MODERN MATHEMATICAL STATISTICSW/APPLICATIONS/CD - Hardcover

Devore, Jay; Berk, Kenneth

Hardcover

ISBN 10: 0534404731 ISBN 13: 9780534404734

Publisher: Duxbury Press, 2006

Synopsis

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.

About this title

Review

1.OVERVIEW AND DESCRIPTIVE STATISTICS. Introduction. Populations, Samples, and Processes. Pictorial and Tabular Methods in Descriptive Statistics. Measures of Location. Measures of Variability. 2.PROBABILITY. Introduction. Sample Spaces and Events. Axioms, Interpretations, and Properties of Probability. Counting Techniques. Conditional Probability. Independence. 3.DISCRETE RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Introduction. Random Variables. Probability Distributions for Discrete Random Variables. Expected Values of Discrete Random Variables. Moments and Moment Generating Functions. The Binomial Probability Distribution. The Hypergeometric and Negative Binomial Distributions. The Poisson Probability Distribution. 4.CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Introduction. Probability Density Functions and Cumulative Distribution Functions. Expected Values and Moment Generating Functions. The Normal Distribution. The Gamma Distribution and Its Relatives. Other Continuous Distributions. Probability Plots. Transformations of a Random Variable. 5.JOINT PROBABILITY DISTRIBUTIONS. Introduction. Jointly Distributed Random Variables. Expected Values, Covariance, and Correlation. Conditional Distributions. Transformations of Random Variables. Order Statistics. 6.STATISTICS AND SAMPLING DISTRIBUTIONS. Introduction. Statistics and Their Distributions. The Distribution of the Sample Mean. The Distribution of a Linear Combination. Distributions Based on a Normal Random Sample. Appendix. 7.POINT ESTIMATION. Introduction. Some General Concepts of Point Estimation. Methods of Point Estimation. Sufficiency. Information and Efficiency. 8.STATISTICAL INTERVALS BASED ON A SINGLE SAMPLE. Introduction. Basic Properties of Confidence Intervals. Large-Sample Confidence Intervals for a Population Mean and Proportion. Intervals Based on a Normal Population Distribution. Confidence Intervals for the Variance and Standard Deviation of a Normal Population. Bootstrap Confidence Intervals. 9.TESTS OF HYPOTHESES BASED ON A SINGLE SAMPLE. Introduction. Hypotheses and Test Procedures. Tests About a Population Mean. Tests Concerning a Population Proportion. P-Values. Some Comments on Selecting a Test Procedure. 10.INFERENCES BASED ON TWO SAMPLES. Introduction. z Tests and Confidence Intervals for a Difference between Two Population Means. The Two-Sample t Test and Confidence Interval. Analysis of Paired Data. Inferences about Two Population Proportions. Inferences about Two Population Variances. Comparisons Using the Bootstrap and Permutation Methods. 11.THE ANALYSIS OF VARIANCE. Introduction. Single-Factor ANOVA. Multiple Comparisons in ANOVA. More on Single-Factor ANOVA. Two-Factor ANOVA with Kij = 1. Two-Factor ANOVA with Kij > 1. 12.REGRESSION AND CORRELATION. Introduction. The Simple Linear and Logistic Regression Models. Estimating Model Parameters. Inferences about the Regression Coefficient ?O1?|?n Inferences Concerning ?YY?x*?n and the Prediction of Future Y Values. Correlation. Aptness of the Model and Model Checking. Multiple Regression Analysis. Regression with Matrices. 13.GOODNESS-OF-FIT TESTS AND CATEGORICAL DATA ANALYSIS. Introduction. Goodness-of-Fit Tests When Category Probabilities Are Completely Specified. Goodness-of-Fit Tests for Composite Hypotheses. Two-Way Contingency Tables. 14.ALTERNATIVE APPROACHES TO INFERENCE. Introduction. The Wilcoxon Signed-Rank Test. The Wilcoxon Rank-Sum Test. Distribution-Free Confidence Intervals. Bayesian Methods. Sequential Methods.

From the Back Cover

Many mathematical statistics texts are heavily oriented toward a rigorous mathematical development of probability and statistics, without much attention paid to how statistics is actually used.. In contrast, Modern Mathematical Statistics with Applications, Second Edition strikes a balance between mathematical foundations and statistical practice. In keeping with the recommendation that every math student should study statistics and probability with an emphasis on data analysis, accomplished authors Jay Devore and Kenneth Berk make statistical concepts and methods clear and relevant through careful explanations and a broad range of applications involving real data.

 

The main focus of the book is on presenting and illustrating methods of inferential statistics that are useful in research.  It begins with a chapter on descriptive statistics that immediately exposes the reader to real data.  The next six chapters develop the probability material that bridges the gap between descriptive and inferential statistics.  Point estimation, inferences based on statistical intervals, and hypothesis testing are then introduced in the next three chapters.  The remainder of the book explores the use of this methodology in a variety of more complex settings.

 

This edition includes a plethora of new exercises, a number of which are similar to what would be encountered on the actuarial exams that cover probability and statistics. Representative applications include investigating whether the average tip percentage in a particular restaurant exceeds the standard 15%, considering whether the flavor and aroma of Champagne are affected by bottle temperature or type of pour, modeling the relationship between college graduation rate and average SAT score, and assessing the likelihood of O-ring failure in space shuttle launches as related to launch temperature.

 

Other features include:

- An extensive range of applications that will appeal to a wide audience, including mathematics and statistics majors, prospective engineers and scientists, and business, economics, and quantitative social science students.

- Nearly 1,500 exercises to help students master the material and better understand sophisticated concepts and arguments.

- An emphasis on the importance of statistical software, including output from the statistical software packages Minitab, R, and SAS.

Edition details

• Publisher: Duxbury Press
• Publication date: 2006
• ISBN 10: 0534404731
• ISBN 13: 9780534404734
• Binding: Hardcover
• Language: English
• Number of pages: 848