Modern Mathematical Statistics with Applications (with CD-ROM),9780534404734

Modern Mathematical Statistics with Applications (with CD-ROM)

by ;
Edition: CD
ISBN13: 9780534404734
ISBN10: 0534404731
Format: Hardcover
Pub. Date: 2006-01-06
Publisher(s): Cengage Learning
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Summary

Many mathematical statistics texts are heavily oriented toward a rigorous mathematical development of probability and statistics, without emphasizing contemporary statistical practice. MODERN MATHEMATICAL STATISTICS WITH APPLICATIONS strikes a balance between mathematical foundations and statistical practice. Accomplished authors Jay Devore and Ken Berk first engage students with real-life problems and scenarios and then provide them with both foundational context and theory. This book follows the spirit of the Committee on the Undergraduate Program in Mathematics (CUPM) recommendation that every math student should study statistics and probability with an emphasis on data analysis.

Table of Contents

Preface viii
Overview and Descriptive Statistics
1(48)
Introduction
1(1)
Populations and Samples
2(7)
Pictorial and Tabular Methods in Descriptive Statistics
9(16)
Measures of Location
25(8)
Measures of Variability
33(16)
Probability
49(45)
Introduction
49(1)
Sample Spaces and Events
50(6)
Axioms, Interpretations, and Properties of Probability
56(9)
Counting Techniques
65(8)
Conditional Probability
73(10)
Independence
83(11)
Discrete Random Variables and Probability Distributions
94(60)
Introduction
94(1)
Random Variables
95(4)
Probability Distributions for Discrete Random Variables
99(10)
Expected Values of Discrete Random Variables
109(9)
Moments and Moment Generating Functions
118(7)
The Binomial Probability Distribution
125(9)
*Hypergeometric and Negative Binomial Distributions
134(8)
*The Poisson Probability Distribution
142(12)
Continuous Random Variables and Probability Distributions
154(75)
Introduction
154(1)
Probability Density Functions and Cumulative Distribution Functions
155(12)
Expected Values and Moment Generating Functions
167(8)
The Normal Distribution
175(15)
*The Gamma Distribution and Its Relatives
190(8)
*Other Continuous Distributions
198(8)
*Probability Plots
206(10)
*Transformations of a Random Variable
216(13)
Joint Probability Distributions
229(49)
Introduction
229(1)
Jointly Distributed Random Variables
230(12)
Expected Values, Covariance, and Correlation
242(7)
*Conditional Distributions
249(13)
*Transformations of Random Variables
262(5)
*Order Statistics
267(11)
Statistics and Sampling Distributions
278(47)
Introduction
278(1)
Statistics and Their Distributions
279(12)
The Distribution of the Sample Mean
291(9)
The Distribution of a Linear Combination
300(9)
Distributions Based on a Normal Random Sample
309(16)
Appendix: Proof of the Central Limit Theorem
323(2)
Point Estimation
325(50)
Introduction
325(1)
General Concepts and Criteria
326(18)
*Methods of Point Estimation
344(11)
*Sufficiency
355(9)
*Information and Efficiency
364(11)
Statistical Intervals Based on a Single Sample
375(42)
Introduction
375(1)
Basic Properties of Confidence Intervals
376(9)
Large-Sample Confidence Intervals for a Population Mean and Proportion
385(8)
Intervals Based on a Normal Population Distribution
393(8)
*Confidence Intervals for the Variance and Standard Deviation of a Normal Population
401(3)
*Bootstrap Confidence Intervals
404(13)
Tests of Hypotheses Based on a Single Sample
417(55)
Introduction
417(1)
Hypotheses and Test Procedures
418(10)
Tests About a Population Mean
428(14)
Tests Concerning a Population Proportion
442(6)
P-Values
448(8)
*Some Comments on Selecting a Test Procedure
456(16)
Inferences Based on Two Samples
472(67)
Introduction
472(1)
z Tests and Confidence Intervals for a Difference Between Two Population Means
473(14)
The Two-Sample t Test and Confidence Interval
487(10)
Analysis of Paired Data
497(10)
Inferences About Two Population Proportions
507(8)
*Inferences About Two Population Variances
515(5)
*Comparisons Using the Bootstrap and Permutation Methods
520(19)
The Analysis of Variance
539(60)
Introduction
539(1)
Single-Factor ANOVA
540(12)
*Multiple Comparisons in ANOVA
552(8)
*More on Single-Factor ANOVA
560(10)
*Two-Factor ANOVA with Kij = 1
570(14)
*Two-Factor ANOVA with Kij > 1
584(15)
Regression and Correlation
599(108)
Introduction
599(1)
The Simple Linear and Logistic Regression Models
600(11)
Estimating Model Parameters
611(15)
Inferences About the Regression Coefficient β1
626(14)
Inferences Concerning μγ, x* and the Prediction of Future Y Values
640(8)
Correlation
648(12)
*Aptness of the Model and Model Checking
660(8)
*Multiple Regression Analysis
668(21)
*Regression with Matrices
689(18)
Goodness-of-Fit Tests and Categorical Data Analysis
707(36)
Introduction
707(1)
Goodness-of-Fit Tests When Category Probabilities Are Completely Specified
708(8)
*Goodness-of-Fit Tests for Composite Hypotheses
716(13)
Two-Way Contingency Tables
729(14)
Alternative Approaches to Inference
743(38)
Introduction
743(1)
*The Wilcoxon Signed-Rank Test
744(8)
*The Wilcoxon Rank-Sum Test
752(5)
*Distribution-Free Confidence Intervals
757(5)
*Bayesian Methods
762(8)
*Sequential Methods
770(11)
Appendix Tables
781(28)
A.1 Cumulative Binomial Probabilities
782(2)
A.2 Cumulative Poisson Probabilities
784(2)
A.3 Standard Normal Curve Areas
786(2)
A.4 The Incomplete Gamma Function
788(1)
A.5 Critical Values for t Distributions
789(1)
A.6 Tolerance Critical Values for Normal Population Distributions
790(1)
A.7 Critical Values for Chi-Squared Distributions
791(1)
A.8 t Curve Tail Areas
792(2)
A.9 Critical Values for F Distributions
794(6)
A.10 Critical Values for Studentized Range Distributions
800(1)
A.11 Chi-Squared Curve Tail Areas
801(2)
A.12 Critical Values for the Ryan--Joiner Test of Normality
803(1)
A.13 Critical Values for the Wilcoxon Signed-Rank Test
804(1)
A.14 Critical Values for the Wilcoxon Rank-Sum Test
805(1)
A.15 Critical Values for the Wilcoxon Signed-Rank Interval
806(1)
A.16 Critical Values for the Wilcoxon Rank-Sum Interval
807(1)
A.17 β Curves for t Tests
808(1)
Answers to Odd-Numbered Exercises 809(20)
Index 829

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