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by Ronald E. Walpole, Raymond H. Myers and Sharon L. Myers

Edition: 6TH 98Copyright: 1998

Publisher: Prentice Hall, Inc.

Published: 1998

International: No

Ronald E. Walpole, Raymond H. Myers and Sharon L. Myers

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This classic text provides a rigorous introduction to basic probability theory and statistical inference that is well motivated by interesting, relevant applications. The new edition features many new, real-data based exercises and examples. Increased emphasis on the analysis of statistical output and greater use of graphical techniques and statistical methods in quality improvement make the 6th edition more useful for today's students.

Flexible organization makes the text appropriate for use in a one or two term course.

Praised for the quality and accuracy of the exercise sets, the authors use a spiraling technique which reintroduces exercises and examples seen previously so that students may apply their growing knowledge of statistics to a familiar problem and data set.

Complete case studies are presented in material dealing with two-sample inference, one-and two-factor analysis of variance, multifactor analysis of variance, and the analysis of 2^k factorial experiments.

NEW--Greater than 20% of the exercises and examples have been updated with new real data.

The standard, boring cards and "balls and urns" examples in the probability chapters have largely been replaced with exercises addressing the scientific aspects of everyday life.

Many new exercises and applications of the poisson, binomial, geometric, hypergeometric, and gamma distributions have been introduced.

NEW--The coverage of maximum likelihood has been expanded to include many new exercises and examples. New material using linear models with matrix development has been added to the coverage of "Analysis of Variance in Regression."

NEW--The book has been redesigned to insure that each figure is presented in closer proximity to the example it illustrates to eliminate the need to flip back and forth between pages in the book. The Answer Appendix now includes answers to the odd exercises only.

NEW--Recognizing the importance of the computer in data analysis, many new SAS and Minitab printouts have been added to the book in numerous chapters including those dealing with two samples (Chs. 9, 10), simple linear regression (Ch. 11), multiple regression (Ch. 12), one factor experiments (Ch. 13), two level factorial (Ch. 14)and fractional factorial experiments (Ch 15).

NEW--In addition some exercises are presented as Case Studies in which a computer printout is presented from which the student is asked to draw conclusions. These exercises refine the students ability to draw conclusions from data and interpret summary results in the most meaningful way.

*(NOTE: Most chapters conclude with Review Exercises.)*

**1. Introduction to Statistics and Data Analysis.**

Overview. The Role of Probability. Measures of Location: The Sample Mean and Median. Measures of Variability. Discrete and Continuous Data. Statistical Modeling, Scientific Inspection, and Graphical Diagnostics.

**2. Probability.**

Sample Space. Events. Counting Sample Points. Probability of an Event. Additive Rules. Conditional Probability. Multiplicative Rules. Bayes' Rule.

**3. Random Variables and Probability Distributions.**

Concept of a Random Variable. Discrete Probability Distributions. Continuous Probability Distributions. Empirical Distributions. Joint Probability Distributions.

**4. Mathematical Expectation.**

Mean of a Random Variable. Variance and Covariance. Means and Variances of Linear Combinations of Random Variables. Chebyshev's Theorem.

**5. Some Discrete Probability Distributions.**

Introduction. Discrete Uniform Distribution. Binomial and Multinomial Distribution. Hypergeometric Distribution. Negative Binomial and Geometric Distributions. Poisson Distribution and the Poisson Process.

**6. Some Continuous Probability Distributions.**

Continuous Probability Distribution. Normal Distribution. Areas Under the Normal Curve. Applications of the Normal Distribution. Normal Approximation to the Binomial. Gamma and Exponential Distributions. Applications of the Exponential and Gamma Distributions. Chi-Squared Distribution. Lognormal Distribution. Weibull Distribution.

**7. Functions of Random Variables.**

Introduction. Transformation of Variables. Moments and Moment-Generating Functions.

**8. Random Sampling, Data Description, and Some Fundamental Sampling Distributions.**

Random Sampling. Some Important Statistics. Data Displays and Graphical Methods. Sampling Distribution. Sampling Distributions of Means. Sampling Distribution of S^2. t-Distribution. F-Distribution.

