Statistics

• Standard statistical techniques are presented in a mathematical context – Allows students to see the underlying hypotheses for the applications.

• Superior treatment of real-world data – 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.

• Numerous and interesting homework exercises – Chosen to engage the student and illuminate the main points of the text.

• Lively writing style – Presents concepts and applications in an engaging narrative.

• Sound coverage of the theoretical aspects of mathematical statistics - Carefully explains the mathematics and development of the statistical theory.

• Accessible mathematical prerequisites – Mediates between a techniques book and a graduate level first course in mathematical statistics.

• Integrated review of calculus – Reinforces students’ prior knowledge by reviewing calculus as necessary throughout the presentation.

• New “Odds and Ends” section at the end of each chapter – Discusses practical problems in the application of the ideas covered in the chapter, as well as common misunderstandings or faulty approaches.

• Streamlined material throughout – Updated based on user feedback, making the length of the text appropriate for a one-semester mathematical statistics course while maintaining its mathematical integrity.

• Reorganized and rewritten Chs. 2 and 3 – Better emphasize important concepts, making the chapters much more teachable for instructors.

• Updated presentation of estimation (Ch. 5) – Includes consistency of notation, strengthened terminology, and improved coverage of sufficiency (Section 5.6).

• Reorganized material on the normal distribution (Ch. 7) – Improved division between theoretical results and their applications, plus a more accessible derivation of the chi-square distribution.

• Revised Minitab sections – Now conform to Version 14, the latest release of Minitab.

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 H 0: 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.

Mathematical Statistics  (Statistics)

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Larsen
©2006 | Pearson | On-line Supplement | Instock
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Student Solutions Manual, 4/E
Larsen
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