com This International Student Edition is for use outside of the U.7% ≈ 95% ≈ 68% µ – 3σ µ – 2σ µ – 1σ µ µ + 1σ µ + 2σ µ + 3σ Second Edition Principles of Statistics for Engineers and Scientists 1 William Navidi 0.com Principles of Statistics for Engineers and Scientists Second Edition William Navidi www.com PRINCIPLES OF STATISTICS FOR ENGINEERS AND SCIENTISTS Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright c 2021 by McGraw-Hill Education. All rights reserved. Printed in the United States of America.
No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 LCR 24 23 22 21 20 ISBN 978-1-260-57073-1 MHID 1-260-57073-8 Cover Image: McGraw-Hill Education All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.com/highered www.com To Catherine, Sarah, and Thomas www.com ABOUT THE AUTHOR William Navidi is Professor of Mathematical and Computer Sciences at the Colorado School of Mines. He received the B. degree in mathematics from New College, the M.
in mathematics from Michigan State University, and the Ph. in statistics from the University of California at Berkeley. Professor Navidi has authored more than 80 research papers both in statistical theory and in a wide variety of applications includ- ing computer networks, epidemiology, molecular biology, chemical engineering, and geophysics.com CONTENTS Preface vii Chapter 1 4.4 The Lognormal Distribution 148 Summarizing Univariate Data 1 4.5 The Exponential Distribution 151 Introduction 1 4.6 Some Other Continuous Distributions 156 1.8 The Central Limit Theorem 166 1.3 Graphical Summaries 21 Chapter 5 Chapter 2 Point and Interval Estimation for Summarizing Bivariate Data 37 a Single Sample 179 Introduction 37 Introduction 179 2.1 The Correlation Coefficient 37 5.2 The Least-Squares Line 49 5.2 Large-Sample Confidence Intervals for 2.3 Features and Limitations of the a Population Mean 183 Least-Squares Line 57 5.3 Confidence Intervals for Proportions Chapter 3 196 Probability 67 5.4 Small-Sample Confidence Intervals for Introduction 67 a Population Mean 202 3.5 Prediction Intervals and Tolerance Intervals 211 3.2 Conditional Probability and Independence 75 Chapter 6 3.3 Random Variables 86 Hypothesis Tests for a Single Sample 219 3.4 Functions of Random Variables 107 Introduction 219 6.1 Large-Sample Tests for a Population Chapter 4 Mean 219 Commonly Used Distributions 122 6.2 Drawing Conclusions from the Results Introduction 122 of Hypothesis Tests 229 4.1 The Binomial Distribution 122 6.3 Tests for a Population Proportion 237 4.2 The Poisson Distribution 130 6.4 Small-Sample Tests for a Population 4.3 The Normal Distribution 137 Mean 242 v www.com vi Contents 6.5 The Chi-Square Test 248 Chapter 9 6.6 Fixed-Level Testing 257 Factorial Experiments 411 6.1 One-Factor Experiments 411 9.2 Pairwise Comparisons in One-Factor Chapter 7 Experiments 430 Inferences for Two Samples 278 9.3 Two-Factor Experiments 436 Introduction 278 9.4 Randomized Complete Block 7.1 Large-Sample Inferences on the Designs 456 Difference Between Two Population 9.5 2p Factorial Experiments 463 Means 278 7.2 Inferences on the Difference Between Chapter 10 Two Proportions 287 Statistical Quality Control 492 7.3 Small-Sample Inferences on the Introduction 492 Difference Between Two Means 295 10.4 Inferences Using Paired Data 305 10.2 Control Charts for Variables 495 7.5 Tests for Variances of Normal 10.3 Control Charts for Attributes 514 Populations 315 10.4 The CUSUM Chart 519 Chapter 8 10.5 Process Capability 522 Inference in Linear Models 325 Introduction 325 Appendix A: Tables 529 8.1 Inferences Using the Least-Squares Coefficients 326 Appendix B: Bibliography 552 8.2 Checking Assumptions 349 Answers to Selected Exercises 555 8.4 Model Selection 377 Index 601 www.com PREFACE MOTIVATION This book is based on the author’s more comprehensive text Statistics for Engineers and Scientists, 5th edition (McGraw-Hill, 2020), which is used for both one- and two- semester courses. The key concepts from that book form the basis for this text, which is designed for a one-semester course.
The emphasis is on statistical methods and how they can be applied to problems in science and engineering, rather than on theory. While the fundamental principles of statistics are common to all disciplines, students in science and engineering learn best from examples that present important ideas in realistic set- tings. Accordingly, the book contains many examples that feature real, contemporary data sets, both to motivate students and to show connections to industry and scientific research. As the text emphasizes applications rather than theory, the mathematical level is appropriately modest.
