Book:Stephen Bernstein/Elements of Statistics II: Inferential Statistics

Subject Matter

 * Statistics

Contents

 * CHAPTER 11: DISCRETE PROBABILITY DISTRIBUTIONS
 * 11.1 Discrete Probability Distributions and Probability Mass Functions
 * 11.2 Bernoulli Experiments and trials
 * 11.3 Binomial Random Variables, Experiments, and Probability Functions
 * 11.4 The Binomial Coefficient
 * 11.5 The Binomial Probability Function
 * 11.6 Mean, Variance, and Standard Deviation of the Binomial Probability Distribution
 * 11.7 The Binomial Expansion and the Binomial Theorem
 * 11.8 Pascal's Triangle and the Binomial Coefficient
 * 11.9 The Family of Binomial Distributions
 * 11.10 The Cumulative Binomial Probability Table
 * 11.11 Lot-Acceptance Sampling
 * 11.12 Consumer's Risk and Producer's Risk
 * 11.13 Multivariate Probability Distributions and Joint Probability Distributions
 * 11.14 The Multinomial Experiment
 * 11.15 The Multinomial Coefficient
 * 11.16 The Multinomial Probability Function
 * 11.17 The Family of Multinomial Probability Distributions
 * 11.18 The Means of the Multinomial Probability Distribution
 * 11.19 The Multinomial Expansion and the Multinomial Theorem
 * 11.20 The Hypergeometric Experiment
 * 11.21 The Hypergeometric Probability Function
 * 11.22 The Family of Hypergeometric Probability Distributions
 * 11.23 The Mean, Variance, and Standard Deviation of the Hypergeometric Probability Distribution
 * 11.24 The Generalization of the Hypergeometric Probability Distribution
 * 11.25 The Binomial and Multinomial Approximations to the Hypergeometric Distribution
 * 11.26 Poisson Processes, Random Variables, and Experiments
 * 11.27 The Poisson Probability Function
 * 11.28 The Family of Poisson Probability Distributions
 * 11.29 The Mean, Variance, and Standard Deviation of the Poisson Probability Distribution
 * 11.30 The Cumulative Poisson Probability Table
 * 11.31 The Poisson Distribution as an Approximation to the Binomial Distribution


 * CHAPTER 12 The Normal Distribution and Other Continuous Probability Distributions
 * 12.1 Continuous Probability Distributions
 * 12.2 The Normal Probability Distributions and the Normal Probability Density Function
 * 12.3 The Family of Normal Probability Distributions
 * 12.4 The Normal Distribution: Relationship between the Mean $$(\mu)$$, Median $$(\overline \mu)$$, and the Mode
 * 12.5 Kurtosis
 * 12.6 The Standard Normal Distribution
 * 12.7 Relationship Between the Standard Normal Distribution and the Standard Normal Variable
 * 12.8 Table of Areas in the Standard Normal Distribution
 * 12.9 Finding Probabilities Within any Normal Distribution by Applying the Z Transformation
 * 12.10 One-tailed Probabilities


 * 12.11
 * 12.12
 * 12.13
 * 12.14
 * 12.15
 * 12.16
 * 12.17

chortled Probabilities The Normal Approximation to the Binomial Distribution The Normal Approximation to the Poisson Distribution ne Discrete Uniform Probability Distribution The Continuous Uniform Probability Distribution The Exponential Probability Distribution Relationship between the Exponential Distribution and the Poisson Distribution
 * CHAPTER 13: SAMPLING DISTRIBUTIONS
 * 13.1 Simple Random Sampling Revisited
 * 13.2 Independent Random Variables
 * 13.3 Mathematical and Nonmathematical Definitions of Simple

Random Sampling
 * 13.4 Assumptions of the Sampling Technique
 * 13.5 The Random Variable X
 * 13.6 'Theoretical and Empirical Sampling Distributions of the
 * Mean

