Statistics for Engineering and the Sciences

by Mendenhall, William; Sincich, Terry

• ISBN13: 9780131877061
• ISBN10: 0131877062
• Edition: 5th
• Format: Paperback
• Copyright: 2006-07-13
• Publisher: Pearson

Summary

This text is designed for a two-semester introductory course in statistics for students majoring in engineering or any of the physical sciences. Inevitably, once these students graduate and are employed, they will be involved in the collection and analysis of data and will be required to think critically about the results. Consequently, they need to acquire knowledge of the basic concepts of data description and statistical inference and familiarity with statistical methods they are required to use on the job.

Table of Contents

Preface	ix
Introduction	1	(11)
Statistics: The Science of Data	2	(1)
Fundamental Elements of Statistics	2	(3)
Types of Data	5	(2)
The Role of Statistics in Critical Thinking	7	(2)
A Guide to Statistical Methods Presented in This Text	9	(3)
Statistics In Action Contamination of Fish in the Tennessee River: Collecting the Data	10	(2)
Descriptive Statistics	12	(47)
Graphical and Numerical Methods for Describing Qualitative Data	13	(6)
Graphical Methods for Describing Quantitative Data	19	(8)
Numerical Methods for Describing Quantitative Data	27	(1)
Measures of Central Tendency	28	(4)
Measures of Variation	32	(6)
Measures of Relative Standing	38	(3)
Methods for Detecting Outliers	41	(4)
Distorting the Truth with Descriptive Statistics	45	(14)
Statistics in Action Characteristics of Contaminated Fish in the Tennessee River, Alabama	56	(3)
Probability	59	(58)
The Role of Probability in Statistics	60	(1)
Events, Sample Spaces, and Probability	60	(10)
Compound Events	70	(2)
Complementary Events	72	(4)
Conditional Probability	76	(4)
Probability Rules for Unions and Intersections	80	(10)
Bayes' Rule (Optional)	90	(3)
Some Counting Rules	93	(10)
Probability and Statistics: An Example	103	(2)
Random Sampling	105	(12)
Statistics in Action Assessing Predictors of Software Defects in NASA Spacecraft instrument Code	114	(3)
Discrete Random Variables	117	(51)
Discrete Random Variables	118	(1)
The Probability Distribution for a Discrete Random Variable	118	(5)
Expected Values for Random Variables	123	(4)
Some Useful Expectation Theorems	127	(2)
Bernoulli Trials	129	(1)
The Binomial Probability Distribution	130	(7)
The Multinomial Probability Distribution	137	(5)
The Negative Binomial and the Geometric Probability Distributions	142	(4)
The Hypergeometric Probability Distribution	146	(5)
The Poisson Probability Distribution	151	(6)
Moments and Moment Generating Functions (Optional)	157	(11)
Statistics in Action The Reliability of a ``One-Shot'' Device	165	(3)
Continuous Random Variables	168	(43)
Continuous Random Variables	169	(1)
The Density Function for a Continuous Random Variable	170	(2)
Expected Values for Continuous Random Variables	172	(5)
The Uniform Probability Distribution	177	(3)
The Normal Probability Distribution	180	(4)
Descriptive Methods for Assessing Normality	184	(6)
Gamma-Type Probability Distributions	190	(4)
The Weibull Probability Distribution	194	(3)
Beta-Type Probability Distributions	197	(3)
Moments and Moment Generating Functions (Optional)	200	(11)
Statistics in Action Super Weapons Development---Optimizing the Hit Ratio	206	(5)
Bivariate Probability Distributions and Sampling Distributions	211	(51)
Bivariate Probability Distributions for Discrete Random Variables	212	(5)
Bivariate Probability Distributions for Continuous Random Variables	217	(4)
The Expected Value of Functions of Two Random Variables	221	(2)
Independence	223	(2)
The Covariance and Correlation of Two Random Variables	225	(3)
Probability Distributions and Expected Values of Functions of Random Variables (Optional)	228	(8)
Sampling Distributions	236	(1)
Approximating a Sampling Distribution by Monte Carlo Simulation	237	(3)
The Sampling Distributions of Means and Sums	240	(5)
Normal Approximation to the Binomial Distribution	245	(3)
Sampling Distributions Related to the Normal Distribution	248	(14)
Statistics in Action Availability of an Up/Down Maintained System	259	(3)
Estimation Using Confidence Intervals	262	(73)
Point Estimators and their Properties	263	(4)
Finding Point Estimators: Classical Methods of Estimation	267	(7)
