Paperback
Published: 2nd September 1999
ISBN: 9780071346375
Number Of Pages: 350
The book is the second half of a comprehensive outline of statistics, presenting the material in a user-friendly question-and-answer format. "Elements of Statistics II" will benefit students in beginning statistics courses, and is geared to students who need to know statistics in their specific field of study, which may range from business to the social sciences. It continues the introduction to general statistics begun in "Elements of Statistics I: Descriptive Statistics and Probability", and covers the material with added focus on inferential statistics. It provides an integrated step-by-step presentation with problems cross-referenced throughout.
Discrete Probability Distributions | p. 1 |
Discrete Probability Distributions and Probability Mass Functions | p. 1 |
Bernoulli Experiments and trials | p. 1 |
Binomial Random Variables, Experiments, and Probability Functions | p. 2 |
The Binomial Coefficient | p. 3 |
The Binomial Probability Function | p. 4 |
Mean, Variance, and Standard Deviation of the Binomial Probability Distribution | p. 5 |
The Binomial Expansion and the Binomial Theorem | p. 6 |
Pascal's Triangle and the Binomial Coefficient | p. 8 |
The Family of Binomial Distributions | p. 8 |
The Cumulative Binomial Probability Table | p. 10 |
Lot-Acceptance Sampling | p. 12 |
Consumer's Risk and Producer's Risk | p. 13 |
Multivariate Probability Distributions and Joint Probability Distributions | p. 14 |
The Multinomial Experiment | p. 16 |
The Multinomial Coefficient | p. 16 |
The Multinomial Probability Function | p. 17 |
The Family of Multinomial Probability Distributions | p. 18 |
The Means of the Multinomial Probability Distribution | p. 19 |
The Multinomial Expansion and the Multinomial Theorem | p. 19 |
The Hypergeometric Experiment | p. 20 |
The Hypergeometric Probability Function | p. 20 |
The Family of Hypergeometric Probability Distributions | p. 22 |
The Mean, Variance, and Standard Deviation of the Hypergeometric Probability Distribution | p. 23 |
The Generalization of the Hypergeometric Probability Distribution | p. 24 |
The Binomial and Multinomial Approximations to the Hypergeometric Distribution | p. 24 |
Poisson Processes, Random Variables, and Experiments | p. 25 |
The Poisson Probability Function | p. 26 |
The Family of Poisson Probability Distributions | p. 27 |
The Mean, Variance, and Standard Deviation of the Poisson Probability Distribution | p. 28 |
The Cumulative Poisson Probability Table | p. 29 |
The Poisson Distribution as an Approximation to the Binomial Distribution | p. 30 |
The Normal Distribution and Other Continuous Probability Distributions | p. 46 |
Continuous Probability Distributions | p. 46 |
The Normal Probability Distributions and the Normal Probability Density Function | p. 48 |
The Family of Normal Probability Distributions | p. 49 |
The Normal Distribution: Relationship between the Mean ([mu]), the Median ([mu]), and the Mode | p. 50 |
Kurtosis | p. 50 |
The Standard Normal Distribution | p. 51 |
Relationship Between the Standard Normal Distribution and the Standard Normal Variable | p. 52 |
Table of Areas in the Standard Normal Distribution | p. 53 |
Finding Probabilities Within any Normal Distribution by Applying the Z Transformation | p. 55 |
One-tailed Probabilities | p. 56 |
Two-tailed Probabilities | p. 58 |
The Normal Approximation to the Binomial Distribution | p. 59 |
The Normal Approximation to the Poisson Distribution | p. 61 |
The Discrete Uniform Probability Distribution | p. 62 |
The Continuous Uniform Probability Distribution | p. 64 |
The Exponential Probability Distribution | p. 65 |
Relationship between the Exponential Distribution and the Poisson Distribution | p. 67 |
Sampling Distributions | p. 89 |
Simple Random Sampling Revisited | p. 89 |
Independent Random Variables | p. 89 |
Mathematical and Nonmathematical Definitions of Simple Random Sampling | p. 90 |
Assumptions of the Sampling Technique | p. 92 |
The Random Variable X | p. 92 |
Theoretical and Empirical Sampling Distributions of the Mean | p. 93 |
The Mean of the Sampling Distribution of the Mean | p. 98 |
The Accuracy of an Estimator | p. 99 |
The Variance of the Sampling Distribution of the Mean: Infinite Population or Sampling with Replacement | p. 99 |
The Variance of the Sampling Distribution of the Mean: Finite Population Sampled without Replacement | p. 100 |
The Standard Error of the Mean | p. 101 |
The Precision of An Estimator | p. 102 |
Determining Probabilities with a Discrete Sampling Distribution of the Mean | p. 103 |
