Introductory Statistics for Business and Economics: Theory, Exercises and Solutions (Springer Texts in Business and Economics)

This textbook discusses central statistical concepts and their use in business and economics. To endure the hardship of abstract statistical thinking, business and economics students need to see interesting applications at an early stage. Accordingly, the book predominantly focuses on exercises, several of which draw on simple applications of non-linear theory. The main body presents central ideas in a simple, straightforward manner; the exposition is concise, without sacrificing rigor. The book bridges the gap between theory and applications, with most exercises formulated in an economic context. Its simplicity of style makes the book suitable for students at any level, and every chapter starts out with simple problems. Several exercises, however, are more challenging, as they are devoted to the discussion of non-trivial economic problems where statistics plays a central part.-- Provided by publisher Preface 8 Contents 10 1 Descriptive Statistics 14 1.1 Population and Samples 14 1.2 The Median 17 1.3 Quartiles and Mode 19 1.4 Relative Frequency and Histograms 20 1.5 The Mean 21 1.6 Sample Variance and Sample Standard Deviation 23 1.7 Sample Covariance and Coefficient of Variation 25 1.8 Using Excel 30 1.9 Summary of Chap. 1 31 1.10 Problems for Chap. 1 33 2 Probability 40 2.1 Sample Space 40 2.2 Probability 42 2.2.1 Events 43 2.2.2 Uniform Probability 43 2.2.3 Set Theory 44 2.2.4 Computing Probabilities 46 2.2.5 The Negation Principle 48 2.3 Summary of Chap. 2 48 2.4 Problems for Chap. 2 49 3 Combinatorics 53 3.1 Counting Combinations 53 3.1.1 Ordered Selections 54 3.1.2 Unordered Choices Without Replacement 56 3.1.3 Combinatorial Probabilities 59 3.2 Summary of Chap. 3 61 3.3 Problems for Chap. 3 61 4 Conditional Probability 66 4.1 Conditional Probability 66 4.1.1 Computing Conditional Probabilities 68 4.1.2 Splitting the Sample Space 70 4.1.3 Probability Trees 71 4.2 Subjective Probabilities 75 4.3 Independence 76 4.4 Summary of Chap. 4 77 4.5 Problems for Chap. 4 78 5 Random Variables, Mean, and Variance 86 5.1 Random Variables 86 5.2 Expectation 91 5.2.1 Computing Expectations 93 5.2.2 General Expectations and Variance 94 5.3 Some Simple Facts About Option Pricing 96 5.3.1 Hedging Portfolios 97 5.4 Summary of Chap. 5 99 5.5 Problems for Chap. 5 100 6 Joint Distributions 108 6.1 Simultaneous Distributions 108 6.2 Covariance 114 6.2.1 An Alternative Formula for the Covariance 115 6.2.2 Sums of Random Variables 116 6.3 Summary of Chap. 6 117 6.4 Problems for Chap. 6 117 7 Basic Probability Distributions 123 7.1 The Indicator Distribution 123 7.2 The Binomial Distribution 124 7.3 The Hypergeometric Distribution 128 7.4 The Poisson Distribution 131 7.5 The Normal Distribution 134 7.5.1 The General Normal Distribution 137 7.5.2 Standardizing Random Variables 138 7.5.3 The Central Limit Theorem 139 7.5.4 Integer Correction 145 7.5.5 Normal Approximation of Hypergeometric and Poisson Distributions 146 7.5.6 Summing Normal Distributions 147 7.5.7 Applications to Option Pricing 148 7.6 Summary of Chap. 7 150 7.7 Problems for Chap. 7 152 8 Estimation 168 8.1 Estimation 168 8.1.1 