**9. One- and Two-Sample Estimation Problems.**

Introduction. Statistical Inference. Classical Methods of Estimation. Single Sample: Estimating the Mean. Standard Error of a Point Estimate. Tolerance Limits. Two Samples: Estimating the Difference Between Two Means. Paired Observations. Single Sample: Estimating a Proportion. Two Samples: Estimating the Difference Between Two Proportions. Single Sample: Estimating the Variance. Two Samples: Estimating the Ratio of Two Variances. Bayesian Methods of Estimation. Maximum Likelihood Estimation.

**10. One- and Two- Sample Tests of Hypotheses (Continuous and Discrete Data).**

Statistical Hypotheses: General Concepts. Testing a Statistical Hypothesis. One- and Two-Tailed Tests. The Use of P- Values in Decision Making. Single Sample: Tests Concerning a Single Mean (Variance Known). Relationship to Confidence Interval Estimation. Single Sample: Tests on a Single Mean (Variance Unknown). Two Samples: Tests on Two Means. Choice of Sample Size for Testing Means. Graphical Methods for Comparing Means. One Sample: Test on a Single Proportion. Two Samples: Tests on Two Proportions. One- and Two-Sample Tests Concerning Variances. Goodness-of-Fit Test. Test for Independence (Categorical Data). Test for Homogeneity. Testing for Several Proportions. Two-Sample Case Study.

**11. Simple Linear Regression and Correlation.**

Introduction to Linear Regression. Simple Linear Regression. Properties of the Least Squares Estimators. Inferences Concerning the Regression Coefficients. Prediction. Choice of a Regression Model. Analysis-of Variance Approach. Test for Linearity of Regression: Data with Repeated Observations. Data Plots and Transformations. Simple Linear Regression Case Study. Correlation.

**12. Multiple Linear Regression.**

Introduction. Estimating the Coefficients. Linear Regression Model Using Matrices. Properties of the Least Squares Estimators. Inferences in Multiple Linear Regression. Choice of a Fitted Model Through Hypothesis Testing. Special Case of Orthogonality. Sequential Methods for Model Selection. Study of Residuals and Violation of Assumptions. Cross Validation, Cp, and Other Criteria for Model Selection.

**13. One-Factor Experiments: General.**

Analysis-of-Variance Technique. The Strategy of Experimental Design. One-Way Analysis of Variance: Completely Randomized Design. Tests for the Equality of Several Variances. Single-Degree-of-Freedom Comparisons. Multiple Comparisons. Comparing Treatments with a Control. Comparing a Set of Treatments in Blocks. Randomized Complete Block Designs. Graphical Methods and Further Diagnostics. Latin Squares. Random Effects Models. Regression Approach to Analysis of Variance. Power of Analysis-of-Variance Tests. Case Study.

**14. Factorial Experiments.**

Introduction. Interaction and the Two-Factor Experiment. Two-Factor Analysis of Variance. Graphical Analysis in the Two-Factor Problem. Three-Factor Experiments. Specific Multifactor Models. MODEL II and III Factorial Experiments. Choice of Sample Size.

**15. 2^k Factorial Experiments and Fractions.**

Introduction. Analysis of Variance. Nonreplicated 2^k Factorial Experiment. Case Study. Factorial Experiments in Incomplete Blocks. Partial Confounding. Factorial Experiments in a Regression Setting. Case Study: Coal Cleansing Experiment. Fractional Factorial Experiments. Analysis of Fractional Factorial Experiments. Higher Fractions and Screening Designs. Construction of Resolution III and Resolution IV Designs with 8, 16, and 32 Design Points. Other Two-Level Resolution III Designs; The Plackett-Burman. Designs. Taguchi's Robust Parameter Design.

**16. Nonparametric Statistics.**

Nonparametric Tests. Sign Test. Signed-Rank Test. Rank-Sum Test. Krukal-Wallis Test. Runs Test. Tolerance Limits. Rank Correlation Coefficient.

**17. Statistical Quality Control.**

Introduction. Nature of the Control Limits. Purposes of the Control Chart. Control Charts for Variables. Control Charts for Attributes. Cusum Control Charts.