Determining Probabilities with a Normally Distributed Sampling Distribution of the Mean | p. 103 |
The Central Limit Theorem: Sampling from a Finite Population with Replacement | p. 104 |
The Central Limit Theorem: Sampling from an Infinite Population | p. 108 |
The Central Limit Theorem: Sampling from a Finite Population without Replacement | p. 108 |
How Large is "Sufficiently Large?" | p. 108 |
The Sampling Distribution of the Sample Sum | p. 109 |
Applying the Central Limit Theorem to the Sampling Distribution of the Sample Sum | p. 110 |
Sampling from a Binomial Population | p. 111 |
Sampling Distribution of the Number of Successes | p. 113 |
Sampling Distribution of the Proportion | p. 113 |
Applying the Central Limit Theorem to the Sampling Distribution of the Number of Successes | p. 114 |
Applying the Central Limit Theorem to the Sampling Distribution of the Proportion | p. 115 |
Determining Probabilities with a Normal Approximation to the Sampling Distribution of the Proportion | p. 116 |
One-Sample Estimation of The Population Mean | p. 134 |
Estimation | p. 134 |
Criteria for Selecting the Optimal Estimator | p. 135 |
The Estimated Standard Error of the Mean S[subscript x] | p. 136 |
Point Estimates | p. 136 |
Reporting and Evaluating the Point Estimate | p. 137 |
Relationship between Point Estimates and Interval Estimates | p. 138 |
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] | p. 138 |
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] | p. 139 |
Confidence Interval for the Population Mean [mu]: Known Standard Deviation [sigma], Normally Distributed Population | p. 141 |
Presenting Confidence Limits | p. 142 |
Precision of the Confidence Interval | p. 142 |
Determining Sample Size when the Standard Deviation is Known | p. 144 |
Confidence Interval for the Population Mean [mu]: Known Standard Deviation [sigma], Large Sample (n [greater than or equal] 30) from any Population Distribution | p. 145 |
Determining Confidence Intervals for the Population Mean [mu] when the Population Standard Deviation [sigma] is Unknown | p. 146 |
The t Distribution | p. 146 |
Relationship between the t Distribution and the Standard Normal Distribution | p. 148 |
Degrees of Freedom | p. 148 |
The Term "Student's t Distribution" | p. 149 |
Critical Values of the t Distribution | p. 149 |
Table A.6: Critical Values of the t Distribution | p. 151 |
Confidence Interval for the Population Mean [mu]: Standard Deviation [sigma] not known, Small Sample (n [ 30) from a Normally Distributed Population | p. 153 |
Determining Sample Size: Unknown Standard Deviation, Small Sample from a Normally Distributed Population | p. 155 |
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 | p. 156 |
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 | p. 158 |
Confidence Interval for the Population Mean [mu]: Small Sample (n [ 30) from a Population that is not Normally Distributed | p. 158 |
One-Sample Estimation of the Population Variance, Standard Deviation, and Proportion | p. 173 |
Optimal Estimators of Variance, Standard Deviation, and Proportion | p. 173 |
The Chi-Square Statistic and the Chi-Square Distribution | p. 174 |
Critical Values of the Chi-Square Distribution | p. 175 |
Table A.7: Critical Values of the Chi-Square Distribution | p. 177 |
Deriving the Confidence Interval for the Variance [sigma superscript 2] of a Normally Distributed Population | p. 178 |
Presenting Confidence Limits | p. 179 |
Precision of the Confidence Interval for the Variance | p. 180 |
Determining Sample Size Necessary to Achieve a Desired Quality-of-Estimate for the Variance | p. 181 |
Using Normal-Approximation Techniques To Determine Confidence Intervals for the Variance | p. 181 |
Using the Sampling Distribution of the Sample Variance to Approximate a Confidence Interval for the Population Variance | p. 182 |
Confidence Interval for the Standard Deviation [sigma] of a Normally Distributed Population | p. 183 |
Using the Sampling Distribution of the Sample Standard Deviation to Approximate a Confidence Interval for the Population Standard Deviation | p. 184 |
The Optimal Estimator for the Proportion p of a Binomial Population | p. 185 |
Deriving the Approximate Confidence Interval for the Proportion p of a Binomial Population | p. 186 |
Estimating the Parameter p | p. 187 |
Deciding when n is "Sufficiently Large", p not known | p. 188 |
Approximate Confidence Intervals for the Binomial Parameter p When Sampling From a Finite Population without Replacement | p. 188 |
The Exact Confidence Interval for the Binomial Parameter p | p. 189 |
