Probability and Statistics for Engineers and Scientists

by Walpole, Ronald E.; Myers, Raymond H.; Myers, Sharon L.; Ye, Keying

• ISBN13: 9780130415295
• ISBN10: 0130415294
• Edition: 7th
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: PRENTICE HALL

Summary

This classic book provides a rigorous introduction to basic probability theory and statistical inference that is motivated by interesting, relevant applications. It assumes readers have a background in calculus, and offers a unique balance of theory and methodology.Chapter topics cover an introduction to statistics and data analysis, probability, random variables and probability distributions, mathematical expectation, some discrete probability distributions, some continuous probability distributions, functions of random variables, fundamental sampling distributions and data descriptions, one- and two-sample estimation problems, one- and two-sample tests of hypotheses, simple linear regression and correlation, multiple linear regression and certain nonlinear regression models, one factor experiments: general, factorial experiments (two or more factors), 2 k factorial experiments and fractions, nonparametric statistics, and statistical quality control.For individuals trying to apply statistical concepts to real-life, and analyze and interpret data.

Table of Contents

Preface	xiii
Introduction to Statistics and Data Analysis	1	(21)
Overview: Statistical Inference, Samples, Populations, and Experimental Design	1	(3)
The Role of Probability	4	(3)
Sampling Procedures; Collection of Data	7	(2)
Measures of Location: The Sample Mean	9	(2)
Measures of Variability	11	(3)
Discrete and Continuous Data	14	(1)
Statistical Modeling, Scientific Inspection, and Graphical Diagnostics	14	(2)
Graphical Methods and Data Description	16	(6)
Probability	22	(41)
Sample Space	22	(3)
Events	25	(6)
Counting Sample Points	31	(8)
Probability of an Event	39	(4)
Additive Rules	43	(4)
Conditional Probability	47	(3)
Multiplicative Rules	50	(7)
Bayes' Rule	57	(6)
Review Exercises	61	(2)
Random Variables and Probability Distributions	63	(25)
Concept of a Random Variable	63	(2)
Discrete Probability Distributions	65	(4)
Continuous Probability Distributions	69	(5)
Joint Probability Distributions	74	(14)
Review Exercises	86	(2)
Mathematical Expectation	88	(27)
Mean of a Random Variable	88	(7)
Variance and Covariance	95	(8)
Means and Variances of Linear Combinations of Random Variables	103	(7)
Chebyshev's Theorem	110	(5)
Review Exercises	114	(1)
Some Discrete Probability Distributions	115	(27)
Introduction	115	(1)
Discrete Uniform Distribution	116	(1)
Binomial and Multinomial Distributions	117	(9)
Hypergeometric Distribution	126	(6)
Negative Binomial and Geometric Distributions	132	(3)
Poisson Distribution and the Poisson Process	135	(7)
Review Exercises	140	(2)
Some Continuous Probability Distributions	142	(35)
Continuous Uniform Distribution	142	(1)
Normal Distribution	143	(4)
Areas Under the Normal Curve	147	(5)
Applications of the Normal Distribution	152	(6)
Normal Approximation to the Binomial	158	(7)
Gamma and Exponential Distributions	165	(3)
Applications of the Exponential and Gamma Distributions	168	(2)
Chi-Squared Distribution	170	(1)
Lognormal Distribution	171	(1)
Weibull Distribution	172	(5)
Review Exercises	175	(2)
Functions of Random Variables {Optional)	177	(17)
Introduction	177	(1)
Transformations of Variables	177	(9)
Moments and Moment-Generating Functions	186	(8)
Fundamental Sampling Distributions and Data Descriptions	194	(36)
Random Sampling	194	(3)
Some Important Statistics	197	(4)
Data Displays and Graphical Methods	201	(7)
Sampling Distributions	208	(1)
Sampling Distribution of Means	209	(7)
Sampling Distribution of S2	216	(3)
t-Distribution	219	(5)
F-Distribution	224	(6)
Review Exercises	228	(2)
One- and Two-Sample Estimation Problems	230	(54)
Introduction	230	(1)
Statistical Inference	230	(1)
Classical Methods of Estimation	231	(3)
Single Sample: Estimating the Mean	234	(6)
Standard Error of a Point Estimate	240	(1)
Prediction Interval	241	(2)
Tolerance Limits	243	(3)
Two Samples: Estimating the Difference Between Two Means	246	(7)
Paired Observations	253	(4)
Single Sample: Estimating a Proportion	257	(4)
Two Samples: Estimating the Difference Between Two Proportions	261	(3)
Single Sample: Estimating the Variance	264	(1)
Two Samples: Estimating the Ratio of Two Variances	265	(3)
Bayesian Methods of Estimation (Optional)	268	(7)
Maximum Likelihood Estimation (Optional)	275	(9)
Review Exercises	281	(3)
