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Standard Normal Distribution Table, IFC-1
Copyright, iv
About the Authors, vii
Preface, xix
Chapter 1. Describing Data: Graphical, 1
1.1. Decision Making in an Uncertain Environment, 2
1.2. Classification of Variables, 4
Categorical or Numerical, 4
Measurement Levels, 5
1.3. Graphs to Describe Categorical Variables, 7
Tables, 7
Bar Charts and Pie Charts, 8
Pareto Diagrams, 12
1.4. Graphs to Describe Time-Series Data, 16
1.5. Graphs to Describe Numerical Variables, 19
Frequency Distributions, 19
Histograms and Ogives, 22
Stem-and-Leaf Displays, 23
1.6. Tables and Graphs to Describe Relationships between Variables, 26
Scatter Plots, 26
Cross Tables, 28
1.7. Data Presentation Errors, 33
Misleading Histograms, 33
Misleading Time-Series Plots, 36
Chapter 2. Describing Data: Numerical, 43
2.1. Measures of Central Tendency, 43
Mean, Median, Mode, 43
Shape of a Distribution, 46
Geometric Mean, 49
2.2. Measures of Variability, 51
Range and Interquartile Range, 52
Variance and Standard Deviation, 54
Coefficient of Variation, 57
Chebychev’s Theorem and the Empirical Rule, 59
2.3. Weighted Mean and Measures of Grouped Data, 62
2.4. Measures of Relationships between Variables, 67
Chapter 3. Probability, 77
3.1. Random Experiment, Outcomes, and Events, 78
3.2. Probability and Its Postulates, 85
Classical Probability, 86
Permutations and Combinations, 87
Relative Frequency, 91
Subjective Probability, 92
3.3. Probability Rules, 97
Conditional Probability, 99
Statistical Independence, 103
3.4. Bivariate Probabilities, 110
Odds, 114
Overinvolvement Ratios, 114
3.5. Bayes’ Theorem, 121
Chapter 4. Discrete Random Variables and Probability Distributions, 136
4.1. Random Variables, 137
4.2. Probability Distributions for Discrete Random Variables, 139
4.3. Properties of Discrete Random Variables, 142
Expected Value of a Discrete Random Variable, 143
Variance of a Discrete Random Variable, 144
Mean and Variance of Linear Functions of a Random Variable, 146
4.4. Binomial Distribution, 151
4.5. Hypergeometric Distribution, 159
4.6. The Poisson Probability Distribution, 162
Poisson Approximation to the Binomial Distribution, 166
Comparison of the Poisson and Binomial Probability Distributions, 167
4.7. Jointly Distributed Discrete Random Variables, 169
Conditional Mean and Variance, 173
Computer Applications, 173
Linear Functions of Random Variables, 174
Covariance, 175
Correlation, 175
Portfolio Analysis, 180
Chapter 5. Continuous Random Variables and Probability Distributions, 192
5.1. Continuous Random Variables, 193
The Uniform Distribution, 196
5.2. Expectations for Continuous Random Variables, 198
5.3. The Normal Distribution, 201
Normal Probability Plots, 210
5.4. Normal Distribution Approximation for Binomial Distribution, 215
Proportion Random Variable, 219
5.5. The Exponential Distribution, 221
5.6. Jointly Distributed Continuous Random Variables, 225
Linear Combinations of Random Variables, 228
Financial Investment Portfolios, 229
Chapter 6. Sampling and Sampling Distributions, 241
6.1. Sampling from a Population, 242
6.2. Sampling Distributions of Sample Means, 247
Central Limit Theorem, 252
Acceptance Intervals, 259
6.3. Sampling Distributions of Sample Proportions, 265
6.4. Sampling Distributions of Sample Variances, 270
Chapter 7. Estimation: Single Population, 286
7.1. Properties of Point Estimators, 287
Unbiased Estimator, 288
Efficient Estimator, 289
7.2. Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known, 293
Intervals Based on the Normal Distribution, 294
Reducing Margin of Error, 297
7.3. Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Unknown, 299
Student’s t Distribution, 300
Intervals Based on the Student’s t Distribution, 302
7.4. Confidence Interval Estimation for Population Proportion (Large Samples), 306
7.5. Confidence Interval Estimation for the Variance of a Normal Distribution, 310
7.6. Confidence Interval Estimation: Finite Populations, 314
Population Mean and Population Total, 314
Population Proportion, 317
Chapter 8. Estimation: Additional Topics, 325
8.1. Confidence Interval Estimation of the Difference Between Two Normal Population Means: Dependent Samples, 326