Bibliography.

Appendix: Statistical Tables.

Answers to Exercises.

Index.

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Summary

This classic text provides a rigorous introduction to basic probability theory and statistical inference that is well motivated by interesting, relevant applications. The new edition features many new, real-data based exercises and examples. Increased emphasis on the analysis of statistical output and greater use of graphical techniques and statistical methods in quality improvement make the 6th edition more useful for today's students.

Flexible organization makes the text appropriate for use in a one or two term course.

Praised for the quality and accuracy of the exercise sets, the authors use a spiraling technique which reintroduces exercises and examples seen previously so that students may apply their growing knowledge of statistics to a familiar problem and data set.

Complete case studies are presented in material dealing with two-sample inference, one-and two-factor analysis of variance, multifactor analysis of variance, and the analysis of 2^k factorial experiments.

NEW--Greater than 20% of the exercises and examples have been updated with new real data.

The standard, boring cards and "balls and urns" examples in the probability chapters have largely been replaced with exercises addressing the scientific aspects of everyday life.

Many new exercises and applications of the poisson, binomial, geometric, hypergeometric, and gamma distributions have been introduced.

NEW--The coverage of maximum likelihood has been expanded to include many new exercises and examples. New material using linear models with matrix development has been added to the coverage of "Analysis of Variance in Regression."

NEW--The book has been redesigned to insure that each figure is presented in closer proximity to the example it illustrates to eliminate the need to flip back and forth between pages in the book. The Answer Appendix now includes answers to the odd exercises only.

NEW--Recognizing the importance of the computer in data analysis, many new SAS and Minitab printouts have been added to the book in numerous chapters including those dealing with two samples (Chs. 9, 10), simple linear regression (Ch. 11), multiple regression (Ch. 12), one factor experiments (Ch. 13), two level factorial (Ch. 14)and fractional factorial experiments (Ch 15).

NEW--In addition some exercises are presented as Case Studies in which a computer printout is presented from which the student is asked to draw conclusions. These exercises refine the students ability to draw conclusions from data and interpret summary results in the most meaningful way.

Table of Contents

*(NOTE: Most chapters conclude with Review Exercises.)*

**1. Introduction to Statistics and Data Analysis.**

Overview. The Role of Probability. Measures of Location: The Sample Mean and Median. Measures of Variability. Discrete and Continuous Data. Statistical Modeling, Scientific Inspection, and Graphical Diagnostics.

**2. Probability.**

Sample Space. Events. Counting Sample Points. Probability of an Event. Additive Rules. Conditional Probability. Multiplicative Rules. Bayes' Rule.

**3. Random Variables and Probability Distributions.**

Concept of a Random Variable. Discrete Probability Distributions. Continuous Probability Distributions. Empirical Distributions. Joint Probability Distributions.

**4. Mathematical Expectation.**

Mean of a Random Variable. Variance and Covariance. Means and Variances of Linear Combinations of Random Variables. Chebyshev's Theorem.

**5. Some Discrete Probability Distributions.**

Introduction. Discrete Uniform Distribution. Binomial and Multinomial Distribution. Hypergeometric Distribution. Negative Binomial and Geometric Distributions. Poisson Distribution and the Poisson Process.

**6. Some Continuous Probability Distributions.**

Continuous Probability Distribution. Normal Distribution. Areas Under the Normal Curve. Applications of the Normal Distribution. Normal Approximation to the Binomial. Gamma and Exponential Distributions. Applications of the Exponential and Gamma Distributions. Chi-Squared Distribution. Lognormal Distribution. Weibull Distribution.

**7. Functions of Random Variables.**

Introduction. Transformation of Variables. Moments and Moment-Generating Functions.

**8. Random Sampling, Data Description, and Some Fundamental Sampling Distributions.**

Random Sampling. Some Important Statistics. Data Displays and Graphical Methods. Sampling Distribution. Sampling Distributions of Means. Sampling Distribution of S^2. t-Distribution. F-Distribution.

