Writing Assignment for Probability and statistics class

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Probability and Statistics for Engineering and the Sciences

JAY DEVORE California Polytechnic State University, San Luis Obispo

EIGHTH EDIT ION

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This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. The publisher reserves the right to remove content from this title at any time if subsequent rights restrictions require it. For valuable information on pricing, previous editions, changes to current editions, and alternate formats, please visit www.cengage.com/highered to search by ISBN#, author, title, or keyword for materials in your areas of interest.

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Probability and Statistics for Engineering and the Sciences, Eighth Edition Jay L. Devore

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v

To my grandson

Philip, who is highly

statistically significant.

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vii

Contents

1 Overview and Descriptive Statistics

Introduction 1

1.1 Populations, Samples, and Processes 2

1.2 Pictorial and Tabular Methods in Descriptive Statistics 12

1.3 Measures of Location 28

1.4 Measures of Variability 35

Supplementary Exercises 46

Bibliography 49

2 Probability

Introduction 50

2.1 Sample Spaces and Events 51

2.2 Axioms, Interpretations, and Properties of Probability 55

2.3 Counting Techniques 64

2.4 Conditional Probability 73

2.5 Independence 83

Supplementary Exercises 88

Bibliography 91

Introduction 92

3.1 Random Variables 93

3.2 Probability Distributions for Discrete Random Variables 96

3.3 Expected Values 106

3.4 The Binomial Probability Distribution 114

3.5 Hypergeometric and Negative Binomial Distributions 122

3.6 The Poisson Probability Distribution 128

Supplementary Exercises 133

Bibliography 136

3 Discrete Random Variables and Probability Distributions

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Introduction 137

4.1 Probability Density Functions 138

4.2 Cumulative Distribution Functions and Expected Values 143

4.3 The Normal Distribution 152

4.4 The Exponential and Gamma Distributions 165

4.5 Other Continuous Distributions 171

4.6 Probability Plots 178

Supplementary Exercises 188

Bibliography 192

Introduction 193

5.1 Jointly Distributed Random Variables 194

5.2 Expected Values, Covariance, and Correlation 206

5.3 Statistics and Their Distributions 212

5.4 The Distribution of the Sample Mean 223

5.5 The Distribution of a Linear Combination 230

Supplementary Exercises 235

Bibliography 238

6 Point Estimation

7 Statistical Intervals Based on a Single Sample

Introduction 239

6.1 Some General Concepts of Point Estimation 240

6.2 Methods of Point Estimation 255

Supplementary Exercises 265

Bibliography 266

Introduction 267

7.1 Basic Properties of Confidence Intervals 268

7.2 Large-Sample Confidence Intervals for a Population Mean and Proportion 276

4 Continuous Random Variables and Probability Distributions

5 Joint Probability Distributions and Random Samples

viii Contents

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7.3 Intervals Based on a Normal Population Distribution 285

7.4 Confidence Intervals for the Variance and Standard Deviation of a Normal Population 294

Supplementary Exercises 297

Bibliography 299

8 Tests of Hypotheses Based on a Single Sample

Introduction 300

8.1 Hypotheses and Test Procedures 301

8.2 Tests About a Population Mean 310

8.3 Tests Concerning a Population Proportion 323

8.4 P-Values 328

8.5 Some Comments on Selecting a Test 339

Supplementary Exercises 342

Bibliography 344

9 Inferences Based on Two Samples

Introduction 345

9.1 z Tests and Confidence Intervals for a Difference Between Two Population Means 346

9.2 The Two-Sample t Test and Confidence Interval 357

9.3 Analysis of Paired Data 365

9.4 Inferences Concerning a Difference Between Population Proportions 375

9.5 Inferences Concerning Two Population Variances 382

Supplementary Exercises 386

Bibliography 390

10 The Analysis of Variance

Introduction 391

10.1 Single-Factor ANOVA 392

10.2 Multiple Comparisons in ANOVA 402

10.3 More on Single-Factor ANOVA 408

Supplementary Exercises 417

Bibliography 418

Contents ix

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11 Multifactor Analysis of Variance

