An Introduction to Mathematical Statistics and Its Applications / Edition 3

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Overview

Noted for its integration of real-world data and case studies, this guide offers sound coverage of the theoretical aspects of mathematical statistics. It demonstrates how and when to use statistical methods, while reinforcing the calculus that readers have already mastered. Presents standard statistical techniques in a mathematical context, allowing the reader to see the underlying hypotheses for the applications. Uses case studies and practical worked-out examples to motivate statistical reasoning and demonstrate the application of statistical methods to a wide variety of real-world situations. Discusses practical problems in the application of the ideas covered in each chapter, as well as common misunderstandings or faulty approaches. Revised Minitab sections now conform to the Version 14, the latest release. For anyone interested in learning more about mathematical statistics.
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Product Details

  • ISBN-13: 9780139223037
  • Publisher: Pearson
  • Publication date: 6/7/2000
  • Edition description: Older Edition
  • Edition number: 3
  • Pages: 790
  • Product dimensions: 7.29 (w) x 9.59 (h) x 1.50 (d)

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PREFACE:

Preface

Changes in this third edition have been primarily motivated by our own teaching experiences as well as by the comments of others who use the text. Technology, though, has also dictated certain revisions. The widespread use of statistical software packages has brought certain topics and concepts to the fore, while diminishing the relevance of others. All in all, we feel that this new edition has a sharper focus and that students will find it more accessible and easier to use.

Many of the major changes come in the middle third of the book, much of which has been rewritten. These are the chapters that make the critical transition from probability to statistics. We have taken a variety of steps to make that material come more alive, ranging from the addition of more helpful examples to the frequent use of computer simulations.

Chapter 4, for example, now addresses more fully the important question of why certain measurements are modeled by particular probability functions. Relationships that exist between pdfs are given more attention, and the connection between theoretical models and sample data is explored in greater depth. Chapter 5 has been restructured. In the new edition, methods of estimation come first and the underlying theory is taken up last. That arrangement makes it easier for instructors to adjust the amount of time spent on estimation to whatever suits their individual needs. In Chapter 6, the principles of decision-making are now introduced in the context of testing Ho: µ = µo rather than Ho: p = po. The result is a more streamlined presentation thatavoids the complications inherent in a test statistic whose pdf is discrete.

Positioned between Chapter 7, which deals with the normal distribution, and Chapters 9 through 14, where the various techniques for analyzing data are introduced, is a new chapter on experimental design. Chapter 8 profiles seven of the most frequently encountered "data models." The basic characteristics of each design are discussed as well as the types of questions each seeks to answer. By providing a framework and a theme, Chapter 8 brings cohesion and a sense of order to the chapters that follow.

Chapter 11 (Regression) has also been changed substantially. It now begins with curve-fitting, then introduces the linear model, and eventually concludes with the bivariate normal. Regression "diagnostics" have been added to the new edition, and the various inference procedures associated with the linear model have been explained and delineated more carefully.

Our overriding motivation in deciding which topics to present – and in what order – stem from our objective to write a book that emphasizes the interrelation between probability theory, mathematical statistics, and data analysis. We believe that integrating all three is vitally important, particularly for those students who take only one statistics course during their college careers. Our experience in the classroom has certainly strengthened our faith in this approach: Students can more clearly see the importance of each of the three when viewed in the context of the other two.

