Introductory Statistics

Preface......Page p0007.djvu
Contents......Page p0009.djvu
1-1 Example......Page p0013.djvu
1-2 Induction and Deduction......Page p0015.djvu
1-4 How to Sample......Page p0017.djvu
2-2 Frequency Tables and Graphs......Page p0020.djvu
2-3 Centers (Measures of Location)......Page p0024.djvu
2-4 Deviations (Measures of Spread)......Page p0029.djvu
2-5 Linear Transformations (Coding)......Page p0031.djvu
3-1 Introduction......Page p0039.djvu
3-2 Elementary Properties of Probability......Page p0041.djvu
3-3 Events and Their Probabilities......Page p0042.djvu
3-4 Conditional Probability......Page p0052.djvu
3-5 Independence......Page p0057.djvu
3-6 Other Views of Probability......Page p0060.djvu
4-1 Discrete Random Variables......Page p0064.djvu
4-2 Mean and Variance......Page p0068.djvu
4-3 Binomial Distribution......Page p0071.djvu
4-4 Continuous Distributions......Page p0075.djvu
4-5 The Normal Distribution......Page p0078.djvu
4-6 A Function of a Random Variable......Page p0084.djvu
4-7 Notation......Page p0085.djvu
5-1 Distributions......Page p0089.djvu
5-2 Functions of Two Random Variables......Page p0096.djvu
5-3 Covariance......Page p0100.djvu
5-4 Linear Combination of Two Random Variables......Page p0105.djvu
6-1 Introduction......Page p0114.djvu
6-2 Sample Sum......Page p0117.djvu
6-3 Sample Mean......Page p0119.djvu
6-4 Central Limit Theorem......Page p0124.djvu
6-5 Sampling from a Finite Population, without Replacement......Page p0128.djvu
6-6 Sampling from Bernoulli Populations......Page p0131.djvu
6-7 Summary of Sampling Theory......Page p0136.djvu
7-1 Introduction: Confidence Interval for the Mean......Page p0140.djvu
7-2 Desirable Properties of Estimators......Page p0146.djvu
7-3 Maximum-Likelihood Estimation (MLE)......Page p0153.djvu
8-1 Difference in Two Means......Page p0162.djvu
8-2 Small Sample Estimation: the t Distribution......Page p0164.djvu
8-3 Estimating Population Proportions: The Election Problem Once Again......Page p0169.djvu
8-4 Estimating the Variance of a Normal Population: The Chi-Square Distribution......Page p0175.djvu
9-1 Testing a Simple Hypothesis......Page p0179.djvu
9-2 Composite Hypotheses......Page p0187.djvu
9-3 Two-Sided Tests vs. One-Sided Tests......Page p0197.djvu
9-4 The Relation of Hypothesis Tests to Confidence Intervals......Page p0199.djvu
9-5 Conclusions......Page p0205.djvu
10-2 One-Factor Analysis of Variance......Page p0207.djvu
10-3 Two-Factor Analysis of Variance......Page p0223.djvu
11 Introduction to Regression......Page p0232.djvu
11-1 An Example......Page p0233.djvu
11-2 Possible Criteria for Fitting a Line......Page p0235.djvu
11-3 The Least Squares Solution......Page p0237.djvu
Appendix 11-1 An Alternative Derivation of Least Squares Estimates without Calculus......Page p0243.djvu
12-1 The Mathematical Model......Page p0246.djvu
12-2 The Nature of the Error Term......Page p0248.djvu
12-3 Estimating alpha and beta......Page p0249.djvu
12-4 The Mean and Variance of a and b......Page p0250.djvu
12-5 The Gauss-Markov Theorem......Page p0252.djvu
12-6 The Distribution of a and b......Page p0253.djvu
12-7 Confidence Intervals and Testing Hypotheses about beta......Page p0255.djvu
12-8 Prediction Interval for Y_0......Page p0257.djvu
12-9 Dangers of Extrapolation......Page p0261.djvu
12-10 Maximum Likelihood Estimation......Page p0262.djvu
12-11 The Characteristics of the Independent Variable......Page p0266.djvu
13-1 Introductory Example......Page p0267.djvu
13-2 The Mathematical Model......Page p0268.djvu
13-3 Least Squares Estimation......Page p0269.djvu
13-4 Multicollinearity......Page p0272.djvu
13-5 Interpreting an Estimated Regression......Page p0277.djvu
13-6 Dummy Variables......Page p0281.djvu
13-7 Regression, Analysis of Variance, and Analysis of Co-variance......Page p0290.djvu
14-1 Simple Correlation......Page p0297.djvu
14-2 Partial Correlation......Page p0320.djvu
14-3 Multiple Correlation......Page p0322.djvu
15-1 Prior and Posterior Distributions......Page p0324.djvu
15-2 Optimal Decisions......Page p0327.djvu
15-3 Estimation as a Decision......Page p0334.djvu
15-4 Estimation: Bayesian Versus Classical......Page p0336.djvu
15-5 Critique of Bayesian Methods......Page p0343.djvu
15-6 Hypothesis Testing as a Bayesian Decision......Page p0345.djvu
15-7 Game Theory......Page p0352.djvu
Appendix Tables......Page p0362.djvu
Table I Squares and Square Roots......Page p0363.djvu
Table II Random Digits and Normal Variates......Page p0372.djvu
Table III Binomial Coefficients and Probabilities......Page p0374.djvu
Table IV Standard Normal Probabilities......Page p0379.djvu
Table V Student's t Critical Points......Page p0380.djvu
Table VI Modified Chi-Square Critical Points......Page p0381.djvu
Table VII F Critical Points......Page p0382.djvu
Table VIII Common Logarithms......Page p0386.djvu
Acknowledgements......Page p0388.djvu
Answers to Odd-Numbered Problems......Page p0389.djvu
Glossary of Symbols......Page p0405.djvu
Index......Page p0409.djvu