Introduction 419

11.1 Two-Factor ANOVA with Kij � 1 420

11.2 Two-Factor ANOVA with Kij � 1 433

11.3 Three-Factor ANOVA 442

11.4 2p Factorial Experiments 451

Supplementary Exercises 464

Bibliography 467

12 Simple Linear Regression and Correlation

Introduction 468

12.1 The Simple Linear Regression Model 469

12.2 Estimating Model Parameters 477

12.3 Inferences About the Slope Parameter �1 490

12.4 Inferences Concerning and the Prediction of Future Y Values 499

12.5 Correlation 508

Supplementary Exercises 518

Bibliography 522

mY #x*

13 Nonlinear and Multiple Regression

Introduction 523

13.1 Assessing Model Adequacy 524

13.2 Regression with Transformed Variables 531

13.3 Polynomial Regression 543

13.4 Multiple Regression Analysis 553

13.5 Other Issues in Multiple Regression 574

Supplementary Exercises 588

Bibliography 593

14 Goodness-of-Fit Tests and Categorical Data Analysis

Introduction 594

14.1 Goodness-of-Fit Tests When Category Probabilities Are Completely Specified 595

x Contents

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14.2 Goodness-of-Fit Tests for Composite Hypotheses 602

14.3 Two-Way Contingency Tables 613

Supplementary Exercises 621

Bibliography 624

15 Distribution-Free Procedures

Introduction 625

15.1 The Wilcoxon Signed-Rank Test 626

15.2 The Wilcoxon Rank-Sum Test 634

15.3 Distribution-Free Confidence Intervals 640

15.4 Distribution-Free ANOVA 645

Supplementary Exercises 649

Bibliography 650

16 Quality Control Methods

Introduction 651

16.1 General Comments on Control Charts 652

16.2 Control Charts for Process Location 654

16.3 Control Charts for Process Variation 663

16.4 Control Charts for Attributes 668

16.5 CUSUM Procedures 672

16.6 Acceptance Sampling 680

Supplementary Exercises 686

Bibliography 687

Appendix Tables

A.1 Cumulative Binomial Probabilities A-2

A.2 Cumulative Poisson Probabilities A-4

A.3 Standard Normal Curve Areas A-6

A.4 The Incomplete Gamma Function A-8

A.5 Critical Values for t Distributions A-9

A.6 Tolerance Critical Values for Normal Population Distributions A-10

A.7 Critical Values for Chi-Squared Distributions A-11

A.8 t Curve Tail Areas A-12

A.9 Critical Values for F Distributions A-14

A.10 Critical Values for Studentized Range Distributions A-20

Contents xi

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A.11 Chi-Squared Curve Tail Areas A-21

A.12 Critical Values for the Ryan-Joiner Test of Normality A-23

A.13 Critical Values for the Wilcoxon Signed-Rank Test A-24

A.14 Critical Values for the Wilcoxon Rank-Sum Test A-25

A.15 Critical Values for the Wilcoxon Signed-Rank Interval A-26

A.16 Critical Values for the Wilcoxon Rank-Sum Interval A-27

A.17 � Curves for t Tests A-28

Answers to Selected Odd-Numbered Exercises A-29 Glossary of Symbols/Abbreviations G-1 Index I-1

xii Contents

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xiii

Preface Purpose

The use of probability models and statistical methods for analyzing data has become common practice in virtually all scientific disciplines. This book attempts to provide a comprehensive introduction to those models and methods most likely to be encoun- tered and used by students in their careers in engineering and the natural sciences. Although the examples and exercises have been designed with scientists and engi- neers in mind, most of the methods covered are basic to statistical analyses in many other disciplines, so that students of business and the social sciences will also profit from reading the book.

Approach

Students in a statistics course designed to serve other majors may be initially skeptical of the value and relevance of the subject matter, but my experience is that students can be turned on to statistics by the use of good examples and exercises that blend their every- day experiences with their scientific interests. Consequently, I have worked hard to find examples of real, rather than artificial, data—data that someone thought was worth col- lecting and analyzing. Many of the methods presented, especially in the later chapters on statistical inference, are illustrated by analyzing data taken from published sources, and many of the exercises also involve working with such data. Sometimes the reader may be unfamiliar with the context of a particular problem (as indeed I often was), but I have found that students are more attracted by real problems with a somewhat strange context than by patently artificial problems in a familiar setting.