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Table of Contents


1. Introduction.
A Brief History. Some Examples. A Chapter Summary.
2. Probability.
Sample Spaces and the Algebra of Sets. The Probability Function. Conditional Probability. Independence. Combinatorics. Combinatorial Probability.
3. Random Variables.
Binomial and Hypergeometric Probabilities. Discrete Random Variables. Continuous Random Variables. Expected Values. The Variance. Joint Densities. Combining Random Variables. Further Properties of the Mean and Variance. Order Statistics. Conditional Densities. Moment Generating Functions. Odds and Ends.
4. Special Distributions.
The Poisson Distribution. The Normal Distribution. The Geometric Distribution. The Negative Binomial Distribution. The Gamma Distribution. Appendix 4.A.1: MINITAB Applications. Appendix 4.A.2: A Proof of the Central Limit Theorem.
5. Estimation.
Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments. Interval Estimation. Properties of Estimators. Minimum-Variance Estimators: The Cramer-Rao Lower Bound. Sufficiency. Consistency. Appendix 5.A.1: MINITAB Applications.
6. Hypothesis Testing.
The Decision Rule. Testing Binomial Data-H0: p = p 0. Type I and Type II Errors. A Notion of Optimality: The Generalized Likelihood Ratio.
7. The Normal Distribution.
Comparing and . Deriving the distribution of . Drawing inferences about m. Drawing inferences about . Odds and Ends.
8. Types of Data: A Brief Overview.
Classifying Data.
9. Two-Sample Problems.
Testing H 0: …mx = …mY-The Two-Sample t Test. Testing H0: …s2x = …s2Y-The F Test. Binomial Data: Testing H0: px = py. Confidence Intervals for the Two-Sample Problem. Appendix 9.A.1: A Derivation of the Two-Sample t Test (A Proof of Theorem 9.2.2.). Appendix 9.A.2: Power Calculations for a Two-Sample t Test. Appendix 9.A.3: MINITAB Applications.
10. Goodness-of-Fit Tests.
The Multinomial Distribution. Goodness-of-Fit Tests: All Parameters Known. Goodness-of-Fit Tests: Parameters Unknown. Contingency Tables. Appendix 10.A.1: MINITAB Applications.
11. Regression.
The Method of Least Squares. The Linear Model. Covariance and Correlation. The Bivariate Normal Distribution. Appendix 11.A.1: MINITAB Applications. Appendix 11.A.2: A Proof of Theorem 11.3.3.
12. The Analysis of Variance.
The F Test. Multiple Comparisons: Tukey's Method. Testing Subhypotheses with Orthogonal Contrasts. Data Transformations. Appendix 12.A.1: MINITAB Applications. Appendix 12.A.2: A Proof of Theorem 12.2.2. Appendix 12.A.3: The Distribution of <$E{ down 12 SSTR/ up 12 (k-1)} over { down 12 SSE/ up 12 (n-k)}> When H1 Is True.
13. Randomized Block Designs.
The F Test for a Randomized Block Design. The Paired t Test. Appendix 13.A.1: MINITAB Applications.
14. Nonparametric Statistics.
The Sign Test. The Wilcoxon Signed Rank Test. The Kruskal-Wallis Test. The Friedman Test. Appendix 14.A.1: MINITAB Applications.
Appendix: Statistical Tables.
Answers to Selected Odd-Numbered Questions.
Bibliography.
Index.
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Preface

PREFACE:

Preface

Changes in this third edition have been primarily motivated by our own teaching experiences as well as by the comments of others who use the text. Technology, though, has also dictated certain revisions. The widespread use of statistical software packages has brought certain topics and concepts to the fore, while diminishing the relevance of others. All in all, we feel that this new edition has a sharper focus and that students will find it more accessible and easier to use.

Many of the major changes come in the middle third of the book, much of which has been rewritten. These are the chapters that make the critical transition from probability to statistics. We have taken a variety of steps to make that material come more alive, ranging from the addition of more helpful examples to the frequent use of computer simulations.

Chapter 4, for example, now addresses more fully the important question of why certain measurements are modeled by particular probability functions. Relationships that exist between pdfs are given more attention, and the connection between theoretical models and sample data is explored in greater depth. Chapter 5 has been restructured. In the new edition, methods of estimation come first and the underlying theory is taken up last. That arrangement makes it easier for instructors to adjust the amount of time spent on estimation to whatever suits their individual needs. In Chapter 6, the principles of decision-making are now introduced in the context of testing Ho: µ = µo rather than Ho: p = po. The result is a more streamlined presentationthatavoids the complications inherent in a test statistic whose pdf is discrete.

Positioned between Chapter 7, which deals with the normal distribution, and Chapters 9 through 14, where the various techniques for analyzing data are introduced, is a new chapter on experimental design. Chapter 8 profiles seven of the most frequently encountered "data models." The basic characteristics of each design are discussed as well as the types of questions each seeks to answer. By providing a framework and a theme, Chapter 8 brings cohesion and a sense of order to the chapters that follow.

Chapter 11 (Regression) has also been changed substantially. It now begins with curve-fitting, then introduces the linear model, and eventually concludes with the bivariate normal. Regression "diagnostics" have been added to the new edition, and the various inference procedures associated with the linear model have been explained and delineated more carefully.

Our overriding motivation in deciding which topics to present – and in what order – stem from our objective to write a book that emphasizes the interrelation between probability theory, mathematical statistics, and data analysis. We believe that integrating all three is vitally important, particularly for those students who take only one statistics course during their college careers. Our experience in the classroom has certainly strengthened our faith in this approach: Students can more clearly see the importance of each of the three when viewed in the context of the other two.

Read More Show Less

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  • Anonymous

    Posted December 4, 2001

    A great into. to probability and statistics.

    This text strikes a perfect balance between mathematical rigor and conceptual understanding. A perfect text for a math/science student at the intermediate level.

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