Most of the book will be mathematically accessible to those whose background includes one semester of calculus. COMPUTER USE Over the past 40 years, the development of fast and cheap computing has revolutionized statistical practice; indeed, this is one of the main reasons that statistical methods have been penetrating ever more deeply into scientific work. Scientists and engineers today must not only be adept with computer software packages; they must also have the skill to draw conclusions from computer output and to state those conclusions in words. Ac- cordingly, the book contains exercises and examples that involve interpreting, as well as generating, computer output, especially in the chapters on linear models and factorial experiments.
Many instructors integrate the use of statistical software into their courses; this book may be used effectively with any package. CONTENT Chapter 1 covers sampling and descriptive statistics. The reason that statistical methods work is that samples, when properly drawn, are likely to resemble their populations. Therefore, Chapter 1 begins by describing some ways to draw valid samples.
The second part of the chapter discusses descriptive statistics for univariate data. Chapter 2 presents descriptive statistics for bivariate data. The correlation coeffi- cient and least-squares line are discussed. The discussion emphasizes that linear models are appropriate only when the relationship between the variables is linear, and it de- scribes the effects of outliers and influential points.
Placing this chapter early enables instructors to present some coverage of these topics in courses where there is not enough time for a full treatment from an inferential point of view. Alternatively, this chapter may be postponed and covered just before the inferential procedures for linear models in Chapter 8.com viii Preface Chapter 3 is about probability. The goal here is to present the essential ideas with- out a lot of mathematical derivations. I have attempted to illustrate each result with an example or two, in a scientific context where possible, to present the intuition behind the result.
Chapter 4 presents many of the probability distribution functions commonly used in practice. Probability plots and the Central Limit Theorem are also covered. Only the normal and binomial distribution are used extensively in the remainder of the text; in- structors may choose which of the other distributions to cover. Chapters 5 and 6 cover one-sample methods for confidence intervals and hypoth- esis testing, respectively.
Point estimation is covered as well, in Chapter 5. The P-value approach to hypothesis testing is emphasized, but fixed-level testing and power calcula- tions are also covered. A discussion of the multiple testing problem is also presented. Chapter 7 presents two-sample methods for confidence intervals and hypothesis testing.
There is often not enough time to cover as many of these methods as one would like; instructors who are pressed for time may choose which of the methods they wish to cover. Chapter 8 covers inferential methods in linear regression. In practice, scatterplots often exhibit curvature or contain influential points. Therefore, this chapter includes material on checking model assumptions and transforming variables.
In the coverage of multiple regression, model selection methods are given particular emphasis, because choosing the variables to include in a model is an essential step in many real-life analyses. Chapter 9 discusses some commonly used experimental designs and the methods by which their data are analyzed. One-way and two-way analysis of variance methods, along with randomized complete block designs and 2p factorial designs, are covered fairly extensively. Chapter 10 presents the topic of statistical quality control, covering control charts, CUSUM charts, and process capability, and concluding with a brief discussion of sixsigma quality.
RECOMMENDED COVERAGE The book contains enough material for a one-semester course meeting four hours per week. For a three-hour course, it will probably be necessary to make some choices about coverage. One option is to cover the first three chapters, going lightly over the last two sections of Chapter 3, then cover the binomial, Poisson, and normal distributions in Chapter 4, along with the Central Limit Theorem. One can then cover the confidence intervals and hypothesis tests in Chapters 5 and 6, and finish either with the two-sample procedures in Chapter 7 or by covering as much of the material on inferential methods in regression in Chapter 8 as time permits.
For a course that puts more emphasis on regression and factorial experiments, one can go quickly over the power calculations and multiple testing procedures, and cover Chapters 8 and 9 immediately following Chapter 6. Alternatively, one could substitute Chapter 10 on statistical quality control for Chapter 9.com Preface ix NEW FOR THIS EDITION The second edition of this book is intended to extend the strengths of the first. Some of the changes are: ■ More than 250 new problems have been included. ■ Many examples have been updated.
■ Material on resistance to outliers has been added to Chapter 1. ■ Material on interpreting the slope of the least-squares line has been added to Chapter 2. ■ Material on the F-test for variance has been added to Chapter 7. ■ The exposition has been improved in a number of places.
ACKNOWLEDGMENTS I am indebted to many people for contributions at every stage of development. I re- ceived many valuable suggestions from my colleagues Gus Greivel, Ashlyn Munson, and Melissa Laeser at the Colorado School of Mines. I am particularly grateful to Jack Miller of The University of Michigan, who found many errors and made many valuable suggestions for improvement. The staff at McGraw-Hill has been extremely capable and supportive.
In particu- lar, I would like to express thanks to Product Developer Tina Bower, Content Project Manager Jeni McAtee and Senior Project Manager Sarita Yadav for their patience and guidance in the preparation of this edition. William Navidi Affordability & Outcomes = Academic Freedom! www.com You deserve choice, flexibility, and control. You know what’s best for your students and selecting the course materials that will help them succeed should be in your hands. That’s why providing you with a wide range of options that lower costs and drive better outcomes is our highest priority.
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