**9. One- and Two-Sample Estimation Problems.**

Introduction. Statistical Inference. Classical Methods of Estimation. Single Sample: Estimating the Mean. Standard Error of a Point Estimate. Tolerance Limits. Two Samples: Estimating the Difference Between Two Means. Paired Observations. Single Sample: Estimating a Proportion. Two Samples: Estimating the Difference Between Two Proportions. Single Sample: Estimating the Variance. Two Samples: Estimating the Ratio of Two Variances. Bayesian Methods of Estimation. Maximum Likelihood Estimation.

**10. One- and Two- Sample Tests of Hypotheses (Continuous and Discrete Data).**

Statistical Hypotheses: General Concepts. Testing a Statistical Hypothesis. One- and Two-Tailed Tests. The Use of P- Values in Decision Making. Single Sample: Tests Concerning a Single Mean (Variance Known). Relationship to Confidence Interval Estimation. Single Sample: Tests on a Single Mean (Variance Unknown). Two Samples: Tests on Two Means. Choice of Sample Size for Testing Means. Graphical Methods for Comparing Means. One Sample: Test on a Single Proportion. Two Samples: Tests on Two Proportions. One- and Two-Sample Tests Concerning Variances. Goodness-of-Fit Test. Test for Independence (Categorical Data). Test for Homogeneity. Testing for Several Proportions. Two-Sample Case Study.

**11. Simple Linear Regression and Correlation.**

Introduction to Linear Regression. Simple Linear Regression. Properties of the Least Squares Estimators. Inferences Concerning the Regression Coefficients. Prediction. Choice of a Regression Model. Analysis-of Variance Approach. Test for Linearity of Regression: Data with Repeated Observations. Data Plots and Transformations. Simple Linear Regression Case Study. Correlation.

**12. Multiple Linear Regression.**

Introduction. Estimating the Coefficients. Linear Regression Model Using Matrices. Properties of the Least Squares Estimators. Inferences in Multiple Linear Regression. Choice of a Fitted Model Through Hypothesis Testing. Special Case of Orthogonality. Sequential Methods for Model Selection. Study of Residuals and Violation of Assumptions. Cross Validation, Cp, and Other Criteria for Model Selection.

**13. One-Factor Experiments: General.**

Analysis-of-Variance Technique. The Strategy of Experimental Design. One-Way Analysis of Variance: Completely Randomized Design. Tests for the Equality of Several Variances. Single-Degree-of-Freedom Comparisons. Multiple Comparisons. Comparing Treatments with a Control. Comparing a Set of Treatments in Blocks. Randomized Complete Block Designs. Graphical Methods and Further Diagnostics. Latin Squares. Random Effects Models. Regression Approach to Analysis of Variance. Power of Analysis-of-Variance Tests. Case Study.

**14. Factorial Experiments.**

Introduction. Interaction and the Two-Factor Experiment. Two-Factor Analysis of Variance. Graphical Analysis in the Two-Factor Problem. Three-Factor Experiments. Specific Multifactor Models. MODEL II and III Factorial Experiments. Choice of Sample Size.

**15. 2^k Factorial Experiments and Fractions.**

Introduction. Analysis of Variance. Nonreplicated 2^k Factorial Experiment. Case Study. Factorial Experiments in Incomplete Blocks. Partial Confounding. Factorial Experiments in a Regression Setting. Case Study: Coal Cleansing Experiment. Fractional Factorial Experiments. Analysis of Fractional Factorial Experiments. Higher Fractions and Screening Designs. Construction of Resolution III and Resolution IV Designs with 8, 16, and 32 Design Points. Other Two-Level Resolution III Designs; The Plackett-Burman. Designs. Taguchi's Robust Parameter Design.

**16. Nonparametric Statistics.**

Nonparametric Tests. Sign Test. Signed-Rank Test. Rank-Sum Test. Krukal-Wallis Test. Runs Test. Tolerance Limits. Rank Correlation Coefficient.

**17. Statistical Quality Control.**

Introduction. Nature of the Control Limits. Purposes of the Control Chart. Control Charts for Variables. Control Charts for Attributes. Cusum Control Charts.

Bibliography.

Appendix: Statistical Tables.

