INSEAD Library

Doriot: for 2020-2021 courses

Includes index

Digitized

Theory and Problems of Business Statistics Contents CHAPTER 1 Analyzing Business Data 1.1 Definition of Business Statistics 1.2 Descriptive and Inferential Statistics 1.3 Types of Applications in Business 1.4 Discrete and Continuous Variables 1.5 Obtaining Data Through Direct Observation vs. Surveys 1.6 Methods of Random Sampling 1.7 Other Sampling Methods 1.8 Using Excel and Minitab to Generate Random Numbers 1 1 1 2 2 2 3 4 4 CHAPTER 2 Statistical Presentations and Graphical Displays 2.1 Frequency Distributions 2.2 Class Intervals 2.3 Histograms and Frequency Polygons 2.4 Frequency Curves 2.5 Cumulative Frequency Distributions 2.6 Relative Frequency Distributions 2.7 The "And-Under" Type of Frequency Distribution 2.8 Stem-and-Leaf Diagrams 2.9 Dotplots 2.10 Pareto Charts 2.11 Bar Charts and Line Graphs 2.12 Run Charts 2.13 Pie Charts 2.14 Using Excel and Minitab 10 10 11 12 12 13 14 15 15 16 16 16 18 19 19 CHAPTER 3 Describing Business Data: Measures of Location 3.1 Measures of Location in Data Sets 3.2 The Arithmetic Mean 3.3 The Weighted Mean 3.4 The Median 3.5 The Mode 3.6 Relationship Between the Mean and the Median 3.7 Mathematical Criteria Satisfied by the Median and the Mean 3.8 Use of the Mean, Median, and Mode 3.9 Use of the Mean in Statistical Process Control vii 44 44 44 45 45 46 46 46 47 48 viii CONTENTS 3.10 Quartiles, Deciles, and Percentiles 3.11 Using Excel and Minitab 48 48 CHAPTER 4 Describing Business Data: Measures of Dispersion 4.1 Measures of Variability in Data Sets 4.2 The Range 4.3 Modified Ranges 4.4 Box Plots 4.5 The Mean Absolute Deviation 4.6 The Variance and Standard Deviation 4.7 Simplified Calculations for the Variance and Standard Deviation 4.8 The Mathematical Criterion Associated with the Variance and Standard Deviation 4.9 Use of the Standard Deviation in Data Description 4.10 Use of the Range and Standard Deviation in Statistical Process Control 4.11 The Coefficient of Variation 4.12 Pearson's Coefficient of Skewness 4.13 Using Excel and Minitab 57 57 57 58 58 59 60 61 62 62 62 63 64 64 CHAPTER 5 Probability 5.1 Basic Definitions of Probability 5.2 Expressing Probability 5.3 Mutually Exclusive and Nonexclusive Events 5.4 The Rules of Addition 5.5 Independent Events, Dependent Events, and Conditional Probability 5.6 The Rules of Multiplication 5.7 Bayes' Theorem 5.8 Joint Probability Tables 5.9 Permutations 5.10 Combinations 74 74 75 76 76 77 78 80 81 82 83 CHAPTER 6 Probability Distributions for Discrete Random Variables: Binomial, Hypergeometric, and Poission 99 6.1 What Is a Random Variable? 6.2 Describing a Discrete Random Variable 6.3 The Binomial Distribution 6.4 The Binomial Variable Expressed by Proportions 6.5 The Hypergeometric Distribution 6.6 The Poisson Distribution 6.7 Poisson Approximation of Binomial Probabilities 6.8 Using Excel and Minitab 99 100 102 103 104 104 106 107 CONTENTS ix CHAPTER 7 Probability Distributions for Continuous Random Variables: Normal and Exponential 7.1 Continuous Random Variables 7.2 The Normal Probability Distribution 7.3 Percentile Points for Normally Distributed Variables 7.4 Normal Approximation of Binomial Probabilities 7.5 Normal Approximation of Poisson Probabilities 7.6 The Exponential Probability Distribution 7.7 Using Excel and Minitab 122 122 123 125 126 128 128 129 CHAPTER 8 Sampling Distributions and Confidence Intervals for the Mean 8.1 Point Estimation of a Population or Process Parameter 8.2 The Concept of a Sampling Distribution 8.3 Sampling Distribution of the Mean 8.4 The Central Limit Theorem 8.5 Determining Probability Values for the Sample Mean 8.6 Confidence Intervals