Schaum's Outline of Elements of Statistics II: Inferential Statistics

, by Bernstein, Ruth; Bernstein, Stephen

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ISBN: 9780071346375 | 0071346376
Cover: Paperback
Copyright: 9/2/1999

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Picking up where Elements of Statistics I leaves off, this study guide clearly explains discrete probability distribution, including normal, continuing, sampling, and other distributions. The practical, cross-referenced problems throughout are drawn from such fields as anthropology, biology, business, government, medecine, psychology and sociology, and the solutions are fully explained. A perfect supplement to the leading textbooks, students will also find this book ideal for independent study. Supplementary questions aid self-testing.

Discrete Probability Distributions

(45)

Discrete Probability Distributions and Probability Mass Functions

(1)

Bernoulli Experiments and trials

(1)

Binomial Random Variables, Experiments, and Probability Functions

(1)

The Binomial Coefficient

(1)

The Binomial Probability Function

(1)

Mean, Variance, and Standard Deviation of the Binomial Probability Distribution

(1)

The Binomial Expansion and the Binomial Theorem

(2)

Pascal's Triangle and the Binomial Coefficient

(1)

The Family of Binomial Distributions

(2)

The Cumulative Binomial Probability Table

(2)

Lot-Acceptance Sampling

(1)

Consumer's Risk and Producer's Risk

(1)

Multivariate Probability Distributions and Joint Probability Distributions

(2)

The Multinomial Experiment

(1)

The Multinomial Coefficient

(1)

The Multinomial Probability Function

(1)

The Family of Multinomial Probability Distributions

(1)

The Means of the Multinomial Probability Distribution

(1)

The Multinomial Expansion and the Multinomial Theorem

(1)

The Hypergeometric Experiment

(1)

The Hypergeometric Probability Function

(2)

The Family of Hypergeometric Probability Distributions

(1)

The Mean, Variance, and Standard Deviation of the Hypergeometric Probability Distribution

(1)

The Generalization of the Hypergeometric Probability Distribution

(1)

The Binomial and Multinomial Approximations to the Hypergeometric Distribution

(1)

Poisson Processes, Random Variables, and Experiments

(1)

The Poisson Probability Function

(1)

The Family of Poisson Probability Distributions

(1)

The Mean, Variance, and Standard Deviation of the Poisson Probability Distribution

(1)

The Cumulative Poisson Probability Table

(1)

The Poisson Distribution as an Approximation to the Binomial Distribution

(16)

The Normal Distribution and Other Continuous Probability Distributions

(43)

Continuous Probability Distributions

(2)

The Normal Probability Distributions and the Normal Probability Density Function

(1)

The Family of Normal Probability Distributions

(1)

The Normal Distribution: Relationship between the Mean (μ), the Median (μ), and the Mode

(1)

Kurtosis

(1)

The Standard Normal Distribution

(1)

Relationship Between the Standard Normal Distribution and the Standard Normal Variable

(1)

Table of Areas in the Standard Normal Distribution

(2)

Finding Probabilities Within any Normal Distribution by Applying the Z Transformation

(1)

One-tailed Probabilities

(2)

Two-tailed Probabilities

(1)

The Normal Approximation to the Binomial Distribution

(2)

The Normal Approximation to the Poisson Distribution

(1)

The Discrete Uniform Probability Distribution

(2)

The Continuous Uniform Probability Distribution

(1)

The Exponential Probability Distribution

(2)

Relationship between the Exponential Distribution and the Poisson Distribution

(22)

Sampling Distributions

(45)

Simple Random Sampling Revisited

(1)

Independent Random Variables

(1)

Mathematical and Nonmathematical Definitions of Simple Random Sampling

(2)

Assumptions of the Sampling Technique

(1)

The Random Variable X

(1)

Theoretical and Empirical Sampling Distributions of the Mean

(5)

The Mean of the Sampling Distribution of the Mean

(1)

The Accuracy of an Estimator

(1)

The Variance of the Sampling Distribution of the Mean: Infinite Population or Sampling with Replacement

(1)

The Variance of the Sampling Distribution of the Mean: Finite Population Sampled without Replacement

100

(1)

The Standard Error of the Mean

101

(1)

The Precision of an Estimator

102

(1)

Determining Probabilities with a Discrete Sampling Distribution of the Mean

103

(1)

Determining Probabilities with a Normally Distributed Sampling Distribution of the Mean

103

(1)

The Central Limit Theorem: Sampling from a Finite Population with Replacement

104

(4)

The Central Limit Theorem: Sampling from an Infinite Population

108

(1)

The Central Limit Theorem: Sampling from a Finite Population without Replacement

108

(1)

How Large is ``Sufficiently Large?''