Answers to Exercises.

Index.

Publisher Info

Publisher: Prentice Hall, Inc.

Published: 1998

International: No

Published: 1998

International: No

This classic text provides a rigorous introduction to basic probability theory and statistical inference that is well motivated by interesting, relevant applications. The new edition features many new, real-data based exercises and examples. Increased emphasis on the analysis of statistical output and greater use of graphical techniques and statistical methods in quality improvement make the 6th edition more useful for today's students.

Flexible organization makes the text appropriate for use in a one or two term course.

Praised for the quality and accuracy of the exercise sets, the authors use a spiraling technique which reintroduces exercises and examples seen previously so that students may apply their growing knowledge of statistics to a familiar problem and data set.

Complete case studies are presented in material dealing with two-sample inference, one-and two-factor analysis of variance, multifactor analysis of variance, and the analysis of 2^k factorial experiments.

NEW--Greater than 20% of the exercises and examples have been updated with new real data.

The standard, boring cards and "balls and urns" examples in the probability chapters have largely been replaced with exercises addressing the scientific aspects of everyday life.

Many new exercises and applications of the poisson, binomial, geometric, hypergeometric, and gamma distributions have been introduced.

NEW--The coverage of maximum likelihood has been expanded to include many new exercises and examples. New material using linear models with matrix development has been added to the coverage of "Analysis of Variance in Regression."

NEW--The book has been redesigned to insure that each figure is presented in closer proximity to the example it illustrates to eliminate the need to flip back and forth between pages in the book. The Answer Appendix now includes answers to the odd exercises only.

NEW--Recognizing the importance of the computer in data analysis, many new SAS and Minitab printouts have been added to the book in numerous chapters including those dealing with two samples (Chs. 9, 10), simple linear regression (Ch. 11), multiple regression (Ch. 12), one factor experiments (Ch. 13), two level factorial (Ch. 14)and fractional factorial experiments (Ch 15).

NEW--In addition some exercises are presented as Case Studies in which a computer printout is presented from which the student is asked to draw conclusions. These exercises refine the students ability to draw conclusions from data and interpret summary results in the most meaningful way.

*(NOTE: Most chapters conclude with Review Exercises.)*

**1. Introduction to Statistics and Data Analysis.**

Overview. The Role of Probability. Measures of Location: The Sample Mean and Median. Measures of Variability. Discrete and Continuous Data. Statistical Modeling, Scientific Inspection, and Graphical Diagnostics.

**2. Probability.**

Sample Space. Events. Counting Sample Points. Probability of an Event. Additive Rules. Conditional Probability. Multiplicative Rules. Bayes' Rule.

**3. Random Variables and Probability Distributions.**

Concept of a Random Variable. Discrete Probability Distributions. Continuous Probability Distributions. Empirical Distributions. Joint Probability Distributions.

**4. Mathematical Expectation.**

Mean of a Random Variable. Variance and Covariance. Means and Variances of Linear Combinations of Random Variables. Chebyshev's Theorem.

**5. Some Discrete Probability Distributions.**

Introduction. Discrete Uniform Distribution. Binomial and Multinomial Distribution. Hypergeometric Distribution. Negative Binomial and Geometric Distributions. Poisson Distribution and the Poisson Process.

**6. Some Continuous Probability Distributions.**

Continuous Probability Distribution. Normal Distribution. Areas Under the Normal Curve. Applications of the Normal Distribution. Normal Approximation to the Binomial. Gamma and Exponential Distributions. Applications of the Exponential and Gamma Distributions. Chi-Squared Distribution. Lognormal Distribution. Weibull Distribution.

**7. Functions of Random Variables.**

Introduction. Transformation of Variables. Moments and Moment-Generating Functions.

**8. Random Sampling, Data Description, and Some Fundamental Sampling Distributions.**

Random Sampling. Some Important Statistics. Data Displays and Graphical Methods. Sampling Distribution. Sampling Distributions of Means. Sampling Distribution of S^2. t-Distribution. F-Distribution.