One- and Two-Sample Tests of Hypotheses	284	(66)
Statistical Hypotheses: General Concepts	284	(2)
Testing a Statistical Hypothesis	286	(8)
One- and Two-Tailed Tests	294	(1)
The Use of P-Values for Decision Making	295	(5)
Single Sample: Tests Concerning a Single Mean (Variance Known)	300	(3)
Relationship to Confidence Interval Estimation	303	(1)
Single Sample: Tests on a Single Mean (Variance Unknown)	304	(3)
Two Samples: Tests on Two Means	307	(5)
Choice of Sample Size for Testing Means	312	(4)
Graphical Methods for Comparing Means	316	(7)
One Sample: Test on a Single Proportion	323	(3)
Two Samples: Tests on Two Proportions	326	(2)
One- and Two-Sample Tests Concerning Variances	328	(5)
Goodness-of-Fit Test	333	(3)
Test for Independence (Categorical Data)	336	(3)
Test for Homogeneity	339	(1)
Testing for Several Proportions	340	(2)
Two-Sample Case Study	342	(8)
Review Exercises	347	(3)
Simple Linear Regression and Correlation	350	(50)
Introduction to Linear Regression	350	(1)
Simple Linear Regression	351	(4)
Least Squares and The Fitted Model	355	(5)
Properties of the Least Squares Estimators	360	(3)
Inferences Concerning the Regression Coefficients	363	(5)
Prediction	368	(4)
Choice of a Regression Model	372	(1)
Analysis-of-Variance Approach	373	(2)
Test for Linearity of Regression: Data with Repeated Observations	375	(8)
Data Plots and Transformations	383	(4)
Simple Linear Regression Case Study	387	(3)
Correlation	390	(10)
Review Exercises	396	(4)
Multiple Linear Regression and Certain Nonlinear Regression Models	400	(61)
Introduction	400	(1)
Estimating the Coefficients	401	(3)
Linear Regression Model Using Matrices (Optional)	404	(7)
Properties of the Least Squares Estimators	411	(2)
Inferences in Multiple Linear Regression	413	(7)
Choice of a Fitted Model Through Hypothesis Testing	420	(3)
Special Case of Orthogonality (Optional)	423	(4)
Categorical or Indicator Variables	427	(5)
Sequential Methods for Model Selection	432	(6)
Study of Residuals and Violation of Assumptions	438	(4)
Cross Validation, Cp, and Other Criteria for Model Selection	442	(10)
Special Nonlinear Models for Nonideal Conditions	452	(9)
Review Exercises	456	(5)
One-Factor Experiments: General	461	(58)
Analysis-of-Variance Technique	461	(2)
The Strategy of Experimental Design	463	(1)
One-Way Analysis of Variance: Completely Randomized Design	463	(6)
Tests for the Equality Of Several Variances	469	(4)
Single-Degree-of-Freedom Comparisons	473	(4)
Multiple Comparisons	477	(4)
Comparing Treatments with a Control	481	(5)
Comparing a Set of Treatments in Blocks	486	(1)
Randomized Complete Block Designs	487	(7)
Graphical Methods and Further Diagnostics	494	(2)
Latin Squares (Optional)	496	(6)
Random Effects Models	502	(5)
Power of Analysis-of-Variance Tests	507	(4)
Case Study	511	(8)
Review Exercises	515	(4)
Factorial Experiments (Two or More Factors)	519	(36)
Introduction	519	(2)
Interaction and the Two-Factor Experiment	521	(1)
Two-Factor Analysis of Variance	522	(8)
Graphical Analysis in the Two-Factor Problem	530	(5)
Three-Factor Experiments	535	(10)
Model II and III Factorial Experiments	545	(4)
Choice of Sample Size	549	(6)
Review Exercises	552	(3)
2k Factorial Experiments and Fractions	555	(45)
Introduction	555	(1)
Analysis of Variance and the Calculation of Effects	556	(4)
Nonreplicated 2k Factorial Experiment	560	(1)
Injection Molding Case Study	561	(6)
Factorial Experiments in Incomplete Blocks	567	(5)
Partial Confounding	572	(3)
Factorial Experiments in a Regression Setting	575	(4)
The Orthogonal Design	579	(3)
Fractional Factorial Experiments	582	(3)
Analysis of Fractional Factorial Experiments	585	(4)
Higher Fractions and Screening Designs	589	(1)
Construction of Resolution III and IV Designs with 8,16, and 32 Design Points	590	(1)
Other Two-Level Resolution III Designs; The Plackett-Burman Designs	591	(1)
Taguchi's Robust Parameter Design	592	(8)
Review Exercises	598	(2)
Nonparametric Statistics	600	(25)
Nonparametric Tests	600	(1)
Sign Test	601	(4)
Signed-Rank Test	605	(5)
Rank-Sum Test	610	(3)
Kruskal-Wallis Test	613	(3)
Runs Test	616	(3)
Tolerance Limits	619	(1)
Rank Correlation Coefficient	620	(5)
Review Exercises	624	(1)
Statistical Quality Control	625	(31)
Introduction	625	(2)
Nature of the Control Limits	627	(1)
Purposes of the Control Chart	627	(1)
Control Charts for Variables	628	(15)
Control Charts for Attributes	643	(6)
Cusum Control Charts	649	(7)
Review Exercises	653	(3)
Bibliography	656	(3)
Appendix: Statistical Tables and Proofs	659	(56)
Answers to Odd-Numbered Exercises	715	(11)
Index	726