108

(1)

The Sampling Distribution of the Sample Sum

109

(1)

Applying the Central Limit Theorem to the Sampling Distribution of the Sample Sum

110

(1)

Sampling from a Binomial Population

111

(2)

Sampling Distribution of the Number of Successes

113

(1)

Sampling Distribution of the Proportion

113

(1)

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

114

(1)

Applying the Central Limit Theorem to the Sampling Distribution of the Proportion

115

(1)

Determining Probabilities with a Normal Approximation to the Sampling Distribution of the Proportion

116

(18)

One-Sample Estimation of the Population Mean

134

(39)

Estimation

134

(1)

Criteria for Selecting the Optimal Estimator

135

(1)

The Estimated Standard Error of the Mean Sx

136

(1)

Point Estimates

136

(1)

Reporting and Evaluating the Point Estimate

137

(1)

Relationship between Point Estimates and Interval Estimates

138

(1)

Deriving

138

(1)

Deriving

139

(2)

Confidence Interval for the Population Mean μ: Known Standard Deviation σ, Normally Distributed Population

141

(1)

Presenting Confidence Limits

142

(1)

Precision of the Confidence Interval

142

(2)

Determining Sample Size when the Standard Deviation is Known

144

(1)

Confidence Interval for the Population Mean μ Known Standard Deviation σ Large Sample (n ≥ 30) from any Population Distribution

145

(1)

Determining Confidence Intervals for the Population Mean μ when the Population Standard Deviation σ is Unknown

146

(1)

The t Distribution

146

(2)

Relationship between the t Distribution and the Standard Normal Distribution

148

(1)

Degrees of Freedom

148

(1)

The Term ``Student's t Distribution''

149

(1)

Critical Values of the t Distribution

149

(2)

Table A.6: Critical Values of the t Distribution

151

(2)

Confidence Interval for the Population Mean μ: Standard Deviation σ not known, Small Sample (n < 30) from a Normally Distributed Population

153

(2)

Determining Sample Size: Unknown Standard Deviation, Small Sample from a Normally Distributed Population

155

(1)

Confidence Interval for the Population Mean μ Standard Deviation σ not known, large sample (n ≥ 30) from a Normally Distributed Population

156

(2)

Confidence Interval for the Population Mean μ: Standard Deviation σ not known, Large Sample (n ≥ 30) from a Population that is not Normally Distributed

158

(1)

Confidence Interval for the Population Mean μ: Small Sample (n < 30) from a Population that is not Normally Distributed

158

(15)

One-Sample Estimation of the Population Variance, Standard Deviation, and Proportion

173

(32)

Optimal Estimators of Variance, Standard Deviation, and Proportion

173

(1)

The Chi-Square Statistic and the Chi-Square Distribution

174

(1)

Critical Values of the Chi-Square Distribution

175

(2)

Table A.7: Critical Values of the Chi-Square Distribution

177

(1)

Deriving the Confidence Interval for the Variance σ2 of a Normally Distributed Population

178

(1)

Presenting Confidence Limits

179

(1)

Precision of the Confidence Interval for the Variance

180

(1)

Determining Sample Size Necessary to Achieve a Desired Quality-of-Estimate for the Variance

181

(1)

Using Normal-Approximation Techniques To Determine Confidence Intervals for the Variance

181

(1)

Using the Sampling Distribution of the Sample Variance to Approximate a Confidence Interval for the Population Variance

182

(1)

Confidence Interval for the Standard Deviation σ of a Normally Distributed Population

183

(1)

Using the Sampling Distribution of the Sample Standard Deviation to Approximate a Confidence Interval for the Population Standard Deviation

184

(1)

The Optimal Estimator for the Proportion p of a Binomial Population

185

(1)

Deriving the Approximate Confidence Interval for the Proportion p of a Binomial Population

186

(1)

Estimating the Parameter p

187

(1)

Deciding when n is ``Sufficiently Large'', p not known

188

(1)

Approximate Confidence Intervals for the Binomial Parameter p When Sampling From a Finite Population without Replacement

188

(1)

The Exact Confidence Interval for the Binomial Parameter p

189

(1)

Precision of the Approximate Confidence-Interval Estimate of the Binomial Parameter p

189

(1)

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

189

(2)

Approximate Confidence Interval for the Percentage of a Binomial Population

191

(1)

Approximate Confidence Interval for the Total Number in a Category of a Binomial Population

192

(1)

The Capture--Recapture Method for Estimating Population Size N

192

(13)

One-Sample Hypothesis Testing

205

(42)

Statistical Hypothesis Testing

205

(1)

The Null Hypothesis and the Alternative Hypothesis

205

(1)

Testing the Null Hypothesis

206

(1)

Two-Sided Versus One-Sided Hypothesis Tests

207

(1)

Testing Hypotheses about the Population Mean μ: Known Standard Deviation σ, Normally Distributed Population

207

(1)

The P Value

208

(1)

Type I Error versus Type II Error

209

(1)