The Mean of the Sampling rite accuracy
 * 13.7
 * 13.8
 * 13.9
 * Distribution of the Mean

of an Estimator
 * 13.10
 * 13.11
 * 13.12
 * 13.13

ne 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
 * 13.14 Determining Probabilities with a Normally Distributed

Sampling Distribution of the Mean


 * 13.15 The Central Limit Theorem: Sampling from a Finite

Population with Replacement
 * 13.16 The Central Limit Theorem: Sampling from an Infinite

Population '
 * 13.17 ne Central Limit Theorem: Sampling from a Finite

Population without Replacement
 * 13.18 How Large is Gsumciently largesse
 * 13.19 ne Sampling Distribution of the Sample Slim
 * 13.20 Applying the Central Limit 'Theorem to the Sampling

Distribution of the Sample Sum
 * 13.21 Sampling from a Binomial Population
 * 13.22 Sampling Distribution of the filmier of Successes
 * 13.23 Sampling Distribution of the Proportion
 * 13.24 Applying the Central Limit Theorem to the Snmpling

Distribution of the Number of Successes
 * 13.25 Applying the Central Limit Theorem to the Sampling

Distribution of the Proportion
 * 13.26 Determining Probabilities with a Normal Approximation

to the Sampling Distribution of the Proportion


 * CHAPTER 14 ONE-SAMPLE ESTIMATION OF THE POPULATION MEAN
 * 14.1 Estimation
 * 14.2 Criteria for Selecting the Optimal Estimator
 * 14.3 The Estimated Standard Error of the Mean SR
 * 14.4 Point Estimates
 * 14.5 Reporting and Evaluating the Point Estimate
 * 14.6 Relationship between Point Estimates and Interval Estimates
 * 14.7 Deriving Plk|-|jz S 2 S kxjz) = Pt-zzp S Z S buzz) = 1 - a
 * 14.8 Deriving 82 - za/zc.k S p S 2 + zaps) = 1 - a
 * 14.9 Confidence Interval for the Population Mean /1: Known

Standard Deviation c, Normally Distributed Population
 * 14.10 Presenting Confidence' Limits
 * 14.11 Precision of the Confidence Interval
 * 14.12 Determining Sample Size when the Standard Deviation is

Known
 * 14.13 Confidence Interval for the Population Mean /1: Known

Standard Deviation c, Large Sample an a 30) from any Population Distribution
 * 14.14 Determining Confidence Intervals for the Population Mean

p when the Population Standard Deviation or is Unknown
 * 14.15 The t Distribution
 * 14.16 Relationship between the / Distribution and the Standard

Normal Distribution
 * 14.17 Degrees of Freedom
 * 14.18 The Term student's t Distribution''


 * 14.19 Critical Values of the t Distribution
 * 14.20 Table A.6: Critical Values of the t Distribution
 * 14.21 Confidence Interval for the Population Mean p: Standard

Deviation c not known, Small Sample (a < 30) from a Normally Determining Sample Size: Small Sample from a Normally Distributed Population Confidence Interval for the Population Mean p: Standard Deviation c not known, large sample (a a 30) from a Distributed Population
 * 14.22

Unknown Standard Deviation,
 * 14.23

Normally incidence Distributed
 * 14.24

Population Interval for the Population
 * 14.25

Deviation c not known, Large Population that is not Normally Confidence Interval for the Sample Distributed Mean p: Standard Sample (a I 30) from a Distributed Population Mean /,1: (,1 < 30) from a Population that is not Small Normally
 * CHAPTER 15 ONE-SAMPLE ESTIMATION OF THE POPULATION VARIANCE, STANDARD DEVIATION, AND PROPORTION
 * 15.1
 * 15.2
 * 15.3
 * 15.4

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 qf the Chi-square Distribution Deriving the Variance co Presenting
 * 15.5

Confidence Interval for the of a Normally Distributed Population Confidence Limits
 * 15.6
 * 15.7

Precision of the Confidence Interval for the Variance
 * 15.8 Determining jumble Size Necessary to Achieve a Desired

Quality-of-Estimate for the Variance
 * 15.9 Using Normal-Approximation Techniques To Determine