Precision of the Approximate Confidence-Interval Estimate of the Binomial Parameter p | p. 189 |
Determining Sample Size for the Confidence Interval of the Binomial Parameter p | p. 189 |
Approximate Confidence Interval for the Percentage of a Binomial Population | p. 191 |
Approximate Confidence Interval for the Total Number in a Category of a Binomial Population | p. 192 |
The Capture--Recapture Method for Estimating Population Size N | p. 192 |
One-Sample Hypothesis Testing | p. 205 |
Statistical Hypothesis Testing | p. 205 |
The Null Hypothesis and the Alternative Hypothesis | p. 205 |
Testing the Null Hypothesis | p. 206 |
Two-Sided Versus One-Sided Hypothesis Tests | p. 207 |
Testing Hypotheses about the Population Mean [mu]: Known Standard Deviation [sigma], Normally Distributed Population | p. 207 |
The P Value | p. 208 |
Type I Error versus Type II Error | p. 209 |
Critical Values and Critical Regions | p. 210 |
The Level of Significance | p. 212 |
Decision Rules for Statistical Hypothesis Tests | p. 213 |
Selecting Statistical Hypotheses | p. 214 |
The Probability of a Type II Error | p. 214 |
Consumer's Risk and Producer's Risk | p. 215 |
Why It is Not Possible to Prove the Null Hypothesis | p. 216 |
Classical Inference Versus Bayesian Inference | p. 216 |
Procedure for Testing the Null Hypothesis | p. 217 |
Hypothesis Testing Using X as the Test Statistic | p. 218 |
The Power of a Test, Operating Characteristic Curves, and Power Curves | p. 219 |
Testing Hypothesis about the Population Mean [mu]: Standard Deviation [sigma] Not Known, Small Sample (n [ 30) from a Normally Distributed Population | p. 221 |
The P Value for the t Statistic | p. 221 |
Decision Rules for Hypothesis Tests with the t Statistic | p. 222 |
[beta], 1 - [beta], Power Curves, and OC Curves | p. 223 |
Testing Hypotheses about the Population Mean [mu]: Large Sample (n [greater than or equal] 30) from any Population Distribution | p. 223 |
Assumptions of One-Sample Parametric Hypothesis Testing | p. 224 |
When the Assumptions are Violated | p. 225 |
Testing Hypothesis about the Variance [sigma superscript 2] of a Normally Distributed Population | p. 226 |
Testing Hypotheses about the Standard Deviation [sigma] of a Normally Distributed Population | p. 227 |
Testing Hypotheses about the Proportion p of a Binomial Population: Large Samples | p. 228 |
Testing Hypotheses about the Proportion p of a Binomial Population: Small Samples | p. 229 |
Two-Sample Estimation and Hypothesis Testing | p. 247 |
Independent Samples Versus Paired Samples | p. 247 |
The Optimal Estimator of the Difference Between Two Population Means ([mu subscript 1] - [mu subscript 2]) | p. 248 |
The Theoretical Sampling Distribution of the Difference Between Two Means | p. 248 |
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 | p. 249 |
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 | p. 250 |
The Estimated Standard Error of the Difference Between Two Means | p. 252 |
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 | p. 253 |
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 | p. 254 |
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 | p. 255 |
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 | p. 256 |
Confidence Interval for the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Paired Samples | p. 257 |
Testing Hypotheses about the Difference Between Means ([mu subscript 1] - [mu subscript 2]): Paired Samples | p. 260 |
Assumptions of Two-Sample Parametric Estimation and Hypothesis Testing about Means | p. 261 |
When the Assumptions are Violated | p. 262 |
Comparing Independent-Sampling and Paired-Sampling Techniques on Precision and Power | p. 263 |
The F Statistic | p. 263 |
The F Distribution | p. 264 |
Critical Values of the F Distribution | p. 266 |
Table A.8: Critical Values of the F Distribution | p. 268 |
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 | p. 269 |
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 | p. 270 |
When to Test for Homogeneity of Variance | p. 272 |
The Optimal Estimator of the Difference Between Proportions (p[subscript 1] - p[subscript 2]): Large Independent Samples | p. 273 |
The Theoretical Sampling Distribution of the Difference Between Two Proportions | p. 273 |
Approximate Confidence Interval for the Difference Between Proportions from Two Binomial Populations (p[subscript 1] - p[subscript 2]): Large Independent Samples | p. 274 |
Testing Hypotheses about the Difference Between Proportions from Two Binomial Populations (p[subscript 1] - p[subscript 2]): Large Independent Samples | p. 276 |
