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Elements of Statistics II Inferential Statistics

ISBN-10: 0071346376

ISBN-13: 9780071346375

Edition: 2000

Authors: Stephen Bernstein, Ruth Bernstein

List price: $29.00
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Book details

List price: $29.00
Copyright year: 2000
Publisher: McGraw-Hill Education
Publication date: 9/2/1999
Binding: Paperback
Pages: 472
Size: 8.00" wide x 11.25" long x 1.00" tall
Weight: 1.892
Language: English

Discrete Probability Distributions
Discrete Probability Distributions and Probability Mass Functions
Bernoulli Experiments and trials
Binomial Random Variables, Experiments, and Probability Functions
The Binomial Coefficient
The Binomial Probability Function
Mean, Variance, and Standard Deviation of the Binomial Probability Distribution
The Binomial Expansion and the Binomial Theorem
Pascal's Triangle and the Binomial Coefficient
The Family of Binomial Distributions
The Cumulative Binomial Probability Table
Lot-Acceptance Sampling
Consumer's Risk and Producer's Risk
Multivariate Probability Distributions and Joint Probability Distributions
The Multinomial Experiment
The Multinomial Coefficient
The Multinomial Probability Function
The Family of Multinomial Probability Distributions
The Means of the Multinomial Probability Distribution
The Multinomial Expansion and the Multinomial Theorem
The Hypergeometric Experiment
The Hypergeometric Probability Function
The Family of Hypergeometric Probability Distributions
The Mean, Variance, and Standard Deviation of the Hypergeometric Probability Distribution
The Generalization of the Hypergeometric Probability Distribution
The Binomial and Multinomial Approximations to the Hypergeometric Distribution
Poisson Processes, Random Variables, and Experiments
The Poisson Probability Function
The Family of Poisson Probability Distributions
The Mean, Variance, and Standard Deviation of the Poisson Probability Distribution
The Cumulative Poisson Probability Table
The Poisson Distribution as an Approximation to the Binomial Distribution
The Normal Distribution and Other Continuous Probability Distributions
Continuous Probability Distributions
The Normal Probability Distributions and the Normal Probability Density Function
The Family of Normal Probability Distributions
The Normal Distribution: Relationship between the Mean ([mu]), the Median ([mu]), and the Mode
Kurtosis
The Standard Normal Distribution
Relationship Between the Standard Normal Distribution and the Standard Normal Variable
Table of Areas in the Standard Normal Distribution
Finding Probabilities Within any Normal Distribution by Applying the Z Transformation
One-tailed Probabilities
Two-tailed Probabilities
The Normal Approximation to the Binomial Distribution
The Normal Approximation to the Poisson Distribution
The Discrete Uniform Probability Distribution
The Continuous Uniform Probability Distribution
The Exponential Probability Distribution
Relationship between the Exponential Distribution and the Poisson Distribution
Sampling Distributions
Simple Random Sampling Revisited
Independent Random Variables
Mathematical and Nonmathematical Definitions of Simple Random Sampling
Assumptions of the Sampling Technique
The Random Variable X
Theoretical and Empirical Sampling Distributions of the Mean
The Mean of the Sampling Distribution of the Mean
The Accuracy of an Estimator
The Variance of the Sampling Distribution of the Mean: Infinite Population or Sampling with Replacement
The Variance of the Sampling Distribution of the Mean: Finite Population Sampled without Replacement
The Standard Error of the Mean
The Precision of An Estimator
Determining Probabilities with a Discrete Sampling Distribution of the Mean
Determining Probabilities with a Normally Distributed Sampling Distribution of the Mean
The Central Limit Theorem: Sampling from a Finite Population with Replacement
The Central Limit Theorem: Sampling from an Infinite Population
The Central Limit Theorem: Sampling from a Finite Population without Replacement
How Large is "Sufficiently Large?"
The Sampling Distribution of the Sample Sum
Applying the Central Limit Theorem to the Sampling Distribution of the Sample Sum
Sampling from a Binomial Population