Finding Interval Estimators: The Pivotal Method	274	(7)
Estimation of a Population Mean	281	(6)
Estimation of the Difference Between Two Population Means: Independent Samples	287	(7)
Estimation of the Difference Between Two Population Means: Matched Pairs	294	(5)
Estimation of a Population Proportion	299	(3)
Estimation of the Difference Between Two Population Proportions	302	(3)
Estimation of a Population Variance	305	(4)
Estimation of the Ratio of Two Population Variances	309	(6)
Choosing the Sample Size	315	(3)
Alternative Interval Estimation Methods: Bootstrapping and Bayesian Methods (Optional)	318	(17)
Statistics in Action Bursting Strength of PET Beverage Bottles	332	(3)
Tests of Hypotheses	335	(65)
The Relationship Between Statistical Tests of Hypotheses and Confidence Intervals	336	(1)
Elements and Properties of a Statistical Test	336	(6)
Finding Statistical Tests: Classical Methods	342	(4)
Choosing the Null and Alternative Hypotheses	346	(2)
Testing a Population Mean	348	(6)
The Observed Significance Level for a Test	354	(3)
Testing the Difference Between Two Population Means: Independent Samples	357	(7)
Testing the Difference Between Two Population Means: Matched Pairs	364	(5)
Testing a Population Proportion	369	(3)
Testing the Difference Between Two Population Proportions	372	(4)
Testing a Population Variance	376	(3)
Testing the Ratio of Two Population Variances	379	(4)
Alternative Testing Procedures: Bootstrapping and Bayesian Methods (Optional)	383	(17)
Statistics in Action Comparing Methods for Dissolving Drug Tablets---Dissolution Method Equivalence Testing	395	(5)
Categorical Data Analysis	400	(39)
Categorical Data and Multinomial Probabilities	401	(1)
Estimating Category Probabilities in a One-Way Table	401	(4)
Testing Category Probabilities in a One-Way Table	405	(4)
Inferences About Category Probabilities in a Two-Way (Contingency) Table	409	(8)
Contingency Tables with Fixed Marginal Totals	417	(5)
Exact Tests for Independence in a Contingency Table Analysis (Optional)	422	(17)
Statistics in Action The Public's Perception of Engineers and Engineering	432	(7)
Simple Linear Regression	439	(56)
Regression Models	440	(1)
Model Assumptions	441	(2)
Estimating β0 and β1: The Method of Least Squares	443	(11)
Properties of the Least Squares Estimators	454	(2)
An Estimator of σ2	456	(4)
Assessing the Utility of the Model: Making Inferences About the Slope β1	460	(5)
The Coefficient of Correlation	465	(4)
The Coefficient of Determination	469	(4)
Using the Model for Estimation and Prediction	473	(7)
A Complete Example	480	(3)
A Summary of the Steps to Follow in Simple Linear Regression	483	(12)
Statistics in Action Can Dowsers Really Detect Water?	491	(4)
Multiple Regression Analysis	495	(88)
General Form of a Multiple Regression Model	496	(1)
Model Assumptions	497	(1)
Fitting the Model: The Method of Least Squares	498	(1)
Computations Using Matrix Algebra: Estimating and Making Inferences About the Individual β Parameters	499	(7)
Assessing Overall Model Adequacy	506	(4)
A Confidence Interval for E(y) and a Prediction Interval for a Future Value of y	510	(9)
A First-Order Model with Quantitative Predictors	519	(9)
An Interaction Model with Quantitative Predictors	528	(5)
A Quadratic (Second-Order) Model with a Quantitative Predictor	533	(7)
Checking Assumptions: Residual Analysis	540	(19)
Some Pitfalls: Estimability, Multicollinearity, and Extrapolation	559	(9)
A Summary of the Steps to Follow in a Multiple Regression Analysis	568	(15)
Statistics in Action Bid-Rigging in the Highway Construction Industry	575	(8)
Model Building	583	(65)
Introduction: Why Model Building Is Important	584	(1)
The Two Types of Independent Variables: Quantitative and Qualitative	585	(1)
Models with a Single Quantitative Independent Variable	586	(7)
Models with Two Quantitative Independent Variables	593	(7)
Coding Quantitative Independent Variables (Optional)	600	(5)
Models with One Qualitative Independent Variable	605	(6)
Models with Both Quantitative and Qualitative Independent Variables	611	(10)
Tests for Comparing Nested Models	621	(7)
External Model Validation (Optional)	628	(2)
Stepwise Regression	630	(18)
Statistics in Action Deregulation of the Intrastate Trucking Industry	640	(8)
Principles of Experimental Design	648	(23)
Introduction	649	(1)