Critical Values and Critical Regions

210

(2)

The Level of Significance

212

(1)

Decision Rules for Statistical Hypothesis Tests

213

(1)

Selecting Statistical Hypotheses

214

(1)

The Probability of a Type II Error

214

(1)

Consumer's Risk and Producer's Risk

215

(1)

Why It is Not Possible to Prove the Null Hypothesis

216

(1)

Classical Inference Versus Bayesian Inference

216

(1)

Procedure for Testing the Null Hypothesis

217

(1)

Hypothesis Testing Using X as the Test Statistic

218

(1)

The Power of a Test, Operating Characteristic Curves, and Power Curves

219

(2)

Testing Hypothesis about the Population Mean μ: Standard Deviation σ Not Known, Small Sample (n < 30) from a Normally Distributed Population

221

(1)

The P Value for the t Statistic

221

(1)

Decision Rules for Hypothesis Tests with the t Statistic

222

(1)

β, 1 --- β, Power Curves, and OC Curves

223

(1)

Testing Hypotheses about the Population Mean μ: Large Sample (n ≥ 30) from any Population Distribution

223

(1)

Assumptions of One-Sample Parametric Hypothesis Testing

224

(1)

When the Assumptions are Violated

225

(1)

Testing Hypothesis about the Variance σ2 of a Normally Distributed Population

226

(1)

Testing Hypotheses about the Standard Deviation σ of a Normally Distributed Population

227

(1)

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

228

(1)

Testing Hypotheses about the Proportion p of a Binomial Population: Small Samples

229

(18)

Two-Sample Estimation and Hypothesis Testing

247

(49)

Independent Samples Versus Paired Samples

247

(1)

The Optimal Estimator of the Difference Between Two Population Means (μ1 --- μ2)

248

(1)

The Theoretical Sampling Distribution of the Difference Between Two Means

248

(1)

Confidence Interval for the Difference Between Means (μ1 --- μ2): Standard Deviations (σ1 and σ2) Known, Independent Samples from Normally Distributed Populations

249

(1)

Testing Hypotheses about the Difference Between Means (μ1 --- μ2): Standard Deviations (σ1 and σ2) known, Independent Samples from Normally Distributed Populations

250

(2)

The Estimated Standard Error of the Difference Between Two Means

252

(1)

Confidence Interval for the Difference Between Means (μ1 --- μ2): Standard Deviations not known but Assumed Equal (σ1 = σ2), Small (n1 < 30 and n2 < 30) Independent Samples from Normally Distributed Populations

253

(1)

Testing Hypotheses about the Difference Between Means (μ1 --- μ2): Standard Deviations not Known but Assumed Equal (σ1 = σ2), Small (n1 < 30 and n2 < 30) Independent Samples from Normally Distributed Populations

254

(1)

Confidence Interval for the Difference Between Means (μ1 --- μ2): Standard Deviations (σ1 = σ2) not Known, Large (n1 < 30 and n2 < 30) Independent Samples from any Population Distributions

255

(1)

Testing Hypotheses about the Difference Between Means (μ1 --- μ2): Standard Deviations (σ1 = σ2), not known, Large (n1 ≥ 30 and n2 ≥ 30) Independent Samples from any Populations Distributions

256

(1)

Confidence Interval for the Difference Between Means (μ1 --- μ2): Paired Samples

257

(3)

Testing Hypotheses about the Difference Between Means (μ1 --- μ2): Paired Samples

260

(1)

Assumptions of Two-Sample Parametric Estimation and Hypothesis Testing about Means

261

(1)

When the Assumptions are Violated

262

(1)

Comparing Independent-Sampling and Paired-Sampling Techniques on Precision and Power

263

(1)

The F Statistic

263

(1)

The F Distribution

264

(2)

Critical Values of the F Distribution

266

(2)

Table A.8: Critical Values of the F Distribution

268

(1)

Confidence Interval for the Ratio of Variances Parameters Not Known Independent Samples From Normally Distributed Populations

269

(1)

Testing Hypotheses about the Ratio of Variances Parameters not known, Independent Samples from Normally Distributed Populations

270

(2)

When to Test for Homogeneity of Variance

272

(1)

The Optimal Estimator of the Difference Between Proportions (p1 --- p2): large Independent Samples

273

(1)

The Theoretical Sampling Distribution of the Difference Between Two Proportions

273

(1)

Approximate Confidence Interval for the Difference Between Proportions from Two Binomial Populations (p1 --- p2): Large Independent Samples

274

(2)

Testing Hypotheses about the Difference Between Proportions from Two Binomial Populations (p1 --- p2): Large Independent Samples

276

(20)

Multisample Estimation and Hypothesis Testing

296

(37)

Multisample Inferences

296

(1)

The Analysis of Variance

296

(1)

ANOVA: One-Way, Two-Way, or Multiway

297

(1)

