Statistics for business and economics

Cover......Page 1
Contents......Page 8
Preface......Page 14
 M......Page 20
 W......Page 21
CHAPTER 1 Using Graphs to Describe Data......Page 22
  Random and Systematic Sampling......Page 23
  Sampling and Nonsampling Errors......Page 25
  Categorical and Numerical Variables......Page 26
  Measurement Levels......Page 27
  Tables and Charts......Page 29
  Cross Tables......Page 30
  Pie Charts......Page 32
  Pareto Diagrams......Page 33
 1.4 Graphs to Describe Time-Series Data......Page 36
  Frequency Distributions......Page 41
  Shape of a Distribution......Page 45
  Stem-and-Leaf Displays......Page 47
  Scatter Plots......Page 48
  Misleading Histograms......Page 52
  Misleading Time-Series Plots......Page 54
 2.1 Measures of Central Tendency and Location......Page 60
  Mean, Median, and Mode......Page 61
  Shape of a Distribution......Page 63
  Geometric Mean......Page 64
  Percentiles and Quartiles......Page 65
 2.2 Measures of Variability......Page 69
  Box-and-Whisker Plots......Page 70
  Variance and Standard Deviation......Page 72
  Chebyshev’s Theorem and the Empirical Rule......Page 76
  z-Score......Page 78
 2.3 Weighted Mean and Measures of Grouped Data......Page 81
 2.4 Measures of Relationships Between Variables......Page 85
  Case Study: Mortgage Portfolio......Page 92
CHAPTER 3 Elements of Chance: Probability Methods......Page 94
 3.1 Random Experiment, Outcomes, and Events......Page 95
  Classical Probability......Page 102
  Permutations and Combinations......Page 103
  Relative Frequency......Page 107
  Subjective Probability......Page 108
 3.3 Probability Rules......Page 112
  Conditional Probability......Page 114
  Statistical Independence......Page 117
 3.4 Bivariate Probabilities......Page 123
  Overinvolvement Ratios......Page 127
 3.5 Bayes’ Theorem......Page 133
  Subjective Probabilities in Management Decision Making......Page 139
CHAPTER 4 Discrete Probability Distributions......Page 147
 4.1 Random Variables......Page 148
 4.2 Probability Distributions for Discrete Random Variables......Page 149
  Expected Value of a Discrete Random Variable......Page 153
  Variance of a Discrete Random Variable......Page 154
  Mean and Variance of Linear Functions of a Random Variable......Page 156
 4.4 Binomial Distribution......Page 160
  Developing the Binomial Distribution......Page 161
 4.5 Poisson Distribution......Page 168
  Poisson Approximation to the Binomial Distribution......Page 172
  Comparison of the Poisson and Binomial Distributions......Page 173
 4.6 Hypergeometric Distribution......Page 174
 4.7 Jointly Distributed Discrete Random Variables......Page 177
  Linear Functions of Random Variables......Page 181
  Covariance......Page 182
  Correlation......Page 183
  Portfolio Analysis......Page 187
CHAPTER 5 Continuous Probability Distributions......Page 198
 5.1 Continuous Random Variables......Page 199
  The Uniform Distribution......Page 202
 5.2 Expectations for Continuous Random Variables......Page 204
 5.3 The Normal Distribution......Page 207
  Normal Probability Plots......Page 216
 5.4 Normal Distribution Approximation for Binomial Distribution......Page 220
  Proportion Random Variable......Page 224
 5.5 The Exponential Distribution......Page 226
 5.6 Jointly Distributed Continuous Random Variables......Page 229
  Financial Investment Portfolios......Page 233
  Cautions Concerning Finance Models......Page 237
CHAPTER 6 Distributions of Sample Statistics......Page 245
 6.1 Sampling from a Population......Page 246
  Development of a Sampling Distribution......Page 247
 6.2 Sampling Distributions of Sample Means......Page 250
  Monte Carlo Simulations: Central Limit Theorem......Page 255
  Acceptance Intervals......Page 261
 6.3 Sampling Distributions of Sample Proportions......Page 266
 6.4 Sampling Distributions of Sample Variances......Page 271
CHAPTER 7 Confidence Interval Estimation: One Population......Page 285