Sampling Distribution of the Number of Successes
Sampling Distribution of the Proportion
Applying the Central Limit Theorem to the Sampling Distribution of the Number of Successes
Applying the Central Limit Theorem to the Sampling Distribution of the Proportion
Determining Probabilities with a Normal Approximation to the Sampling Distribution of the Proportion
One-Sample Estimation of The Population Mean
Estimation
Criteria for Selecting the Optimal Estimator
The Estimated Standard Error of the Mean S[subscript x]
Point Estimates
Reporting and Evaluating the Point Estimate
Relationship between Point Estimates and Interval Estimates
Deriving P(x[subscript 1-alpha/2] [less than or equal] X [less than or equal] x[subscript alpha/2]) = P(-z[subscript alpha/2] [less than or equal] Z [less than or equal] z[subscript alpha/2]) = 1 - [alpha]
Deriving P(X - z[subscript alpha/2] [sigma subscript x] [less than or equal] [mu] [less than or equal] X + z[subscript alpha/2] [sigma subscript x]) = 1 - [alpha]
Confidence Interval for the Population Mean [mu]: Known Standard Deviation [sigma], Normally Distributed Population
Presenting Confidence Limits
Precision of the Confidence Interval
Determining Sample Size when the Standard Deviation is Known
Confidence Interval for the Population Mean [mu]: Known Standard Deviation [sigma], Large Sample (n [greater than or equal] 30) from any Population Distribution
Determining Confidence Intervals for the Population Mean [mu] when the Population Standard Deviation [sigma] is Unknown
The t Distribution
Relationship between the t Distribution and the Standard Normal Distribution
Degrees of Freedom
The Term "Student's t Distribution"
Critical Values of the t Distribution
Table A.6: Critical Values of the t Distribution
Confidence Interval for the Population Mean [mu]: Standard Deviation [sigma] not known, Small Sample (n [ 30) from a Normally Distributed Population
Determining Sample Size: Unknown Standard Deviation, Small Sample from a Normally Distributed Population
Confidence Interval for the Population Mean [mu]: Standard Deviation [sigma] not known, large sample (n [greater than or equal] 30) from a Normally Distributed Population
Confidence Interval for the Population Mean [mu]: Standard Deviation [sigma] not known, Large Sample (n [greater than or equal] 30) from a Population that is not Normally Distributed
Confidence Interval for the Population Mean [mu]: Small Sample (n [ 30) from a Population that is not Normally Distributed
One-Sample Estimation of the Population Variance, Standard Deviation, and Proportion
Optimal Estimators of Variance, Standard Deviation, and Proportion
The Chi-Square Statistic and the Chi-Square Distribution
Critical Values of the Chi-Square Distribution
Table A.7: Critical Values of the Chi-Square Distribution
Deriving the Confidence Interval for the Variance [sigma superscript 2] of a Normally Distributed Population
Presenting Confidence Limits
Precision of the Confidence Interval for the Variance
Determining Sample Size Necessary to Achieve a Desired Quality-of-Estimate for the Variance
Using Normal-Approximation Techniques To Determine Confidence Intervals for the Variance
Using the Sampling Distribution of the Sample Variance to Approximate a Confidence Interval for the Population Variance
Confidence Interval for the Standard Deviation [sigma] of a Normally Distributed Population
Using the Sampling Distribution of the Sample Standard Deviation to Approximate a Confidence Interval for the Population Standard Deviation
The Optimal Estimator for the Proportion p of a Binomial Population
Deriving the Approximate Confidence Interval for the Proportion p of a Binomial Population
Estimating the Parameter p
Deciding when n is "Sufficiently Large", p not known
Approximate Confidence Intervals for the Binomial Parameter p When Sampling From a Finite Population without Replacement
The Exact Confidence Interval for the Binomial Parameter p
Precision of the Approximate Confidence-Interval Estimate of the Binomial Parameter p
Determining Sample Size for the Confidence Interval of the Binomial Parameter p
Approximate Confidence Interval for the Percentage of a Binomial Population
Approximate Confidence Interval for the Total Number in a Category of a Binomial Population