Excerpts

Goals, Approach and Mathematical Level The seventh edition emphasizes and illustrates the use of probabilistic models and statistical methodology that is employed in countless applications in all areas of science and engineering. There remains an important balance between theory and methodology that is featured in the text. We do not avoid the use of some theory but our goal is to let the mathematics provide insight rather than be a distraction. We feel that engineers and scientists are trained in mathematics and thus the providing of mathematical support when needed keeps the pedagogy from becoming a series of illustrated recipes in which the concepts are not understood and could never be applied or extended by the student except within very narrow bounds. The text contains an abundance of exercises in which the methodology discussed is illustrated by the use of real-life scientific scenarios and data sets. The complete set of data files which accompany the text are available for download from the text companion website, located at http://www.prenhall.com/walpole . Though we attempt to appeal to engineers, the exercises are not confined to engineering applications. The student is exposed to problems encountered in many sciences including social sciences and biomedical applications. The motivation here stems from the fact that trained engineers are more and more becoming exposed to nontraditional settings, including areas like bioinformatics and bioengineering. While we do let calculus play an important role but it should be noted that its use is confined to elementary probability theory and properties of probability distributions (Chapters 3, 4, 6, and 7). In addition, a modest amount of matrix algebra is used to support the linear regression material in Chapters 11 and 12. This is despite the fact that an "optional" section appears in Chapter 11 that includes the development of the multiple linear regression model with more substantive use of matrices. The student who uses this text should have completed one semester or two quarters of differential and integral calculus. An exposure to matrix algebra would be helpful but not necessary if the course content excludes the aforementioned optional section. Content and Course Planning The text is designed for either a one or two semester course. A reasonable curriculum for a one semester course might include Chapters 1 through 10. One may even choose to teach an early portion of Chapter 11 in order to introduce the student to the concept of simple linear regression. Chapter 1 is an overview of statistical inference, sampling and data analysis. Indeed, some very rudimentary aspects of experimental design are included, along with an appreciation of graphics and certain vital characteristics of data collection. Chapters 2, 3, and 4 deal with basic probability and discrete and continuous random variables. Chapters 5 and 6 cover specific discrete and continuous distributions with illustrations of their use and relationships among them. Chapter 7 deals with transformations of random variables. This chapter is listed as "optional" and would only be covered in a more theoretical course. This chapter is clearly the most mathematical chapter in the text. Chapter 8 includes additional material on graphical methods as well as an introduction to the notion of a sampling distribution. ThetandFdistributions are introduced along with motivation regarding their use in chapters that follow. Chapters 9 and 10 contain material on one and two sample point and interval estimation and hypothesis testing. The flexibility in a single semester course lies in the option of exclusion of Chapter 7 as well as teaching only a subset of the several specific discrete and continuous distributions discussed and illustrated in Chapters 5 and 6. There is additional flexibility involved in dealing with Chapter 9 where ma