8.2. Confidence Interval Estimation of the Difference Between Two Normal Population Means: Independent Samples, 331
Two Means, Independent Samples, and Known Population Variances, 331
Two Means, Independent Samples, and Population Variances Assumed to Be Equal, 333
Two Means, Independent Samples, and Population Variances Not Assumed to Be Equal, 335
8.3. Confidence Interval Estimation of the Difference Between Two Population Proportions (Large Samples), 338
8.4. Sample Size Determination: Large Populations, 341
Mean of a Normally Distributed Population, Known Population Variance, 341
Population Proportion, 343
8.5. Sample Size Determination: Finite Populations, 345
Sample Sizes for Simple Random Sampling: Estimation of the Population Mean or Total, 345
Sample Sizes for Simple Random Sampling: Estimation of Population Proportion, 347
Chapter 9. Hypothesis Testing: Single Population, 353
9.1. Concepts of Hypothesis Testing, 354
9.2. Tests of the Mean of a Normal Distribution: Population Variance Known, 359
p-Value, 362
Two-Sided Alternative Hypothesis, 368
9.3. Tests of the Mean of a Normal Distribution: Population Variance Unknown, 370
9.4. Tests of the Population Proportion (Large Samples), 374
9.5. Assessing the Power of a Test, 377
Tests of the Mean of a Normal Distribution: Population Variance Known, 377
Power of Population Proportion Tests (Large Samples), 380
9.6. Tests of the Variance of a Normal Distribution, 384
Chapter 10. Hypothesis Testing: Additional Topics, 392
10.1. Tests of the Difference between Two Normal Population Means: Dependent Samples, 394
Two Means, Matched Pairs, 394
10.2. Tests of the Difference between Two Normal Population Means: Independent Samples, 398
Two Means, Independent Samples, Known Population Variances, 398
Two Means, Independent Samples, Unknown Population Variances Assumed to Be Equal, 401
Two Means, Independent Samples, Unknown Population Variances Not Assumed to Be Equal, 404
10.3. Tests of the Difference between Two Population Proportions (Large Samples), 406
10.4. Tests of the Equality of the Variances between Two Normally Distributed Populations, 410
10.5. Some Comments on Hypothesis Testing, 414
Chapter 11. Simple Regression, 422
11.1. Overview of Linear Models, 423
11.2. Linear Regression Model, 426
11.3. Least Squares Coefficient Estimators, 432
Computer Computation of Regression Coefficient, 435
11.4. The Explanatory Power of a Linear Regression Equation, 438
Coefficient of Determination R², 441
11.5. Statistical Inference: Hypothesis Tests and Confidence Intervals, 445
Hypothesis Test for Population Slope Coefficient Using the F Distribution, 451
11.6. Prediction, 454
11.7. Correlation Analysis, 460
Hypothesis Test for Correlation, 461
11.8. Beta Measure of Financial Risk, 464
11.9. Graphical Analysis, 468
Chapter 12. Multiple Regression, 481
12.1. The Multiple Regression Model, 482
Model Specification, 483
Model Development, 485
Three-Dimensional Graphing, 488
12.2. Estimation of Coefficients, 490
Least Squares Procedure, 491
12.3. Explanatory Power of a Multiple Regression Equation, 497
12.4. Confidence Intervals and Hypothesis Tests for Individual Regression Coefficients, 503
Confidence Intervals, 506
Tests of Hypotheses, 507
12.5. Tests on Regression Coefficients, 516
Tests on All Coefficients, 516
Test on a Subset of Regression Coefficients, 518
Comparison of F and t Tests, 519
12.6. Prediction, 523
12.7. Transformations for Nonlinear Regression Models, 525
Quadratic Transformations, 526
Logarithmic Transformations, 529
12.8. Dummy Variables for Regression Models, 534
Differences in Slope, 537
12.9. Multiple Regression Analysis Application Procedure, 541
Model Specification, 542
Multiple Regression, 544
Effect of Dropping a Statistically Significant Variable, 546
Analysis of Residuals, 547
Chapter 13. Additional Topics in Regression Analysis, 563
13.1. Model-Building Methodology, 564
Model Specification, 564
Coefficient Estimation, 565
Model Verification, 566
Model Interpretation and Inference, 567
13.2. Dummy Variables and Experimental Design, 567
Experimental Design Models, 571
Public Sector Applications, 576