The Capture--Recapture Method for Estimating Population Size N
One-Sample Hypothesis Testing
Statistical Hypothesis Testing
The Null Hypothesis and the Alternative Hypothesis
Testing the Null Hypothesis
Two-Sided Versus One-Sided Hypothesis Tests
Testing Hypotheses about the Population Mean [mu]: Known Standard Deviation [sigma], Normally Distributed Population
The P Value
Type I Error versus Type II Error
Critical Values and Critical Regions
The Level of Significance
Decision Rules for Statistical Hypothesis Tests
Selecting Statistical Hypotheses
The Probability of a Type II Error
Consumer's Risk and Producer's Risk
Why It is Not Possible to Prove the Null Hypothesis
Classical Inference Versus Bayesian Inference
Procedure for Testing the Null Hypothesis
Hypothesis Testing Using X as the Test Statistic
The Power of a Test, Operating Characteristic Curves, and Power Curves
Testing Hypothesis about the Population Mean [mu]: Standard Deviation [sigma] Not Known, Small Sample (n [ 30) from a Normally Distributed Population
The P Value for the t Statistic
Decision Rules for Hypothesis Tests with the t Statistic
[beta], 1 - [beta], Power Curves, and OC Curves
Testing Hypotheses about the Population Mean [mu]: Large Sample (n [greater than or equal] 30) from any Population Distribution
Assumptions of One-Sample Parametric Hypothesis Testing
When the Assumptions are Violated
Testing Hypothesis about the Variance [sigma superscript 2] of a Normally Distributed Population
Testing Hypotheses about the Standard Deviation [sigma] of a Normally Distributed Population
Testing Hypotheses about the Proportion p of a Binomial Population: Large Samples
Testing Hypotheses about the Proportion p of a Binomial Population: Small Samples
Two-Sample Estimation and Hypothesis Testing
Independent Samples Versus Paired Samples
The Optimal Estimator of the Difference Between Two Population Means ([mu subscript 1] - [mu subscript 2])
The Theoretical Sampling Distribution of the Difference Between Two Means
Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations ([sigma subscript 1] and [sigma subscript 2]) Known, Independent Samples from Normally Distributed Populations
Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations ([sigma subscript 1] and [sigma subscript 2]) known, Independent Samples from Normally Distributed Populations
The Estimated Standard Error of the Difference Between Two Means
Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations not known but Assumed Equal ([sigma subscript 1] = [sigma subscript 2]), Small (n[subscript 1] [ 30 and n[subscript 2] [ 30) Independent Samples from Normally Distributed Populations
Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations not Known but Assumed Equal ([sigma subscript 1] = [sigma subscript 2]), Small (n[subscript 1] [ 30 and n[subscript 2] [ 30) Independent Samples from Normally Distributed Populations
Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations ([sigma subscript 1] and [sigma subscript 2]) not Known, Large (n[subscript 1] [greater than or equal] 30 and n[subscript 2] [greater than or equal] 30) Independent Samples from any Populations Distributions
Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Standard Deviations ([sigma subscript 1] and [sigma subscript 2]), not known, Large (n[subscript 1] [greater than or equal] 30 and n[subscript 2] [greater than or equal] 30) Independent Samples from any Populations Distributions
Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Paired Samples
Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Paired Samples
Assumptions of Two-Sample Parametric Estimation and Hypothesis Testing about Means
When the Assumptions are Violated
Comparing Independent-Sampling and Paired-Sampling Techniques on Precision and Power
The F Statistic
The F Distribution
Critical Values of the F Distribution
Table A.8: Critical Values of the F Distribution
Confidence Interval for the Ratio of Variances ([sigma superscript 2 subscript 1]/[sigma superscript 2 subscript 2]): Parameters ([sigma superscript 2 subscript 1], [sigma subscript 1], [mu subscript 1] and [sigma superscript 2 subscript 2], [sigma subscript 2], [mu subscript 2]) Not Known, Independent Samples From Normally Distributed Populations