**9. One- and Two-Sample Estimation Problems.**

Introduction. Statistical Inference. Classical Methods of Estimation. Single Sample: Estimating the Mean. Standard Error of a Point Estimate. Tolerance Limits. Two Samples: Estimating the Difference Between Two Means. Paired Observations. Single Sample: Estimating a Proportion. Two Samples: Estimating the Difference Between Two Proportions. Single Sample: Estimating the Variance. Two Samples: Estimating the Ratio of Two Variances. Bayesian Methods of Estimation. Maximum Likelihood Estimation.

**10. One- and Two- Sample Tests of Hypotheses (Continuous and Discrete Data).**

Statistical Hypotheses: General Concepts. Testing a Statistical Hypothesis. One- and Two-Tailed Tests. The Use of P- Values in Decision Making. Single Sample: Tests Concerning a Single Mean (Variance Known). Relationship to Confidence Interval Estimation. Single Sample: Tests on a Single Mean (Variance Unknown). Two Samples: Tests on Two Means. Choice of Sample Size for Testing Means. Graphical Methods for Comparing Means. One Sample: Test on a Single Proportion. Two Samples: Tests on Two Proportions. One- and Two-Sample Tests Concerning Variances. Goodness-of-Fit Test. Test for Independence (Categorical Data). Test for Homogeneity. Testing for Several Proportions. Two-Sample Case Study.

**11. Simple Linear Regression and Correlation.**

Introduction to Linear Regression. Simple Linear Regression. Properties of the Least Squares Estimators. Inferences Concerning the Regression Coefficients. Prediction. Choice of a Regression Model. Analysis-of Variance Approach. Test for Linearity of Regression: Data with Repeated Observations. Data Plots and Transformations. Simple Linear Regression Case Study. Correlation.

**12. Multiple Linear Regression.**

Introduction. Estimating the Coefficients. Linear Regression Model Using Matrices. Properties of the Least Squares Estimators. Inferences in Multiple Linear Regression. Choice of a Fitted Model Through Hypothesis Testing. Special Case of Orthogonality. Sequential Methods for Model Selection. Study of Residuals and Violation of Assumptions. Cross Validation, Cp, and Other Criteria for Model Selection.

**13. One-Factor Experiments: General.**

Analysis-of-Variance Technique. The Strategy of Experimental Design. One-Way Analysis of Variance: Completely Randomized Design. Tests for the Equality of Several Variances. Single-Degree-of-Freedom Comparisons. Multiple Comparisons. Comparing Treatments with a Control. Comparing a Set of Treatments in Blocks. Randomized Complete Block Designs. Graphical Methods and Further Diagnostics. Latin Squares. Random Effects Models. Regression Approach to Analysis of Variance. Power of Analysis-of-Variance Tests. Case Study.

**14. Factorial Experiments.**

Introduction. Interaction and the Two-Factor Experiment. Two-Factor Analysis of Variance. Graphical Analysis in the Two-Factor Problem. Three-Factor Experiments. Specific Multifactor Models. MODEL II and III Factorial Experiments. Choice of Sample Size.

**15. 2^k Factorial Experiments and Fractions.**

Introduction. Analysis of Variance. Nonreplicated 2^k Factorial Experiment. Case Study. Factorial Experiments in Incomplete Blocks. Partial Confounding. Factorial Experiments in a Regression Setting. Case Study: Coal Cleansing Experiment. Fractional Factorial Experiments. Analysis of Fractional Factorial Experiments. Higher Fractions and Screening Designs. Construction of Resolution III and Resolution IV Designs with 8, 16, and 32 Design Points. Other Two-Level Resolution III Designs; The Plackett-Burman. Designs. Taguchi's Robust Parameter Design.

**16. Nonparametric Statistics.**

Nonparametric Tests. Sign Test. Signed-Rank Test. Rank-Sum Test. Krukal-Wallis Test. Runs Test. Tolerance Limits. Rank Correlation Coefficient.

**17. Statistical Quality Control.**

Introduction. Nature of the Control Limits. Purposes of the Control Chart. Control Charts for Variables. Control Charts for Attributes. Cusum Control Charts.

Bibliography.

Appendix: Statistical Tables.

Answers to Exercises.

Index.