Confidence Intervals for the Variance
 * 15.10 Using the Sampling Distribution of the Sample Variance to

a Confidence Interval for the Population Approximate Variance
 * 15.11 Confidence

Normally Distributed Population
 * 15.12 Using the Sampling Distribution of the Sample Standard

Deviation to Approximate a Confidence Interval for the Population Standard Deviation
 * 15.13 ne Optimal Estimator for the Proportion p of a Binomial

Population
 * 15.14 Deriving the Approximate Confidence Interval for the

Proportion p of a Binomial Population Interval for the Standard Deviation or of a


 * 15.15 Estimating the Parameter p
 * 15.16 Deciding when n is Hsuëciently largest, p not down
 * 15.17 Approximate Confidence Intervals fof the Binomial

Parameter p When Sampling From a Finite Population without Replacement
 * 15.18 The Exact Confidence Interval for the Binomial Parameter p
 * 15.19 Precision of the Approximate Confidence-interval Estimate

of the Binomial Parameter p
 * 15.20 Determining Sample Size for the Confidence Interval of the

Binomial Parameter p
 * 15.21 Approximate Confidence Interval for the Percentage of a

Binomial Population
 * 15.22 Approximate Confidence Internal for the Total Number in

a Category of a Binomial Population
 * 15.23 The Capture-R|ecaptlzre Method for Estimating Population

jize N
 * CHAPTER 16 ONE-SAMPLE HYPOTHESIS TESTING
 * 16.1 Statistical Hypothesis Testing
 * 16.2 The Null Hypothesis and the Alternative Hypothesis
 * 16.3 Testing the Null Hypothesis
 * 16.4 Two-sided Versus One-sided Hypothesis Tests
 * 16.5 Testing Hypotheses about the Population Mean p: Known

Standard Deviation 0., Normally Distributed Population.
 * 16.6 The # Value
 * 16.7 'type 1 Error versus Type H Error
 * 16.8 Critical Values and Critical Regions
 * 16.9 The Level of Significance
 * 16.10 Decision Rules for Statistical Hypothesis Tests
 * 16.11 Selecting Statistical Hypotheses
 * 16.12 The Probability of a Type 11 Error
 * 16.1à Conszlmer's Risk and Producer's Risk
 * 16.14 Why It is Not Possible to Prove the Null Hypothesis
 * 16.15 Classical Inference Versus Bayesian Inference
 * 16.16 Procedure for Testily the null Hypothesis
 * 16.17 Hypothesis Testing Using X as the Test Statistic
 * 16.18 The Power of a Test, operating Characteristic Curves, and

Power Curves
 * 16.19 Testing Hypothesis about the Population med p: Standard

Deviation c Not Known, Small Sample an < 30) from a Normally Distributed Population
 * 16.20 ne # Value for the f Statistic
 * 16.21 Decision Rules for Hypothesis Tests with the t Statistic
 * 16.22 je 1 - p, Power Curves, and OC Curves
 * 16.23 Testing Hypotheses about the Population Mean p: Large

Sample (a I 30) from any Population Distribution
 * 16.24 Assumptions of One-sample Parametric Hypothesis Testing


 * 16.25 When the Assllmptions are Violated
 * 16.26 Testing Hypothesis about the Variance |2 of a Normally

Distributed Population
 * 16.27 Testing Hypotheses about the Standard Deviation c of a

Normally Distributed Population
 * 16.28 Testing Hypotheses about the Proportion p of a Binomial

Population: Large Samples
 * 16.29 Testing Hypotheses about the Proportion p of a Binomial

Population: Small Samples


 * CHAPTER 17 TWO-SAMPLE ESTIMATION AND HYPOTHESIS TESTING
 * 17.1 Independent Samples Versus Paired Samples
 * 17.2 The Optimal Estimator of the Difference Between Two

Population Means (pj - pz)
 * 17.3 The 'Theoretical Sampling Distribution of the Difference