Mathematical Level

The exposition is relatively modest in terms of mathematical development. Substantial use of the calculus is made only in Chapter 4 and parts of Chapters 5 and 6. In particu- lar, with the exception of an occasional remark or aside, calculus appears in the inference part of the book only—in the second section of Chapter 6. Matrix algebra is not used at all. Thus almost all the exposition should be accessible to those whose mathematical background includes one semester or two quarters of differential and integral calculus.

Content

Chapter 1 begins with some basic concepts and terminology—population, sample, descriptive and inferential statistics, enumerative versus analytic studies, and so on— and continues with a survey of important graphical and numerical descriptive methods. A rather traditional development of probability is given in Chapter 2, followed by prob- ability distributions of discrete and continuous random variables in Chapters 3 and 4, respectively. Joint distributions and their properties are discussed in the first part of Chapter 5. The latter part of this chapter introduces statistics and their sampling distri- butions, which form the bridge between probability and inference. The next three chapters cover point estimation, statistical intervals, and hypothesis testing based on a single sample. Methods of inference involving two independent samples and paired data are presented in Chapter 9. The analysis of variance is the subject of Chapters 10 and 11 (single-factor and multifactor, respectively). Regression makes its initial appearance in Chapter 12 (the simple linear regression model and correlation) and

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returns for an extensive encore in Chapter 13. The last three chapters develop chi- squared methods, distribution-free (nonparametric) procedures, and techniques from statistical quality control.

Helping Students Learn

Although the book’s mathematical level should give most science and engineering students little difficulty, working toward an understanding of the concepts and gain- ing an appreciation for the logical development of the methodology may sometimes require substantial effort. To help students gain such an understanding and appreci- ation, I have provided numerous exercises ranging in difficulty from many that involve routine application of text material to some that ask the reader to extend con- cepts discussed in the text to somewhat new situations. There are many more exer- cises than most instructors would want to assign during any particular course, but I recommend that students be required to work a substantial number of them; in a problem-solving discipline, active involvement of this sort is the surest way to iden- tify and close the gaps in understanding that inevitably arise. Answers to most odd- numbered exercises appear in the answer section at the back of the text. In addition, a Student Solutions Manual, consisting of worked-out solutions to virtually all the odd-numbered exercises, is available.

To access additional course materials and companion resources, please visit www.cengagebrain.com. At the CengageBrain.com home page, search for the ISBN of your title (from the back cover of your book) using the search box at the top of the page. This will take you to the product page where free companion resources can be found.

New for This Edition

• A Glossary of Symbols/Abbreviations appears at the end of the book (the author apologizes for his laziness in not getting this together for earlier editions!) and a small set of sample exams appears on the companion website (available at www.cengage.com/login).

• Many new examples and exercises, almost all based on real data or actual prob- lems. Some of these scenarios are less technical or broader in scope than what has been included in previous editions—for example, weights of football players (to illustrate multimodality), fundraising expenses for charitable organizations, and the comparison of grade point averages for classes taught by part-time faculty with those for classes taught by full-time faculty.

• The material on P-values has been substantially rewritten. The P-value is now ini- tially defined as a probability rather than as the smallest significance level for which the null hypothesis can be rejected. A simulation experiment is presented to illustrate the behavior of P-values.

• Chapter 1 contains a new subsection on “The Scope of Modern Statistics” to indicate how statisticians continue to develop new methodology while working on problems in a wide spectrum of disciplines.

• The exposition has been polished whenever possible to help students gain an intuitive understanding of various concepts. For example, the cumulative distribution function is more deliberately introduced in Chapter 3, the first example of maximum likeli- hood in Section 6.2 contains a more careful discussion of likelihood, more attention is given to power and type II error probabilities in Section 8.3, and the material on residuals and sums of squares in multiple regression is laid out more explicitly in Section 13.4.

xiv Preface

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Acknowledgments

My colleagues at Cal Poly have provided me with invaluable support and feedback over the years. I am also grateful to the many users of previous editions who have made suggestions for improvement (and on occasion identified errors). A special note of thanks goes to Matt Carlton for his work on the two solutions manuals, one for instructors and the other for students.