Experimental Design Terminology	649	(2)
Controlling the Information in an Experiment	651	(1)
Noise-Reducing Designs	652	(6)
Volume-Increasing Designs	658	(5)
Selecting the Sample Size	663	(2)
The Importance of Randomization	665	(6)
Statistics in Action Anticorrosive Behavior of Epoxy Coatings Augmented with Zinc	668	(3)
The Analysis of Variance for Designed Experiments	671	(84)
Introduction	672	(1)
The Logic Behind an Analysis of Variance	672	(2)
One-Factor Completely Randomized Designs	674	(11)
Randomized Block Designs	685	(13)
Two-Factor Factorial Experiments	698	(16)
More Complex Factorial Designs (Optional)	714	(7)
Nested Sampling Designs (Optional)	721	(11)
Multiple Comparisons of Treatment Means	732	(7)
Checking ANOVA Assumptions	739	(16)
Statistics in Action On the Trail of the Cockroach	751	(4)
Nonparametric Statistics	755	(45)
Introduction: Distribution-Free Tests	756	(1)
Testing for Location of a Single Population	757	(5)
Comparing Two Populations: Independent Random Samples	762	(7)
Comparing Two Populations: Matched-Pairs Design	769	(6)
Comparing Three or More Populations: Completely Randomized Design	775	(5)
Comparing Three or More Populations: Randomized Block Design	780	(4)
Nonparametric Regression	784	(16)
Statistics in Action Deadly Exposure: Agent Orange and Vietnam Vets	796	(4)
Statistical Process and Quality Control	800	(57)
Total Quality Management	801	(1)
Variable Control Charts	801	(5)
Control Chart for Means: x-Chart	806	(8)
Control Chart for Process Variation: R-Chart	814	(5)
Detecting Trends in a Control Chart: Runs Analysis	819	(2)
Control Chart for Percent Defectives: p-Chart	821	(4)
Control Chart for the Number of Defectives per Item: c-Chart	825	(4)
Tolerance Limits	829	(3)
Capability Analysis (Optional)	832	(7)
Acceptance Sampling for Defectives	839	(5)
Other Sampling Plans (Optional)	844	(1)
Evolutionary Operations (Optional)	845	(12)
Statistics in Action Testing Jet Fuel Additive for Safety	851	(6)
Product and System Reliability	857	(25)
Introduction	858	(1)
Failure Time Distributions	858	(1)
Hazard Rates	859	(4)
Life Testing: Censored Sampling	863	(1)
Estimating the Parameters of an Exponential Failure Time Distribution	864	(3)
Estimating the Parameters of a Weibull Failure Time Distribution	867	(5)
System Reliability	872	(10)
Statistics in Action Modeling the Hazard Rate of Reinforced Concrete Bridge Deck Deterioration	879	(3)
Appendix A Matrix Algebra	882	(14)
Matrices and Matrix Multiplication	882	(4)
Identity Matrices and Matrix Inversion	886	(3)
Solving Systems of Simultaneous Linear Equations	889	(2)
A Procedure for Inverting a Matrix	891	(5)
Appendix B Useful Statistical Tables	896	(40)
Table 1 Random Numbers	897	(4)
Table 2 Cumulative Binomial Probabilities	901	(4)
Table 3 Exponentials	905	(1)
Table 4 Cumulative Poisson Probabilities	906	(2)
Table 5 Normal Curve Areas	908	(1)
Table 6 Gamma Function	909	(1)
Table 7 Critical Values for Student's T	910	(1)
Table 8 Critical Values of X2	911	(2)
Table 9 Percentage Points of the F Distribution, α = .10	913	(2)
Table 10 Percentage Points of the F Distribution, α = .05	915	(2)
Table 11 Percentage Points of the F Distribution, α = .025	917	(2)
Table 12 Percentage Points of the F Distribution, α = .01	919	(2)
Table 13 Percentage Points of the Studentized Range q (p, v), α = .05	921	(2)
Table 14 Percentage Points of the Studentized Range q (p, v), α = .01	923	(2)
Table 15 Critical Values of TL and TU for the Wilcoxon Rank Sum Test: Independent Samples	925	(1)
Table 16 Critical Values of T0 for the Wilcoxon Matched-Pairs Signed Rank Test	926	(1)
Table 17 Critical Values of Spearman's Rank Correlation Coefficient	927	(1)
Table 18 Critical Values of C for the Theil Zero-Slope Test	928	(4)
Table 19 Factors Used When Constructing Control Charts	932	(1)
Table 20 Values of K for Tolerance Limits for Normal Distributions	933	(1)
Table 21 Sample Size n for Nonparametric Tolerance Limits	934	(1)
Table 22 Sample Size Code Letters: MIL-STD-105D	934	(1)
Table 23 A Portion of the Master Table for Normal Inspection (Single Sampling): MIL-STD-105D	935	(1)
Appendix C SAS for Windows Tutorial	936	(29)
Appendix D MINITAB for Windows Tutorial	965	(33)
Appendix E SPSS for Windows Tutorial	998	(30)
References	1028	(8)
Selected Short Answers	1036	(13)
Credits	1049	(5)
Index	1054