples: Tests on Two Proportions 364 Exercises 366 10.13 One- and Two-Sample Tests Concerning Variances 367 Contents xi Exercises 370 10.14 Goodness-of-Fit Test 371 10.15 Test for Independence (Categorical Data) 374 10.16 Test for Homogeneity 377 10.17 Testing for Several Proportions 378 10.18 Two-Sample Case Study 380 Exercises 383 Review Exercises 385 10.19 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 387 11 Simple Linear Regression and Correlation.. 389 11.1 Introduction to Linear Regression 389 11.2 The Simple Linear Regression Model 390 11.3 Least Squares and the Fitted Model 394 Exercises 397 11.4 Properties of the Least Squares Estimators 400 11.5 Inferences Concerning the Regression Coefficients 402 11.6 Prediction 409 Exercises 412 11.7 Choice of a Regression Model 414 11.8 Analysis-of-Variance Approach 415 11.9 Test for Linearity of Regression: Data with Repeated Observations 417 Exercises 423 11.10 Data Plots and Transformations 425 11.11 Simple Linear Regression Case Study 430 11.12 Correlation 432 Exercises 438 Review Exercises 438 11.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 443 12 Multiple Linear Regression and Certain Nonlinear Regression Models 445 12.1 Introduction 445 12.2 Estimating the Coefficients 446 12.3 Linear Regression Model Using Matrices (Optional) 449 Exercises 452 12.4 Properties of the Least Squares Estimators 456 12.5 Inferences in Multiple Linear Regression 458 Exercises 464 xii Contents 12.6 Choice of a Fitted Model through Hypothesis Testing 465 12.7 Special Case of Orthogonality (Optional) 469 Exercises 473 12.8 Categorical or Indicator Variables 474 Exercises 478 12.9 Sequential Methods for Model Selection 479 12.10 Study of Residuals and Violation of Assumptions 485 12.11 Cross Validation, C , and Other Criteria for Model Selection 490 ;) Exercises 496 12.12 Special Nonlinear Models for Nonideal Conditions 499 Review Exercises 503 12.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 508 13 One-Factor Experiments: General 511 13.1 Analysis-of-Variance Technique 511 13.2 The Strategy of Experimental Design 512 13.3 One-Way Analysis of Variance: Completely Randomized Design (One-Way ANOVA) 513 13.4 Tests for the Equality of Several Variances 518 Exercises 521 13.5 Single-Dcgree-of-Freedom Comparisons 523 13.6 Multiple Comparisons 527 13.7 Comparing Treatments with a Control 531 Exercises 533 13.8 Comparing a Set of Treatments in Blocks 535 13.9 Randomized Complete Block Designs 537 13.10 Graphical Methods and Model Checking 544 13.11 Data Transformations In Analysis of Variance) 547 13.12 Latin Squares (Optional) 549 Exercises 551 13.13 Random Effects Models 555 13.14 Power of Analysis-of-Variance Tests 559 13.15 Case Study 563 Exercises 565 Review Exercises 567 13.16 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters 571