13.3. Lagged Values of the Dependent Variables as Regressors, 580
13.4. Specification Bias, 584
13.5. Multicollinearity, 588
13.6. Heteroscedasticity, 591
13.7. Autocorrelated Errors, 596
Estimation of Regressions with Autocorrelated Errors, 601
Autocorrelated Errors in Models with Lagged Dependent Variables, 605
Chapter 14. Analysis of Categorical Data, 614
14.1. Goodness-of-Fit Tests: Specified Probabilities, 615
14.2. Goodness-of-Fit Tests: Population Parameters Unknown, 622
A Test for the Poisson Distribution, 622
A Test for the Normal Distribution, 624
14.3. Contingency Tables, 627
14.4. Nonparametric Tests for Paired or Matched Samples, 632
Sign Test for Paired or Matched Samples, 633
Wilcoxon Signed Rank Test for Paired or Matched Samples, 635
Normal Approximation to the Sign Test, 637
Normal Approximation to the Wilcoxon Signed Rank Test, 638
Sign Test for Single Population Median, 640
14.5. Nonparametric Tests for Independent Random Samples, 643
Mann–Whitney U Test, 643
Wilcoxon Rank Sum Test, 645
14.6. Spearman Rank Correlation, 649
Chapter 15. Analysis of Variance, 659
15.1. Comparison of Several Population Means, 660
15.2. One-Way Analysis of Variance, 662
Multiple Comparisons Between Subgroup Means, 668
Population Model for One-Way Analysis of Variance, 670
15.3. The Kruskal–Wallis Test, 673
15.4. Two-Way Analysis of Variance: One Observation per Cell, Randomized Blocks, 676
15.5. Two-Way Analysis of Variance: More Than One Observation per Cell, 686
Chapter 16. Time-Series Analysis and Forecasting, 702
16.1. Index Numbers, 704
Price Index for a Single Item, 705
Unweighted Aggregate Price Index, 706
Weighted Aggregate Price Index, 707
Weighted Aggregate Quantity Index, 709
Change in Base Period, 710
16.2. A Nonparametric Test for Randomness, 713
16.3. Components of a Time Series, 716
16.4. Moving Averages, 719
Extraction of the Seasonal Component through Moving Averages, 721
16.5. Exponential Smoothing, 728
The Holt–Winters Exponential Smoothing Forecasting Model, 730
Forecasting Seasonal Time Series, 735
16.6. Autoregressive Models, 739
16.7. Autoregressive Integrated Moving Average Models, 744
Chapter 17. Additional Topics in Sampling, 748
17.1. Stratified Sampling, 748
Analysis of Results from Stratified Random Sampling, 750
Allocation of Sample Effort Among Strata, 756
Determining Sample Sizes for Stratified Random Sampling with Specified Degree of Precision, 758
17.2. Other Sampling Methods, 762
Cluster Sampling, 763
Two-Phase Sampling, 767
Nonprobabilistic Sampling Methods, 769
Chapter 18. Statistical Decision Theory, 773
18.1. Decision Making Under Uncertainty, 774
18.2. Solutions Not Involving Specification of Probabilities, 777
Maximin Criterion, 778
Minimax Regret Criterion, 780
18.3. Expected Monetary Value, 782
Decision Trees, 784
Sensitivity Analysis, 788
18.4. Sample Information: Bayesian Analysis and Value, 792
Use of Bayes’ Theorem, 792
The Value of Sample Information, 797
The Value of Sample Information Viewed by Means of Decision Trees, 800
18.5. Allowing for Risk: Utility Analysis, 806
The Concept of Utility, 807
Expected Utility Criterion for Decision Making, 810
Appendix Tables, 815
Table 1. Cumulative Distribution Function of the Standard Normal Distribution, 815
Table 2. Probability Function of the Binomial Distribution, 817
Table 3. Cumulative Binomial Probabilities, 822
Table 4. Values of e^–λ, 826
Table 5. Individual Poisson Probabilities, 827
Table 6. Cumulative Poisson Probabilities, 835
Table 7. Cutoff Points of the Chi-Square Distribution Function, 843
Table 8. Cutoff Points for the Student’s t Distribution, 844
Table 9. Cutoff Points for the F Distribution, 845
Table 10. Cutoff Points for the Distribution of the Wilcoxon Test Statistic, 848
Table 11. Cutoff Points for the Distribution of Spearman Rank Correlation Coefficient, 849
Table 12. Cutoff Points for the Distribution of the Durbin–Watson Test Statistic, 850
Table 13. Critical Values^a of the Studentized Range Q, 852
Table 14. Cumulative Distribution Function of the Runs Test Statistic, 854
Answers to Selected Even-Numbered Exercises, 855
Index, I-1
End Paper, EP-1

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