 7.1 Properties of Point Estimators......Page 286
  Unbiased......Page 287
  Most Efficient......Page 288
 7.2 Confidence Interval Estimation for the Mean of a Normal Distribution: Population Variance Known......Page 292
  Intervals Based on the Normal Distribution......Page 293
  Reducing Margin of Error......Page 296
  Student’s t Distribution......Page 298
  Intervals Based on the Student’s t Distribution......Page 300
 7.4 Confidence Interval Estimation for Population Proportion (Large Samples)......Page 304
 7.5 Confidence Interval Estimation for the Variance of a Normal Distribution......Page 307
  Population Mean and Population Total......Page 310
  Population Proportion......Page 313
  Mean of a Normally Distributed Population, Known Population Variance......Page 316
  Population Proportion......Page 318
 7.8 Sample-Size Determination: Finite Populations......Page 320
  Sample Sizes for Simple Random Sampling: Estimation of the Population Mean or Total......Page 321
  Sample Sizes for Simple Random Sampling: Estimation of Population Proportion......Page 322
CHAPTER 8 Confidence Interval Estimation: Further Topics......Page 329
 8.1 Confidence Interval Estimation of the Difference Between Two Normal Population Means: Dependent Samples......Page 330
  Two Means, Independent Samples, and Known Population Variances......Page 334
  Two Means, Independent Samples, and Unknown Population Variances Assumed to Be Equal......Page 336
  Two Means, Independent Samples, and Unknown Population Variances Not Assumed to Be Equal......Page 338
 8.3 Confidence Interval Estimation of the Difference Between Two Population Proportions (Large Samples)......Page 341
CHAPTER 9 Hypothesis Tests of a Single Population......Page 347
 9.1 Concepts of Hypothesis Testing......Page 348
 9.2 Tests of the Mean of a Normal Distribution: Population Variance Known......Page 353
  p-Value......Page 355
  Two-Sided Alternative Hypothesis......Page 361
 9.3 Tests of the Mean of a Normal Distribution: Population Variance Unknown......Page 363
 9.4 Tests of the Population Proportion (Large Samples)......Page 367
 9.5 Assessing the Power of a Test......Page 369
  Tests of the Mean of a Normal Distribution: Population Variance Known......Page 370
  Power of Population Proportion Tests (Large Samples)......Page 372
 9.6 Tests of the Variance of a Normal Distribution......Page 376
CHAPTER 10 Two Population Hypothesis Tests......Page 386
  Two Means, Matched Pairs......Page 388
  Two Means, Independent Samples, Known Population Variances......Page 392
  Two Means, Independent Samples, Unknown Population Variances Assumed to Be Equal......Page 394
  Two Means, Independent Samples, Unknown Population Variances Not Assumed to Be Equal......Page 397
 10.3 Tests of the Difference Between Two Population Proportions (Large Samples)......Page 400
 10.4 Tests of the Equality of the Variances Between Two Normally Distributed Populations......Page 404
 10.5 Some Comments on Hypothesis Testing......Page 407
CHAPTER 11 Two Variable Regression Analysis......Page 418
 11.1 Overview of Linear Models......Page 419
 11.2 Linear Regression Model......Page 422
 11.3 Least Squares Coefficient Estimators......Page 428
  Computer Computation of Regression Coefficients......Page 430
 11.4 The Explanatory Power of a Linear Regression Equation......Page 432
  Coefficient of Determination, R[sup(2)]......Page 434
 11.5 Statistical Inference: Hypothesis Tests and Confidence Intervals......Page 439
  Hypothesis Test for Population Slope Coefficient Using the F Distribution......Page 444
 11.6 Prediction......Page 447
  Hypothesis Test for Correlation......Page 453
 11.8 Beta Measure of Financial Risk......Page 457
 11.9 Graphical Analysis......Page 459
CHAPTER 12 Multiple Variable Regression Analysis......Page 474
  Model Specification......Page 475
  Model Objectives......Page 477
  Model Development......Page 478
  Three-Dimensional Graphing......Page 481
