Essential Statistics for Economics, Business and Management

CHAPTER 1: Data Collection and its Graphical Presentation 5

1.1 Introduction to statistics 6

1.2 Data collection: Samples, surveys and experiments 8

1.3 Some sources of statistical data 16

1.4 Sorting and classifying data 18

1.5 Charts: Bar charts, pie charts and plotting in Excel 23

1.6 Graphs: Histograms and Ogives. Graphs in Excel 42

1.7 Line and Lorenz graphs 52

1.8 Misleading graphs 59

CHAPTER 2: Descriptive Statistics 63

2.1 Summary statistics for raw data: Mean, quartiles and mode 64

2.2 Summary statistics for grouped data: Mean, quartiles and mode 72

2.3 Measures of dispersion for raw data. Variance, QD, IQR 85

2.4 Measures of dispersion for grouped data. Variance, QD, IQR 92

2.5 Use of calculator for descriptive statistics 94

2.6 Other descriptive statistics. CV, skewness and box plots 96

2.7 Descriptive statistics in Excel 101

CHAPTER 3: Regression and Correlation: Introduction 113

3.1 Introduction to regression: Scatter plots and lines 114

3.2 The least-squares line. Criteria and equation for the best fit line 118

3.3 Excel: XY (scatter) plots, the least-squares lines and formulae 127

3.4 Coefficient of determination and correlation 133

3.5 Rank correlation. Calculate and interpret rank correlation 144

3.6 Use the calculator for linear regression and correlation 146

3.7 Why bother with formulae? 154

CHAPTER 4: Probability 159

4.1 Introduction to probability 159

4.2 Multiplication and addition rules for probability 170

4.3 Joint, marginal and conditional probability 184

4.4 Bayes' Rule 192

CHAPTER 5: Introduction to Probability Distributions 205

5.1 Introduction to probability distributions and random variables 206

5.2 The Binomial probability distribution 212

5.3 The Poisson probability distribution 228

5.4 The Normal probability distribution 236

5.5 Expected values (mathematical expectation) 253

CHAPTER 6: Sampling Distributions for Means and Proportions 265

6.1 Statistical inference and the sampling distribution of the mean 265

6.2 Sampling distribution of proportions 275

6.3 Some desirable properties of estimators 282

CHAPTER 7: Confidence Intervals for Means and Proportions 287

7.1 Confidence intervals for the mean 287

7.2 Confidence intervals for proportions 297

7.3 The precision of confidence intervals for the mean 300

7.4 Confidence intervals for differences between means and proportions 304

CHAPTER 8: Tests of Hypothesis for Means and Proportions 319

8.1 Hypothesis tests for means 319

8.2 Hypothesis tests for proportions 334

8.3 Hypothesis tests for the difference between means and proportions 337

8.4 Minitab and Excel for confidence intervals and tests of hypothesis 349

CHAPTER 9: Inference from Small Samples. Confidence Intervals and Tests of Hypothesis 359

9.1 Inference from small samples: Normal populations, s known 360

9.2 The Student's t distribution 362

9.3 Inference from small samples: Normal populations, s NOT known 365

9.4 Difference between means. Small independent samples 370

9.5 F-test for equality of two variances 378

9.6 Difference between means, paired samples 382

CHAPTER 10: Analysis of Variance 393

10.1 The rationale behind one-way analysis of variance 393

10.2 One-way analysis of variance 397

10.3 Two-way ANOVA 419

10.4 ANOVA and design of experiment 430

10.5 Excel and Minitab for ANOVA 435

CHAPTER 11: Chi-squared Tests 453

11.1 Introduction 454

11.2 The ?2 probability distribution 454

11.3 Contingency tables 455

11.4 ?2 tests for independence (no association) 456

11.5 ?2 test for homogeneous populations 464

11.6 ?2 tests for the equality of several proportions 466

11.7 Goodness of fit tests 478

11.8 ?2 tests in Minitab and Excel 490

CHAPTER 12: Regression Analysis 499

12.1 The simple linear regression model 499

12.2 Inference about the population slope (rate of change) 504

12.3 Confidence intervals and prediction intervals at x = x0 513

12.4 Checks on the model assumptions based on residuals plots 518

12.5 Regression analysis in Minitab and Excel 521

12.6 Multiple regression 534

APPENDIX A: Technicalities and Conventions for Defining Class Intervals, Mid-Interval, Widths, Limits, Boundaries 545

APPENDIX B: Formulae for Calculating the Quartiles for Grouped Data 547

APPENDIX C: Outline of Derivation of Formulae (3.2) and (3.3) for the Slope and Intercept of the Least-Squares Line, Y = a + bX 549

APPENDIX D: Brief Review of the Mathematics for the Binomial 551

APPENDIX E: The Number e 555

APPENDIX F: Calculation of Mean and Variance of Proportions by Expected Values 557

APPENDIX G: Confidence Intervals for Means and Proportions 559

APPENDIX H: Degrees of Freedom 561

APPENDIX I: Notes on Summations and Double Summations 563

APPENDIX J: Expressing the Estimates of Variance as Sums of Squares Divided by Degrees of Freedom in Their Simplest Form 567

APPENDIX K: Sums of Squares for the One-Way ANOVA 571

APPENDIX L: Fitted Values and Residuals 573

APPENDIX M: Sums of Squares Identity for Two-Way ANOVA 575

Chapter Solutions 577

Tables 637

Table 1 Cumulative Binomial Probability tables 637

Table 2 Cumulative Poisson Probabilities 639

Table 3 Normal probability Distribution 641

Table 4 Percentage point for the Normal probability distribution 642

Table 5 Percentage points of the Student’s t-distribution 643

Table 6 0.5% points of the F-distribution 644

Table 7 Percentage points for the Chi-squared distribution 648

Table 8 Table of random numbers 649

Glossary 651

Index 653