Statistics for Engineering and the Sciences

by Mendenhall, William; Sincich, Terry L.

Edition: 4th

ISBN13: 9780023805813

ISBN10: 0023805811

Format: Hardcover

Pub. Date: 1995-01-01

Publisher(s): Pearson College Div

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Summary

This book illustrates basic statistical concepts with extensive applications in engineering and scientific contexts. The book includes optional theoretical exercises, allowing readers who choose to emphasize theory to do so with requiring additional materials. The fourth edition contains SAS and MINITAB computer printout results for all analyses performedplus new exercises based on magazine and journal articles and news reports.KEY TOPICS:A section on "Detecting Normal Distributions" (Chapter 5) gives readers insights on when it is reasonable to assume that underlying data is normally distributed. There is a comprehensive example on model building (Chapter 13) and emphasis on the regression approach to a Nova (also presents the traditional approach). There are two sections discussing principles of experimental design, i.e., noise-reducing and volume-increasing design, a section on "Total Quality Management" and coverage of statistical computing. There are optional, calculus-based theoretical exercises, and real data sets, extracted from scientific studies, are provided in an appendix. Numerical answers to all applied exercises are included in an appendixgiving readers immediate feedback on their work.

Preface

xiii

Introduction

(14)

Statistics: The Science of Data

(3)

Types of Data

(2)

The Role of Statistics

(1)

Summary

(7)

Entering and Listing Data

(3)

Accessing an External Data File (Optional)

(2)

Descriptive Statistics

(62)

Graphical and Numerical Methods for Describing Qualitative Data

(9)

Graphical Methods for Describing Quantitative Data

(14)

Numerical Methods for Describing Quantitative Data

(1)

Measures of Central Tendency

(5)

Measures of Variation

(9)

Measures of Relative Standing

(4)

Methods for Detecting Outliers

(5)

Summary

(15)

Graphical and Numerical Data Description

(7)

Probability

(66)

The Role of Probability in Statistics

(1)

Events, Sample Spaces, and Probability

(13)

Compound Events

(3)

Complementary Events

(4)

Conditional Probability

(5)

Probability Rules for Unions and Intersections

103

(13)

Bayes' Rule (Optional)

116

(3)

Some Counting Rules

119

(14)

Probability and Statistics: An Example

133

(3)

Summary

136

(7)

Discrete Random Variables

143

(60)

Discrete Random Variables

144

(1)

The Probability Distribution for a Discrete Random Variable

145

(5)

The Expected Value for a Random Variable y or for a Function g(y) of y

150

(5)

Some Useful Expectation Theorems

155

(2)

Bernoulli Trials

157

(2)

The Binomial Probability Distribution

159

(8)

The Multinomial Probability Distribution

167

(7)

The Negative Binomial and the Geometric Probability Distributions

174

(4)

The Hypergeometric Probability Distribution

178

(6)

The Poisson Probability Distribution

184

(8)

Moments and Moment Generating Functions (Optional)

192

(5)

Summary

197

(6)

Continuous Random Variables

203

(54)

Continuous Random Variables

204

(2)

The Density Function for a Continuous Random Variable

206

(5)

Expected Values for Continuous Random Variables

211

(6)

The Uniform Probability Distribution

217

(4)

The Normal Probability Distribution

221

(7)

Descriptive Methods for Assessing Normality

228

(7)

Gamma-Type Probability Distributions

235

(6)

The Weibull Probability Distribution

241

(3)

Beta-Type Probability Distributions

244

(5)

Moments and Moment Generating Functions (Optional)

249

(2)

Summary

251

(6)

Bivariate Probability Distributions

257

(32)

Bivariate Probability Distributions for Discrete Random Variables

258

(7)

Bivariate Probability Distributions for Continuous Random Variables

265

(6)

The Expected Value of Functions of Two Random Variables

271

(2)

Independence

273

(3)

The Covariance of Two Random Variables

276

(3)

The Correlation Coefficient p

279

(2)

The Expected Value and Variance of Linear Functions of Random Variables (Optional)

281

(4)

Summary

285

(4)

Sampling Distributions

289

(48)

Random Sampling

290

(4)

Sampling Distributions

294

(1)

Probability Distributions of Functions of Random Variables (Optional)

295

(7)

Approximating a Sampling Distribution by Simulation

302

(8)

The Sampling Distributions of Means and Sums

310

(8)

Normal Approximation to the Binomial Distribution

318

(4)

Sampling Distributions Related to the Normal Distribution

322

(6)

Summary

328

(9)

Generating Random Samples

332

(5)

Estimation

337

(84)

Estimators

338

(1)

Properties of Point Estimators

339

(5)