for the Mean Using the Normal Distribution 8.7 Determining the Required Sample Size for Estimating the Mean 8.8 The t Distribution and Confidence Intervals for the Mean 8.9 Summary Table for Interval Estimation of the Population Mean 8.10 Using Excel and Minitab 142 142 143 143 145 145 146 147 148 149 149 CHAPTER 9 Other Confidence Intervals 160 9.1 Confidence Intervals for the Difference Between Two Means Using the Normal Distribution 160 9.2 The t Distribution and Confidence Intervals for the Difference Between Two Means 161 9.3 Confidence Intervals for the Population Proportion 162 9.4 Determining the Required Sample Size for Estimating the Proportion 163 9.5 Confidence Intervals for the Difference Between Two Proportions 163 9.6 The Chi-Square Distribution and Confidence Intervals for the Variance and Standard Deviation 164 9.7 Using Excel and Minitab 165 CHAPTER 10 Testing Hypotheses Concerning the Value of the Population Mean 10.1 Introduction 174 174 x CONTENTS 10.2 Basic Steps in Hypothesis Testing by the Critical Value Approach 10.3 Testing a Hypothesis Concerning the Mean by Use of the Normal Distribution 10.4 Type I and Type II Errors in Hypothesis Testing 10.5 Determining the Required Sample Size for Testing the Mean 10.6 Testing a Hypothesis Concerning the Mean by Use of the t Distribution 10.7 The P-Value Approach to Testing Hypotheses Concerning the Population Mean 10.8 The Confidence Interval Approach to Testing Hypotheses Concerning the Mean 10.9 Testing with Respect to the Process Mean in Statistical Process Control 10.10 Summary Table for Testing a Hypothesized Value of the Mean 10.11 Using Excel and Minitab 175 176 179 181 182 182 183 184 184 185 CHAPTER 11 Testing Other Hypotheses 197 11.1 Testing the Difference Between Two Means Using the Normal Distribution 197 11.2 Testing the Difference Between Means Using the t Distribution 199 11.3 Testing the Difference Between Means Based on Paired Observations 200 11.4 Testing a Hypothesis Concerning the Value of the Population Proportion 201 11.5 Determining the Required Sample Size for Testing the Proportion 202 11.6 Testing with Respect to the Process Proportion in Statistical Process Control 203 11.7 Testing the Difference Between Two Population Proportions 203 11.8 Testing a Hypothesized Value of the Variance Using the Chi-Square Distribution 204 11.9 Testing with Respect to Process Variability in Statistical Process Control 204 11.10 The F Distribution and Testing the Equality of Two Population Variances 205 11.11 Alternative Approaches to Testing Null Hypotheses 206 11.12 Using Excel and Minitab 207 CHAPTER 12 The Chi-Square Test for the Analysis of Qualitative Data 12.1 General Purpose of the Chi-Square Test 12.2 Goodness of Fit Tests 219 219 219 CONTENTS xi 12.3 Tests for the Independence of Two Categorical Variables (Contingency Table Tests) 12.4 Testing Hypotheses Concerning Proportions 12.5 Using Computer Software 222 223 226 CHAPTER 13 Analysis of Variance 13.1 Basic Rationale Associated with Testing the Differences Among Several Population Means 13.2 One-Factor Completely Randomized Design (One-Way ANOVA) 13.3 Two-Way Analysis of Variance (Two-Way ANOVA) 13.4 The Randomized Block Design (Two-Way ANOVA, One Observation per Cell) 13.5 Two-Factor Completely Randomized Design (Two-Way ANOVA, n Observations per Cell) 13.6 Additional Considerations 13.7 Using Excel and Minitab 241 241 242 243 243 244 245 246 CHAPTER 14 Linear Regression and Correlation Analysis 263 14.1 Objectives and Assumptions of Regression Analysis 263 14.2 The Scatter Plot 264 14.3 The Method of Least Squares for Fitting a Regression Line 265 14.4 Residuals and Residual Plots 265 14.5 The