Between Two Means
 * 17.4 Confidence Interval for the Difference Between Means

(IzI - Iza): Standard Deviations (0|1 and ca) Known, Independent Samples from Normally Distributed Populations
 * 17.5 Testing Hypotheses about the Difference Between

Means (p1 - p2): Standard Deviations (0|1 and oh) known, Independent Samples from Normally Distributed Populations
 * 17.6 The Estimated Standard Error of the Difference Between

Two Means
 * 17.7 Confidence Interval for the Difference Between Means

(pj - pa): Standard Deviations not known but Assllmed Equal (c1 = ca), Small (nj < 30 and nz < 30) Independent Samples from Normally Distributed Populations
 * 17.8 Testing Hypotheses about the Difference Between Means

(pj - p2): Standard Deviations not Known but Assllmed Equal (cj = cc), Small (,|1 < 30 and nz < 30) Independent Samples from Normally Distributed Populations
 * 17.9 Confidence Interval for the Difference Between Means

(/11 - pa): Standard Deviations (c1 and c2) not Known, Large (a! I 30 and ne k: 30) Independent Samples from any Population Distributions
 * 17.10 Testing Hypotheses about the Difference Between Means

(Ph - p2): Standard Deviations (0|1 and oz), not known, Large (nj a: 30 and ne a 30) Independent Samples from any P 1 Cions Distributions opu a
 * 17.11 Confidence Interval for the Difference Between Means

(#1 - /|2): Paired Samples
 * 17.12 Testing Hypotheses about the Difference Between Means

(#1 - /22): Paired Samples


 * 17.13 Assumptions of Two-snmple Parametric Estimation and

Hypothesis Testing about Means
 * 17.14 When the Assumptions are Violated
 * 17.15 Comparing lhdependent-sampling and Paired-snmpling

Techniques on Precision and Power
 * 17.16 The F Statistic
 * 17.17 The F Distribution
 * 17.18 Critical Values of the F Distribution
 * 17.19 Table A.8: Critical Values of the F Distribution
 * 17.20 Confidence Interval for the Ratio of Variances (c2j/I2z):

Parameters (02 cj, pj and CIA, n, pz) Not know, 1, Independent Samples From Normally Distributed Populations
 * 17.21 Testing Hypotheses about the Ratio of Variances (c2j/c!):

Parameters (0|2 cj, pj and cc2, oh, pz) not down, 1, Independent Samples from Normally Distributed Populations
 * 17.22 When to Test for Homogeneity of Variance
 * 17.23 The Optimal Estimator of the Difference Between

Proportions (,1 - #2): Large Independent Snmples
 * 17.24 The 'Theoretical Sampling Distribution of the Difference

Between Two Proportions
 * 17.25 Approximate Confidence Interval for the Difference Between

Proportions from Two Binomial Populations (|1 - |2): Large Independent Samples
 * 17.26 Testing Hypotheses about the Difference Between

Proportions from Two Binomial Populations (pi - |2): Large Independent Snmples


 * CHAPTER 18 MULTISAMPLE ESTIMATION AND HYPOTHESIS TESTING
 * 18.1 Multisample Inferences
 * 18.2 The Analysis of Variance
 * 18.3 ANOVA: One-Way, Two-Way, or Multiway
 * 18.4 One-Way ANOVA: Fixed-Effects or Random Effects
 * 18.5 One-way, Fixed-Effects ANOVA: The Assumptions
 * 18.6 Equal-samples, One-Way, Fixed-E|ects ANOVA: he and Hj
 * 18.7 Equal-samples, One-Way, Fixed-Effects ANOVA: Organizing

the Data
 * 18.8 Equal-samples, One-Way, Fixed-Effects ANOVA: the Basic

Rationale
 * 18.9 SST = SSA + SSW
 * 18.10 Computational Formulas for SST and SSA
 * 18.11 Degrees of Freedom and Mean Squares
 * 18.12 The F Test
 * 18.13 The ANOVA Table
 * 18.14 Multiple Comparison Tests


 * 18.15 Dtmcan's multiple|Range Test
 * 18.16 Confidence-interval Calculations Following Multiple