Finding Point Estimators: Methods of Estimation

344

(8)

Finding Interval Estimators: The Pivotal Method

352

(12)

Estimation of a Population Mean

364

(7)

Estimation of the Difference Between Two Population Means: Independent Samples

371

(10)

Estimation of the Difference Between Two Population Means: Matched Pairs

381

(6)

Estimation of a Population Proportion

387

(3)

Estimation of the Difference Between Two Population Proportions

390

(4)

Estimation of a Population Variance

394

(5)

Estimation of the Ratio of Two Population Variances

399

(6)

Choosing the Sample Size

405

(5)

Summary

410

(11)

Confidence Intervals for Means

417

(4)

Tests of Hypotheses

421

(74)

The Relationship Between Statistical Tests of Hypotheses and Confidence Intervals

422

(1)

Elements of a Statistical Test

423

(1)

Evaluation the Properties of a Statistical Test

424

(6)

Finding Statistical Tests: An Example of a Large-Sample Test

430

(6)

Choosing the Null and Alternative Hypotheses

436

(2)

Testing a Population Mean

438

(7)

The Observed Significance Level for a Test

445

(4)

Testing the Difference Between Two Population Means: Independent Samples

449

(10)

Testing the Difference Between Two Population Means: Matched Pairs

459

(6)

Testing a Population Proportion

465

(3)

Testing the Difference Between Two Population Proportions

468

(5)

Testing a Population Variance

473

(3)

Testing the Ratio of Two Population Variances

476

(6)

Summary

482

(13)

Testing Means

489

(6)

Categorical Data Analysis

495

(36)

Categorical Data and Multinomial Probabilities

496

(1)

Estimating Category Probabilities in a One-Way Table

496

(5)

Testing Category Probabilities in a One-Way Table

501

(4)

Inferences About Category Probabilities in a Two-Way (Contingency) Table

505

(10)

Contingency Tables with Fixed Marginal Totals

515

(6)

Summary

521

(10)

Contingency Table Analysis

527

(4)

Simple Linear Regression

531

(68)

Introduction

532

(1)

A Simple Linear Regression Model: Assumptions

533

(3)

Estimating β0 and β1: The Method of Least Squares

536

(11)

Properties of the Least Squares Estimators

547

(3)

An Estimator of σ2

550

(3)

Assessing the Utility of the Model: Making Inferences About the Slope β1

553

(8)

The Coefficient of Correlation

561

(5)

The Coefficient of Determination

566

(6)

Using the Model for Estimation and Prediction

572

(9)

Simple Linear Regression on the Computer

581

(5)

Summary

586

(13)

Simple Linear Regression and Correlation

594

(5)

Multiple Regression Analysis

599

(100)

General Linear Models

600

(3)

Model Assumptions

603

(1)

Fitting the Model: The Method of Least Squares

603

(2)

The Least Squares Equations and Their Solution

605

(7)

Properties of the Least Squares Estimators

612

(1)

Estimating σ2 the Variance of ε

613

(2)

Confidence Intervals and Tests of Hypotheses for β0, β1, ..., βk

615

(10)

Assessing Model Adequacy

625

(13)

A Confidence Interval for E(y)

638

(7)

A Prediction Interval for a Future Value of y

645

(3)

Checking Assumptions: Residual Analysis

648

(25)

Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

673

(11)

Summary

684

(15)

Multiple Regression and Residual Analysis

696

(3)

Model Building

699

(90)

Why Model Building Is Important

700

(1)

The Two Types of Independent Variables: Quantitative and Qualitative

701

(2)

Models with a Single Quantitative Independent Variable

703

(9)

Models with Two Quantitative Independent Variables

712

(9)

Coding Quantitative Independent Variables (Optional)

721

(6)

Tests for Comparing Nested Models

727

(8)

Models with One Qualitative Independent Variable

735

(6)

Comparing the Slopes of Two or More Lines

741

(14)

Comparing Two or More Response Curves

755

(5)

Stepwise Regression

760

(8)

Model Building: An Example

768

(9)

Summary

777

(12)

Stepwise Regression

785

(4)

Analysis of Variance for Designed Experiments

789

(130)

Introduction

790

(1)

Experimental Design: Terminology

791

(1)

Controlling the Information in an Experiment

792

(2)

Noise-Reducing Designs

794

(7)

Volume-Increasing Designs

801

(6)

Selecting the Sample Size

807

(3)

The Logic Behind an Analysis of Variance

810

(3)

ANOVA for Completely Randomized Designs

813

(15)

ANOVA for Randomized Block Designs

828

(15)

ANOVA for Two-Factor Factorial Experiments

843

(21)