The generous feedback provided by the following reviewers of this and previous editions has been of great benefit in improving the book: Robert L. Armacost, University of Central Florida; Bill Bade, Lincoln Land Community College; Douglas M. Bates, University of Wisconsin–Madison; Michael Berry, West Virginia Wesleyan College; Brian Bowman, Auburn University; Linda Boyle, University of Iowa; Ralph Bravaco, Stonehill College; Linfield C. Brown, Tufts University; Karen M. Bursic, University of Pittsburgh; Lynne Butler, Haverford College; Raj S. Chhikara, University of Houston–Clear Lake; Edwin Chong, Colorado State University; David Clark, California State Polytechnic University at Pomona; Ken Constantine, Taylor University; David M. Cresap, University of Portland; Savas Dayanik, Princeton University; Don E. Deal, University of Houston; Annjanette M. Dodd, Humboldt State University; Jimmy Doi, California Polytechnic State University–San Luis Obispo; Charles E. Donaghey, University of Houston; Patrick J. Driscoll, U.S. Military Academy; Mark Duva, University of Virginia; Nassir Eltinay, Lincoln Land Community College; Thomas English, College of the Mainland; Nasser S. Fard, Northeastern University; Ronald Fricker, Naval Postgraduate School; Steven T. Garren, James Madison University; Mark Gebert, University of Kentucky; Harland Glaz, University of Maryland; Ken Grace, Anoka-Ramsey Community College; Celso Grebogi, University of Maryland; Veronica Webster Griffis, Michigan Technological University; Jose Guardiola, Texas A&M University–Corpus Christi; K. L. D. Gunawardena, University of Wisconsin–Oshkosh; James J. Halavin, Rochester Institute of Technology; James Hartman, Marymount University; Tyler Haynes, Saginaw Valley State University; Jennifer Hoeting, Colorado State University; Wei-Min Huang, Lehigh University; Aridaman Jain, New Jersey Institute of Technology; Roger W. Johnson, South Dakota School of Mines & Technology; Chihwa Kao, Syracuse University; Saleem A. Kassam, University of Pennsylvania; Mohammad T. Khasawneh, State University of NewYork–Binghamton; Stephen Kokoska, Colgate University; Hillel J. Kumin, University of Oklahoma; Sarah Lam, Binghamton University; M. Louise Lawson, Kennesaw State University; Jialiang Li, University of Wisconsin–Madison; Wooi K. Lim, William Paterson University; Aquila Lipscomb, The Citadel; Manuel Lladser, University of Colorado at Boulder; Graham Lord, University of California–Los Angeles; Joseph L. Macaluso, DeSales University; Ranjan Maitra, Iowa State University; David Mathiason, Rochester Institute of Technology; Arnold R. Miller, University of Denver; John J. Millson, University of Maryland; Pamela Kay Miltenberger, West Virginia Wesleyan College; Monica Molsee, Portland State University; Thomas Moore, Naval Postgraduate School; Robert M. Norton, College of Charleston; Steven Pilnick, Naval Postgraduate School; Robi Polikar, Rowan University; Ernest Pyle, Houston Baptist University; Steve Rein, California Polytechnic State University–San Luis Obispo; Tony Richardson, University of Evansville; Don Ridgeway, North Carolina State University; Larry J. Ringer, Texas A&M University; Robert M. Schumacher, Cedarville University; Ron Schwartz, Florida Atlantic University; Kevan Shafizadeh, California State University–Sacramento; Mohammed Shayib, Prairie View A&M; Robert K. Smidt, California Polytechnic State University–San Luis Obispo; Alice E. Smith, Auburn University; James MacGregor Smith, University of Massachusetts;

Preface xv

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Paul J. Smith, University of Maryland; Richard M. Soland, The George Washington University; Clifford Spiegelman, Texas A&M University; Jery Stedinger, Cornell University; David Steinberg, Tel Aviv University; William Thistleton, State University of New York Institute of Technology; G. Geoffrey Vining, University of Florida; Bhutan Wadhwa, Cleveland State University; Gary Wasserman, Wayne State University; Elaine Wenderholm, State University of New York–Oswego; Samuel P. Wilcock, Messiah College; Michael G. Zabetakis, University of Pittsburgh; and Maria Zack, Point Loma Nazarene University.

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