Comparisons
 * 18.17 Testing for Homogeneity of Variance
 * 18.18 One-W.ay, Fixed-Effects ANOVA: Equal or Unequal Sample

Sizes
 * 18.19 General-procedure, One-Way, Fixed-effects ANOVA:

Organising the Data
 * 18.20 General-procedure, One-Way, Fixed-effects ANOVA: Sum

of Squares
 * 18.21 General-procedure, One-Way, Fixed-Erects ANOVA

Degrees of Freedom and Mean Squares
 * 18.22 General-procedure, One-Way, Fixed-Effects ANOVA: the

F Test
 * 18.23 General-procedure, One-Way, Fixed-Erects ANOVA: Multiple

Comparisons
 * 18.24 General-procedure, One-Way, Fixed-Effects ANOVA:

Calculating Confidence Intervals and Testing for Homogeneity of Variance
 * 18.25 Violations of ANOVA Assllmptions


 * CHAPTER 19 REGRESSION AND CORRELATION
 * 19.1 Analyzing the Relationship between Two Variables
 * 19.2 The Simple Linear Regression Model
 * 19.3 The Least-squares Regression Line
 * 19.4 The Estimator of the Variance cl.
 * 19.5 Mean and Variance of the y Intercept ; and the Slope I
 * 19.6 Confidence Intervals for the y Intercept a and the Slope b
 * 19.7 Confidence Interval for the Variance Vw
 * 19.8 Prediction Intervals for Expected Values of r
 * 19.9 Testing Hypotheses about the Slope b
 * 19.10 Comparing Simple Linear Regression Equations from Two

or More Snmples
 * 19.11 Multiple Linear Regression
 * 19.12 Simple Linear Correlation
 * 19.13 Derivation of the Correlation Coefficient r
 * 19.14 Confidence Intervals for the Population Correlation

Coefficient p
 * 19.15 Using the r Distribution to Test Hypotheses about the

Population Correlation coefficient p
 * 19.16 Using the f Distribution to Test Hypotheses about p
 * 19.17 Using the Z Distribution to Test the Hypothesis p = c
 * 19.18 Interpreting the Sample Correlation Coefficient r
 * 19.19 Multiple Correlation and Partial Correlation


 * CHAPTER 20

NONPARAMETRIC TECHNIQUES
 * 20.1 Nonpnmmetric vs. Parametric Techniques
 * 20.2 Chi-square Tests
 * 20.3 Chi-square Test for Goodness-of-fit
 * 20.4 Chi-square Test for Independence: Contingency Table

Analysis
 * 20.5 Chi-square Test for Homogeneity Among k Binomial

Proportions
 * 20.6 Rank Order Tests
 * 20.7 One-sample Tests: The Wilcoxon Signed-lbnk Test
 * 20.8 Two-sample Tests: the Wilcoxon Sipled-lbnk| Test for

Dependent Samples
 * 20.9 Two-sample Tests: the Mann-Whitney U Test for

Independent Samples
 * 20.10 Multisample Tests: the Kruskal-Wallis H Test for k

Independent Samples
 * 20.11 The Spearman Test of Rank Correlation


 * Appendix
 * Table A.3 Cumulative Binomial Probabilities
 * Table A.4 Calculative Poisson Probabilities
 * Table A.5 Areas of the Standard Normal Distribution
 * Table A.6 Critical Values of the f Distribution
 * Table A.7 Critical Values of the Chi-square Distribution
 * Table A.8 Critical Values of the F Distribution
 * Table A.9 Least Significant Studentized Ranges rp
 * Table A.10 Transformation of r to zr
 * Table A.11 Critical Values of the Pearson Product-Moment Correlation Coefficient r
 * Table A.12 Critical Values of the Wilcoxon off
 * Table A.13 Critical Values of the Mann-Whi|ey &
 * Table A.14 Critical Values of the Kruskal-Wallis H
 * Table A.15 Critical Values of the Spearman rs


 * Index