ANOVA for a k-Way Classification of Data (Optional)

864

(11)

ANOVA for Nested Sampling Designs (Optional)

875

(15)

Procedures for Making Multiple Comparisons of Treatment Means

890

(8)

Checking ANOVA Assumptions

898

(4)

Summary

902

(17)

Analysis of Variance

915

(4)

Nonparametric Statistics

919

(62)

Introduction

920

(2)

Testing for Location of a Single Population

922

(6)

Comparing Two Populations: Independent Random Samples

928

(9)

Comparing Two Populations: Matched-Pairs Design

937

(8)

Comparing Three or More Populations: Completely Randomized Design

945

(7)

Comparing Three or More Populations: Randomized Block Design

952

(5)

Nonparametric Regression

957

(9)

Summary

966

(15)

Nonparametric Tests

974

(7)

Statistical Process and Quality Control

981

(54)

Total Quality Management

982

(1)

Variable Control Charts

982

(7)

Control Chart for Means: x-Chart

989

(10)

Control Chart for Process Variation: R-Chart

999

(3)

Detecting Trends in a Control Chart: Runs Analysis

1002

(2)

Control Chart for Percent Defectives: p-Chart

1004

(5)

Control Chart for the Number of Defects per Item: c-Chart

1009

(4)

Tolerance Limits

1013

(5)

Acceptance Sampling for Defectives

1018

(6)

Other Sampling Plans (Optional)

1024

(1)

Evolutionary Operations (Optional)

1025

(2)

Summary

1027

(8)

Control Charts

1030

(5)

Product and System Reliability

1035

(30)

Introduction

1036

(1)

Failure Time Distributions

1036

(2)

Hazard Rates

1038

(4)

Life Testing: Censored Sampling

1042

(1)

Estimating the Parameters of an Exponential Failure Time Distribution

1043

(5)

Estimating the Parameters of a Weibull Failure Time Distribution

1048

(5)

System Reliability

1053

(6)

Summary

1059

(6)

APPENDIX I Matrix Algebra

1065

(20)

Matrices and Matrix Multiplication

1066

(6)

Identity Matrices and Matrix Inversion

1072

(3)

Solving Systems of Simultaneous Linear Equations

1075

(3)

A Procedure for Inverting a Matrix

1078

(7)

APPENDIX II Useful Statistical Tables

1085

(40)

Table 1 Cumulative Binomial Probabilities

1087

(4)

Table 2 Exponentials

1091

(1)

Table 3 Cumulative Poisson Probabilities

1092

(2)

Table 4 Normal Curve Areas

1094

(1)

Table 5 Gamma Function

1095

(1)

Table 6 Random Numbers

1096

(3)

Table 7 Critical Values of Student's t

1099

(1)

Table 8 Critical Values of X2

1100

(2)

Table 9 Percentage Points of the F Distribution, α = .10

1102

(2)

Table 10 Percentage Points of the F Distribution, α = .05

1104

(2)

Table 11 Percentage Points of the F Distribution, α = .025

1106

(2)

Table 12 Percentage Points of the F Distribution, α = .01

1108

(2)

Table 13 Percentage Points of the Studentized Range q(p, v), α = .05

1110

(2)

Table 14 Percentage Points of the Studentized Range q(p, v), α = .01

1112

(2)

Table 15 Critical Values of TL and TU for the Wilcoxon Rank Sum Test: Independent Samples

1114

(1)

Table 16 Critical Values of TO in the Wilcoxon Matched-Pairs Signed Rank Test

1115

(1)

Table 17 Critical Values of Spearman's Rank Correlation Coefficient

1116

(1)

Table 18 Critical Values of C for the Theil Zero-Slope Test

1117

(4)

Table 19 Factors Used When Constructing Control Charts

1121

(1)

Table 20 Values of K for Tolerance Limits for Normal Distributions

1122

(1)

Table 21 Sample Size n for Nonparametric Tolerance Limits

1123

(1)

Table 22 Sample Size Code Letters: MIL-STD-105D

1123

(1)

Table 23 A Portion of the Master Table for Normal Inspection (Single Sampling): MIL-STD-105D

1124

(1)

APPENDIX III DDT Analyses on Fish Samples, Tennessee River, Alabama

1125

(4)

APPENDIX IV Central Processing Unit (CPU) Times of 1,000 Computer Jobs

1129

(4)

APPENDIX V Percentage Iron Content for 390 Iron-Ore Specimens

1133

(4)

APPENDIX VI Federal Trade Commission Rankings of Domestic Cigarette Brands

1137

(8)

APPENDIX VII ASP Tutorial

1145

(6)

Answers to the Exercises

1151

(26)

Index

1177

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