Solutions Manual to accompany Miller & Freund’s Probability and Statistics for Engineers 8th edition 0321640772

Introduction

1(11)

Why Study Statistics?

1(1)

Modern Statistics

2(1)

Statistics and Engineering

2(1)

The Role of the Scientist and Engineer in Quality Improvement

3(1)

A Case Study: Visually Inspecting Data to Improve Product Quality

3(2)

Two Basic Concepts—Population and Sample

5(7)

Review Exercises

10(1)

Key Terms

11(1)

Organization and Description of Data

12(33)

Pareto Diagrams and Dot Diagrams

12(2)

Frequency Distributions

14(3)

Graphs of Frequency Distributions

17(4)

Stem-and-Leaf Displays

21(3)

Descriptive Measures

24(5)

Quartiles and Percentiles

29(5)

The Calculation of x and s

34(5)

A Case Study: Problems with Aggregating Data

39(6)

Review Exercises

42(2)

Key Terms

44(1)

Probability

45(36)

Sample Spaces and Events

45(4)

Counting

49(6)

Probability

55(2)

The Axioms of Probability

57(3)

Some Elementary Theorems

60(6)

Conditional Probability

66(6)

Bayes’ Theorem

72(9)

Review Exercises

78(2)

Key Terms

80(1)

Probability Distributions

81(38)

Random Variables

81(4)

The Binomial Distribution

85(4)

The Hypergeometric Distribution

89(4)

The Mean and the Variance of a Probability Distribution

93(7)

Chebyshev’s Theorem

100(4)

The Poisson Approximation to the Binomial Distribution

104(3)

Poisson Processes

107(2)

The Geometric and Negative Binomial Distribution

109(2)

The Multinomial Distribution

111(2)

Simulation

113(6)

Review Exercises

116(2)

Key Terms

118(1)

Probability Densities

119(56)

Continuous Random Variables

119(6)

The Normal Distribution

125(7)

The Normal Approximation to the Binomial Distribution

132(3)

Other Probability Densities

135(1)

The Uniform Distribution

135(1)

The Log-Normal Distribution

136(2)

The Gamma Distribution

138(3)

The Beta Distribution

141(1)

The Weibull Distribution

142(3)

Joint Distributions—Discrete and Continuous

145(12)

Moment Generating Functions

157(6)

Checking if the Data are Normal

163(2)

Transforming Observations to Near Normality

165(2)

Simulation

167(8)

Review Exercises

171(1)

Key Terms

172(3)

Sampling Distributions

175(29)

Populations and Samples

175(4)

The Sampling Distribution of the Mean (& Known)

179(8)

The Sampling Distribution of the Mean (Sigma; unknown)

187(2)

The Sampling Distribution of the Variance

189(3)

Representations of the Normal Theory Distributions

192(2)

The Moment Generating Function Method to Obtain Distributions

194(3)

Transformation Methods to Obtain Distributions

197(7)

Review Exercises

202(1)

Key Terms

203(1)

Inferences Concerning a Mean

204(41)

Point Estimation

204(5)

Interval Estimation

209(6)

Maximum Likelihood Estimation

215(7)

Tests of Hypotheses

222(2)

Null Hypotheses and Tests of Hypotheses

224(5)

Hypotheses Concerning One Mean

229(6)

The Relation between Tests and Confidence Intervals

235(2)

Power, Sample Size, and Operating Characteristic Curves

237(8)

Review Exercises

243(1)

Key Terms

244(1)

Comparing Two Treatments

245(23)

Experimental Designs for Comparing Two Treatments

245(1)

Comparisons—Two Independent Large Samples

246(5)

Comparisons—Two Independent Small Samples

251(8)

Matched Pairs Comparisons

259(4)

Design Issues—Randomization and Pairing

263(5)

Review Exercises

266(1)

Key Terms

266(2)

Inferences Concerning Variances

268(10)

The Estimation of Variances

268(3)

Hypotheses Concerning One Variance

271(1)

Hypotheses Concerning Two Variances

272(6)

Review Exercises

276(1)

Key Terms

277(1)

Inferences Concerning Proportions

278(23)

Estimation of Proportions

278(5)

Hypotheses Concerning One Proportion

283(2)

Hypotheses Concerning Several Proportions

285(7)

Analysis of r x c Tables

292(3)

Goodness of Fit

295(6)

Review Exercises

299(1)

Key Terms

300(1)

Regression Analysis

301(53)

The Method of Least Squares

301(8)

Inferences Based on the Least Squares Estimators

309(12)

Curvilinear Regression

321(5)

Multiple Regression

326(3)

Checking the Adequacy of the Model

329(6)

Correlation

335(10)

Multiple Linear Regression (Matrix Notations)

345(9)

Review Exercises

350(3)

Key Terms

353(1)

Analysis of Variance

354(37)

Some General Principles

354(3)

Completely Randomized Designs

357(13)

Randomized-Block Designs

370(7)

Multiple Comparisons

377(5)

Analysis of Covariance

382(9)

Review Exercises

388(2)

Key Terms

390(1)

Factorial Experimentation

391(56)

Two-Factor Experiments

391(7)

Multifactor Experiments

398(11)

2n Factorial Experiments

409(7)

The Graphic Presentation of 22 and 23 Experiments

416(14)

Response Surface Analysis

430(3)

Confounding in a 2n Factorial Experiment

433(4)

Fractional Replication

437(10)

Review Exercises

442(4)

Key Terms

446(1)

Nonparametric Tests

447(16)

Introduction

447(1)

The Sign Test

447(2)

Rank-Sum Tests

449(4)

Correlation Based on Ranks

453(2)

Tests of Randomness

455(3)

The Kolmogrov-Smirnov and Anderson-Darling Tests

458(5)

Review Exercises

461(1)

Key Terms

462(1)

The Statistical Content of Quality-Improvement Programs

463(24)

Quality-Improvement Programs

463(2)

Starting a Quality-Improvement Program

465(2)

Experimental Designs for Quality

467(2)

Quality Control

469(2)

Control Charts for Measurements

471(5)

Control Charts for Attributes

476(6)

Tolerance Limits

482(5)

Review Exericises

484(2)

Key Terms

486(1)

Application to Reliability and Life Testing

487(16)

Reliability

487(2)

Failure-Time Distribution

489(4)

The Exponential Model in Life Testing

493(3)

The Weibull Model in Life Testing

496(7)

Review Exercises

501(1)

Key Terms

502(1)

Appendix A Bibliography

503(1)

Appendix B Statistical Tables

504(24)

Appendix C Using the R Software Program

528(5)

Introduction to R

528(1)

Entering Data

528(1)

Arithmetic Operations

529(1)

Descriptive Statistics

529(1)

Probability Distributions

530(1)

Normal Probability Calculations

530(1)

Sampling Distributions

530(1)

Confidence Intervals and Tests of Means

531(1)

Inference about Proportions

531(1)

Regression

531(1)

One-Way Analysis of Variance (ANOVA)

532(1)

Appendix D Answers to odd-Numbered Exercises

533(7)

Index

540