Standard Error of Estimate 266 14.6 Inferences Concerning the Slope 266 14.7 Confidence Intervals for the Conditional Mean 267 14.8 Prediction Intervals for Individual Values of the Dependent Variable 267 14.9 Objectives and Assumptions of Correlation Analysis 268 14.10 The Coefficient of Determination 268 14.11 The Coefficient of Correlation 269 14.12 The Covariance Approach to Understanding the Correlation Coefficient 270 14.13 Significance Testing with Respect to the Correlation Coefficient 14.14 Pitfalls and Limitations Associated with Regression and Correlation Analysis 14.15 Using Excel and Minitab 271 271 271 CHAPTER 15 Multiple Regression and Correlation 15.1 Objectives and Assumptions of Multiple Regression Analysis 15.2 Additional Concepts in Multiple Regression Analysis 15.3 The Use of Indicator (Dummy) Variables 15.4 Residuals and Residual Plots 283 283 284 284 285 xii CONTENTS 15.5 15.6 15.7 15.8 Analysis of Variance in Linear Regression Analysis 285 Objectives and Assumptions of Multiple Correlation Analysis287 Additional Concepts in Multiple Correlation Analysis 287 Pitfalls and Limitations Associated with Multiple Regression and Multiple Correlation Analysis 288 15.9 Using Excel and Minitab 288 CHAPTER 16 Time Series Analysis and Business Forecasting 16.1 The Classical Time Series Model 16.2 Trend Analysis 16.3 Analysis of Cyclical Variations 16.4 Measurement of Seasonal Variations 16.5 Applying Seasonal Adjustments 16.6 Forecasting Based on Trend and Seasonal Factors 16.7 Cyclical Forecasting and Business Indicators 16.8 Forecasting Based on Moving Averages 16.9 Exponential Smoothing as a Forecasting Method 16.10 Other Forecasting Methods That Incorporate Smoothing 16.11 Using Computer Software 296 296 297 298 299 299 300 301 301 301 302 303 CHAPTER 17 Nonparametric Statistics 17.1 Scales of Measurement 17.2 Parametric vs. Nonparametric Statistical Methods 17.3 The Runs Test for Randomness 17.4 One Sample: The Sign Test 17.5 One Sample: The Wilcoxon Test 17.6 Two Independent Samples: The Mann-Whitney Test 17.7 Paired Observations: The Sign Test 17.8 Paired Observations: The Wilcoxon Test 17.9 Several Independent Samples: The Kruskal-Wallis Test 17.10 Using Minitab 318 318 319 319 320 320 321 322 322 322 323 CHAPTER 18 Decision Analysis: Payoff Tables and Decision Trees 18.1 18.2 18.3 18.4 336 The Structure of Payoff Tables 336 Decision Making Based upon Probabilities Alone 337 Decision Making Based upon Economic Consequences Alone 338 Decision Making Based upon Both Probabilities and Economic Consequences: The Expected Payoff Criterion 340 18.5 Decision Tree Analysis 342 18.6 Expected Utility as the Decision Criterion 342 CONTENTS xiii CHAPTER 19 Statistical Process Control 19.1 Total Quality Management 19.2 Statistical Quality Control 19.3 Types of Variation in Processes 19.4 Control Charts 19.5 Control Charts for the Process Mean: X Charts 19.6 Standard Tests Used for Interpreting X Charts 19.7 Control Charts for the Process Standard Deviation: s Charts 19.8 Control Charts for the Process Range: R Charts 19.9 Control Charts for the Process Proportion: p Charts 19.10 Using Minitab 356 356 357 358 358 359 360 362 362 363 364 APPENDIX 1 APPENDIX 2 APPENDIX 3 APPENDIX 4 APPENDIX 5 APPENDIX 6 APPENDIX 7 APPENDIX 8 Table of Random Numbers Binomial Probabilities Values of e-X Poission Probabilities Proportions of Area for the Standard Normal Distribution Proportions of Area for the t Distribution Proportions of Area for the x2 Distribution Values of F Exceeded with Probabilities of 5% and 1% Factors for Control Charts Critical Values of T in the Wilcoxon Test 377 378 382 383 388 390 391 393 397 398 401 APPENDIX 9 APPENDIX 10 INDEX