 12.2 Estimation of Coefficients......Page 482
  Least Squares Procedure......Page 483
 12.3 Explanatory Power of a Multiple Regression Equation......Page 489
 12.4 Confidence Intervals and Hypothesis Tests for Individual Regression Coefficients......Page 494
  Confidence Intervals......Page 496
  Tests of Hypotheses......Page 498
  Tests on All Coefficients......Page 506
  Test on a Subset of Regression Coefficients......Page 507
  Comparison of F and t Tests......Page 509
 12.6 Prediction......Page 512
 12.7 Transformations for Nonlinear Regression Models......Page 515
  Quadratic Transformations......Page 516
  Logarithmic Transformations......Page 518
 12.8 Dummy Variables for Regression Models......Page 523
  Differences in Slope......Page 526
  Model Specification......Page 530
  Multiple Regression......Page 532
  Effect of Dropping a Statistically Significant Variable......Page 533
  Analysis of Residuals......Page 535
CHAPTER 13 Additional Topics in Regression Analysis......Page 552
  Model Specification......Page 553
  Coefficient Estimation......Page 554
 13.2 Dummy Variables and Experimental Design......Page 555
  Experimental Design Models......Page 559
  Public Sector Applications......Page 564
 13.3 Lagged Values of the Dependent Variable as Regressors......Page 568
 13.4 Specification Bias......Page 572
 13.5 Multicollinearity......Page 575
 13.6 Heteroscedasticity......Page 578
 13.7 Autocorrelated Errors......Page 583
  Estimation of Regressions with Autocorrelated Errors......Page 587
  Autocorrelated Errors in Models with Lagged Dependent Variables......Page 591
CHAPTER 14 Introduction to Nonparametric Statistics......Page 603
 14.1 Goodness-of-Fit Tests: Specified Probabilities......Page 604
  A Test for the Poisson Distribution......Page 610
  A Test for the Normal Distribution......Page 612
 14.3 Contingency Tables......Page 615
  Sign Test for Paired or Matched Samples......Page 620
  Wilcoxon Signed Rank Test for Paired or Matched Samples......Page 623
  Normal Approximation to the Sign Test......Page 624
  Normal Approximation to the Wilcoxon Signed Rank Test......Page 625
  Sign Test for a Single Population Median......Page 627
  Mann-Whitney U Test......Page 629
  Wilcoxon Rank Sum Test......Page 632
 14.6 Spearman Rank Correlation......Page 635
  Runs Test: Small Sample Size......Page 637
  Runs Test: Large Sample Size......Page 639
 15.1 Comparison of Several Population Means......Page 646
 15.2 One-Way Analysis of Variance......Page 648
  Multiple Comparisons Between Subgroup Means......Page 655
  Population Model for One-Way Analysis of Variance......Page 656
 15.3 The Kruskal-Wallis Test......Page 659
 15.4 Two-Way Analysis of Variance: One Observation per Cell, Randomized Blocks......Page 662
 15.5 Two-Way Analysis of Variance: More Than One Observation per Cell......Page 671
CHAPTER 16 Forecasting with Time-Series Models......Page 685
 16.1 Components of a Time Series......Page 686
 16.2 Moving Averages......Page 690
  Extraction of the Seasonal Component Through Moving Averages......Page 693
 16.3 Exponential Smoothing......Page 698
  The Holt-Winters Exponential Smoothing Forecasting Model......Page 701
  Forecasting Seasonal Time Series......Page 705
 16.4 Autoregressive Models......Page 709
 16.5 Autoregressive Integrated Moving Average Models......Page 714
 17.1 Stratified Sampling......Page 717
  Analysis of Results from Stratified Random Sampling......Page 719
  Allocation of Sample Effort Among Strata......Page 724
  Determining Sample Sizes for Stratified Random Sampling with Specified Degree of Precision......Page 726
  Cluster Sampling......Page 730
  Two-Phase Sampling......Page 733
  Nonprobabilistic Sampling Methods......Page 735
APPENDIX TABLES......Page 739
 C......Page 784
 D......Page 785
 G......Page 786
 L......Page 787
 N......Page 788
 P......Page 789
 R......Page 790
 S......Page 791
 V......Page 792
 Z......Page 793