Multisample Estimation and Hypothesis Testing | p. 296 |
Multisample Inferences | p. 296 |
The Analysis of Variance | p. 296 |
Anova: One-Way, Two-Way, or Multiway | p. 297 |
One-Way Anova: Fixed-Effects or Random Effects | p. 297 |
One-way, Fixed-Effects Anova: The Assumptions | p. 298 |
Equal-Samples, One-Way, Fixed-Effects Anova: H[subscript 0] and H[subscript 1] | p. 298 |
Equal-Samples, One-Way, Fixed-Effects Anova: Organizing the Data | p. 298 |
Equal-Samples, One-Way, Fixed-Effects Anova: the Basic Rationale | p. 300 |
SST = SSA + SSW | p. 301 |
Computational Formulas for SST and SSA | p. 302 |
Degrees of Freedom and Mean Squares | p. 302 |
The F Test | p. 304 |
The Anova Table | p. 306 |
Multiple Comparison Tests | p. 306 |
Duncan's Multiple-Range Test | p. 307 |
Confidence-Interval Calculations Following Multiple Comparisons | p. 308 |
Testing for Homogeneity of Variance | p. 309 |
One-Way, Fixed-Effects ANOVA: Equal or Unequal Sample Sizes | p. 311 |
General-Procedure, One-Way, Fixed-effects ANOVA: Organizing the Data | p. 312 |
General-Procedure, One-Way, Fixed-effects ANOVA: Sum of Squares | p. 312 |
General-Procedure, One-Way, Fixed-Effects ANOVA Degrees of Freedom and Mean Squares | p. 313 |
General-Procedure, One-Way, Fixed-Effects ANOVA: the F Test | p. 314 |
General-Procedure, One-Way, Fixed-Effects ANOVA: Multiple Comparisons | p. 314 |
General-Procedure, One-Way, Fixed-Effects ANOVA: Calculating Confidence Intervals and Testing for Homogeneity of Variance | p. 316 |
Violations of ANOVA Assumptions | p. 317 |
Regression and Correlation | p. 333 |
Analyzing the Relationship between Two Variables | p. 333 |
The Simple Linear Regression Model | p. 334 |
The Least-Squares Regression Line | p. 335 |
The Estimator of the Variance [sigma superscript 2 subscript Y times X] | p. 338 |
Mean and Variance of the y Intercept a and the Slope b | p. 338 |
Confidence Intervals for the y Intercept a and the Slope b | p. 339 |
Confidence Interval for the Variance [sigma superscript 2 subscript Y times X] | p. 341 |
Prediction Intervals for Expected Values of Y | p. 341 |
Testing Hypotheses about the Slope b | p. 342 |
Comparing Simple Linear Regression Equations from Two or More Samples | p. 343 |
Multiple Linear Regression | p. 343 |
Simple Linear Correlation | p. 344 |
Derivation of the Correlation Coefficient r | p. 344 |
Confidence Intervals for the Population Correlation Coefficient [rho] | p. 349 |
Using the r Distribution to Test Hypotheses about the Population Correlation Coefficient [rho] | p. 350 |
Using the t Distribution to Test Hypotheses about p | p. 351 |
Using the Z Distribution to Test the Hypothesis [rho] = c | p. 352 |
Interpreting the Sample Correlation Coefficient r | p. 353 |
Multiple Correlation and Partial Correlation | p. 354 |
Nonparametric Techniques | p. 379 |
Nonparametric vs. Parametric Techniques | p. 379 |
Chi-Square Tests | p. 379 |
Chi-Square Test for Goodness-of-fit | p. 380 |
Chi-Square Test for Independence: Contingency Table Analysis | p. 381 |
Chi-Square Test for Homogeneity Among k Binomial Proportions | p. 383 |
Rank Order Tests | p. 385 |
One-Sample Tests: The Wilcoxon Signed-Rank Test | p. 385 |
Two-Sample Tests: the Wilcoxon Signed-Rank Test for Dependent Samples | p. 387 |
Two-Sample Tests: the Mann-Whitney U Test for Independent Samples | p. 389 |
Multisample Tests: the Kruskal-Wallis H Test for k Independent Samples | p. 392 |
The Spearman Test of Rank Correlation | p. 394 |
Appendix | p. 424 |
Cumulative Binomial Probabilities | p. 424 |
Cumulative Poisson Probabilities | p. 426 |
Areas of the Standard Normal Distribution | p. 427 |
Critical Values of the t Distribution | p. 428 |
Critical Values of the Chi-Square Distribution | p. 429 |
Critical Values of the F Distribution | p. 430 |
Least Significant Studentized Ranges r[subscript p] | p. 436 |
Transformation of r to z[subscript r] | p. 437 |
Critical Values of the Pearson Product-Moment Correlation Coefficient r | p. 439 |
Critical Values of the Wilcoxon W | p. 440 |
Critical Values of the Mann-Whitney U | p. 441 |
Critical Values of the Kruskal-Wallis H | p. 442 |
Critical Values of the Spearman r[subscript S] | p. 443 |
Index | p. 444 |
Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9780071346375
ISBN-10: 0071346376
Series: Schaum's Outlines
Audience:
Tertiary; University or College
Format:
Paperback
Language:
English
Number Of Pages: 350
Published: 2nd September 1999
Publisher: McGraw-Hill Education - Europe
Country of Publication: US
Dimensions (cm): 27.5 x 20.8
x 2.4
Weight (kg): 0.84
Edition Number: 1