Estimators 169 8.1.2 Reporting Estimates 171 8.1.3 The Measurement Model 171 8.2 Confidence Intervals 173 8.2.1 Constructing Confidence Intervals 173 8.2.2 The t-Distribution 175 8.3 The Lottery Model 178 8.4 Summary of Chap. 8 180 8.5 Problems for Chap. 8 181 9 Hypothesis Testing 185 9.1 Basic Ideas 185 9.2 Motivation 187 9.3 General Principles for Hypothesis Testing 189 9.4 Designing Statistical Tests 191 9.4.1 One-Sided and Two-Sided Tests 195 9.4.2 Confidence Intervals and Hypothesis Testing 196 9.4.3 P-Value 197 9.5 Summary of Chap. 9 200 9.6 Problems for Chap. 9 200 10 Commonly Used Tests 209 10.1 Testing Binomial Distributions 209 10.2 t-Test for Expected Value 211 10.3 Comparing Two Groups 214 10.3.1 t-Test for Comparison of Expectation in Two Groups 214 10.3.2 t-Test Executed in Excel 218 10.3.3 t-Test for Comparison of Expectation in Two Groups, Paired Observations 218 10.3.4 t-Test with Paired Observations Executed in Excel 222 10.4 Wilcoxon's Distribution Free Tests 223 10.4.1 The Wilcoxon Signed-Rank Test 226 10.4.2 Comparison of t-Tests and Wilcoxon Test 229 10.5 The U-Test for Comparison of Success Probabilities 229 10.6 Chi-Square Test for Goodness-of-Fit 232 10.6.1 The Chi-Square Test Executed in Excel 234 10.7 The Chi-Square Test for Independence 235 10.7.1 The Chi-Square Test for Independence Executed in Excel 238 10.8 Summary of Chap. 10 238 10.9 Problems for Chap. 10 239 11 Linear Regression 253 11.1 Linear Correspondence 253 11.2 Linear Regression 256 11.3 Residuals and Explanatory Power 259 11.3.1 Naming Variables 261 11.4 Hypothesis Testing in the Regression Model 262 11.5 Prediction/Estimation 265 11.6 Regression Using Excel 269 11.7 Multiple Regression 271 11.7.1 Explanatory Power 271 11.8 Causality 273 11.9 Multicollinearity 274 11.10 Dummy Variables 275 11.11 Analyzing Residuals 277 11.11.1 Histogram 277 11.11.2 Normal Score Plot 277 11.11.3 Residuals in Observed Order 278 11.11.4 Residuals Sorted with Respect to Size 278 11.12 Summary of Chap.11 279 11.13 Problems for Chap. 11 282 Solutions 323 Problems of Chap. 1 323 Problems of Chap. 2 330 Problems of Chap. 3 334 Problems of Chap. 4 341 Problems of Chap. 5 353 Problems of Chap. 6 364 Problems of Chap. 7 375 Problems of Chap. 8 405 Problems of Chap. 9 412 Problems of Chap. 10 423 Problems of Chap. 11 443 Table of the Binomial Distribution 464 Table of the Poisson Distribution 466 Table of the Normal Distribution—Area Table 467 Table of the Normal Distribution—Percentage Points 468 Table of the Chi-Square Distribution—Percentage Points 469 Table of the Chi-square Distribution—Continued 470 Table of the t-Distribution—Percentage Points 471 Index 473 Front Matter ....Pages i-xiv Descriptive Statistics (Jan Ubøe)....Pages 1-26 Probability (Jan Ubøe)....Pages 27-39 Combinatorics (Jan Ubøe)....Pages 41-53 Conditional Probability (Jan Ubøe)....Pages 55-74 Random Variables, Mean, and Variance (Jan Ubøe)....Pages 75-96 Joint Distributions (Jan Ubøe)....Pages 97-111 Basic Probability Distributions (Jan Ubøe)....Pages 113-157 Estimation (Jan Ubøe)....Pages 159-175 Hypothesis Testing (Jan Ubøe)....Pages 177-200 Commonly Used Tests (Jan Ubøe)....Pages 201-244 Linear Regression (Jan Ubøe)....Pages 245-314 Back Matter ....Pages 315-466