Testing Hypotheses about the Ratio of Variances ([sigma superscript 2 subscript 1]/[sigma superscript 2 subscript 2]): Parameters ([sigma superscript 2 subscript 1], [sigma subscript 1], [mu subscript 1] and [sigma superscript 2 subscript 2], [sigma subscript 2], [mu subscript 2]) not known, Independent Samples from Normally Distributed Populations
When to Test for Homogeneity of Variance
The Optimal Estimator of the Difference Between Proportions (p[subscript 1] - p[subscript 2]): Large Independent Samples
The Theoretical Sampling Distribution of the Difference Between Two Proportions
Approximate Confidence Interval for the Difference Between Proportions from Two Binomial Populations (p[subscript 1] - p[subscript 2]): Large Independent Samples
Testing Hypotheses about the Difference Between Proportions from Two Binomial Populations (p[subscript 1] - p[subscript 2]): Large Independent Samples
Multisample Estimation and Hypothesis Testing
Multisample Inferences
The Analysis of Variance
Anova: One-Way, Two-Way, or Multiway
One-Way Anova: Fixed-Effects or Random Effects
One-way, Fixed-Effects Anova: The Assumptions
Equal-Samples, One-Way, Fixed-Effects Anova: H[subscript 0] and H[subscript 1]
Equal-Samples, One-Way, Fixed-Effects Anova: Organizing the Data
Equal-Samples, One-Way, Fixed-Effects Anova: the Basic Rationale
SST = SSA + SSW
Computational Formulas for SST and SSA
Degrees of Freedom and Mean Squares
The F Test
The Anova Table
Multiple Comparison Tests
Duncan's Multiple-Range Test
Confidence-Interval Calculations Following Multiple Comparisons
Testing for Homogeneity of Variance
One-Way, Fixed-Effects ANOVA: Equal or Unequal Sample Sizes
General-Procedure, One-Way, Fixed-effects ANOVA: Organizing the Data
General-Procedure, One-Way, Fixed-effects ANOVA: Sum of Squares
General-Procedure, One-Way, Fixed-Effects ANOVA Degrees of Freedom and Mean Squares
General-Procedure, One-Way, Fixed-Effects ANOVA: the F Test
General-Procedure, One-Way, Fixed-Effects ANOVA: Multiple Comparisons
General-Procedure, One-Way, Fixed-Effects ANOVA: Calculating Confidence Intervals and Testing for Homogeneity of Variance
Violations of ANOVA Assumptions
Regression and Correlation
Analyzing the Relationship between Two Variables
The Simple Linear Regression Model
The Least-Squares Regression Line
The Estimator of the Variance [sigma superscript 2 subscript Y times X]
Mean and Variance of the y Intercept a and the Slope b
Confidence Intervals for the y Intercept a and the Slope b
Confidence Interval for the Variance [sigma superscript 2 subscript Y times X]
Prediction Intervals for Expected Values of Y
Testing Hypotheses about the Slope b
Comparing Simple Linear Regression Equations from Two or More Samples
Multiple Linear Regression
Simple Linear Correlation
Derivation of the Correlation Coefficient r
Confidence Intervals for the Population Correlation Coefficient [rho]
Using the r Distribution to Test Hypotheses about the Population Correlation Coefficient [rho]
Using the t Distribution to Test Hypotheses about p
Using the Z Distribution to Test the Hypothesis [rho] = c
Interpreting the Sample Correlation Coefficient r
Multiple Correlation and Partial Correlation
Nonparametric Techniques
Nonparametric vs. Parametric Techniques
Chi-Square Tests
Chi-Square Test for Goodness-of-fit
Chi-Square Test for Independence: Contingency Table Analysis
Chi-Square Test for Homogeneity Among k Binomial Proportions
Rank Order Tests
One-Sample Tests: The Wilcoxon Signed-Rank Test
Two-Sample Tests: the Wilcoxon Signed-Rank Test for Dependent Samples
Two-Sample Tests: the Mann-Whitney U Test for Independent Samples
Multisample Tests: the Kruskal-Wallis H Test for k Independent Samples
The Spearman Test of Rank Correlation
Appendix
Cumulative Binomial Probabilities
Cumulative Poisson Probabilities
Areas of the Standard Normal Distribution
Critical Values of the t Distribution
Critical Values of the Chi-Square Distribution
Critical Values of the F Distribution
Least Significant Studentized Ranges r[subscript p]
Transformation of r to z[subscript r]
Critical Values of the Pearson Product-Moment Correlation Coefficient r
Critical Values of the Wilcoxon W
Critical Values of the Mann-Whitney U
Critical Values of the Kruskal-Wallis H
Critical Values of the Spearman r[subscript S]
Index