One-Way, ANOVA: Fixed-Effects or Random Effects

297

(1)

One-way, Fixed-Effects ANOVA: The Assumptions

298

(1)

Equal-Samples, One-Way, Fixed-Effects ANOVA: H0 and H1

298

(1)

Equal-Samples, One-Way, Fixed-Effects ANOVA: Organizing the Data

298

(2)

Equal-Samples, One-Way, Fixed-Effects ANOVA: the Basic Rationale

300

(1)

SST = SSA + SSW

301

(1)

Computational Formulas for SST and SSA

302

(1)

Degrees of Freedom and Mean Squares

302

(2)

The F Test

304

(2)

The ANOVA Table

306

(1)

Multiple Comparison Tests

306

(1)

Duncan's Multiple-Range Test

307

(1)

Confidence-Interval Calculations Following Multiple Comparisons

308

(1)

Testing for Homogeneity of Variance

309

(2)

One-Way, Fixed-Effects ANOVA: Equal or Unequal Sample Sizes

311

(1)

General-Procedure, One-Way, Fixed-effects ANOVA: Organizing the Data

312

(1)

General-Procedure, One-Way, Fixed-effects ANOVA: Sum of Squares

312

(1)

General-Procedure, One-Way, Fixed-Effects ANOVA Degrees of Freedom and Mean Squares

313

(1)

General-Procedure, One-Way, Fixed-Effects ANOVA: the F Test

314

(1)

General-Procedure, One-Way, Fixed-Effects ANOVA: Multiple Comparisons

314

(2)

General-Procedure, One-Way, Fixed-Effects ANOVA: Calculating Confidence Intervals and Testing for Homogeneity of Variance

316

(1)

Violations of ANOVA Assumptions

317

(16)

Regression and Correlation

333

(46)

Analyzing the Relationship between Two Variables

333

(1)

The Simple Linear Regression Model

334

(1)

The Least-Squares Regression Line

335

(3)

The Estimator of the Variance σ2y.x

338

(1)

Mean and Variance of the y Intercept a and the Slope b

338

(1)

Confidence Intervals for the y Intercept a and the Slope b

339

(2)

Confidence Interval for the Variance σ2y.x

341

(1)

Prediction Intervals for Expected Values of Y

341

(1)

Testing Hypotheses about the Slope b

342

(1)

Comparing Simple Linear Regression Equations from Two or More Samples

343

(1)

Multiple Linear Regression

343

(1)

Simple Linear Correlation

344

(1)

Derivation of the Correlation Coefficient r

344

(5)

Confidence Intervals for the Population Correlation Coefficient p

349

(1)

Using the r Distribution to Test Hypotheses about the Population Correlation Coefficient p

350

(1)

Using the t Distribution to Test Hypotheses about p

351

(1)

Using the Z Distribution to Test the Hypothesis p = c

352

(1)

Interpreting the Sample Correlation Coefficient r

353

(1)

Multiple Correlation and Partial Correlation

354

(25)

Nonparametric Techniques

379

(45)

Nonparametric vs. Parametric Techniques

379

(1)

Chi-Square Tests

379

(1)

Chi-Square Test for Goodness-of-fit

380

(1)

Chi-Square Test for Independence: Contingency Table Analysis

381

(2)

Chi-Square Test for Homogeneity Among k Binomial Proportions

383

(2)

Rank Order Tests

385

(1)

One-Sample Tests: The Wilcoxon Signed-Rank Test

385

(2)

Two-Sample Tests: the Wilcoxon Signed-Rank Test for Dependent Samples

387

(2)

Two-Sample Tests: the Mann-Whitney U Test for Independent Samples

389

(3)

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

392

(2)

The Spearman Test of Rank Correlation

394

(30)

Appendix

424

(20)

Table A.3 Cumulative Binomial Probabilities

424

(2)

Table A.4 Cumulative Poisson Probabilities

426

(1)

Table A.5 Areas of the Standard Normal Distribution

427

(1)

Table A.6 Critical Values of the t Distribution

428

(1)

Table A.7 Critical Values of the Chi-Square Distribution

429

(1)

Table A.8 Critical Values of the F Distribution

430

(6)

Table A.9 Least Significant Studentized Ranges rp

436

(1)

Table A.10 Transformation of r to zr

437

(2)

Table A.11 Critical Values of the Person Product-Moment Correlation Coefficient r

439

(1)

Table A.12 Critical Values of the Wilcoxon W

440

(1)

Table A.13 Critical Values of the Mann-Whitney U

441

(1)

Table A.14 Critical Values of the Kruskal-Wallis H

442

(1)

Table A.15 Critical Values of the Spearman rs

443

(1)

Index

444

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Schaum's Outline of Elements of Statistics II: Inferential Statistics

Summary

Author Biography

Table of Contents

Supplemental Materials