Introduction to Statistical Modeling

1. Introduction to Statistical inference.
1.1. Population and sample
1.2. Random sampling
1.3. Fundamental sampling distributions
1.4. Point estimation of parameters
1.4.1. Definitions
1.4.2. Method of moments
1.4.3. Maximum likelihood estimation

2. Confidence intervals for a single sample
2.1. Introduction
2.2. CI on the mean
2.2.1. Normal population with known variance
2.2.2. Large sample
2.2.3. Normal population unknown variance
2.3. CI on the proportion
2.3.1. Large-sample
2.4. CI on the variance
2.4.1. Normal population

3. Test of hypotheses for a single sample
3.1. Introduction
3.2. Type I and Type II Errors
3.3. Power of a statistical test
3.4. P-value
3.5. HT on the mean
3.5.1. Normal population with known variance
3.5.2. Large sample
3.5.3. Normal population with unknown variance
3.6. HT on the proportion
3.6.1. Large sample
3.7. HT on the variance
3.7.1. Normal population

4. Statistical inference for two samples
4.1. Introduction
4.2. Difference in means
4.2.1. Normal populations with known variances
4.2.2. Large samples
4.2.3. Normal populations with unknown variances
4.2.4. Normal populations with unknown equal variances
4.2.5. Normal populations, paired observations.
4.3. Difference in proportions
4.3.1. Large samples
4.4. Ratio of the variances
4.4.1. Normal populations

5. Analysis of Variance
5.1. Introduction
5.2. One-way ANOVA
5.3. ANOVA table
5.4. Multiple comparisons
5.5. Two-way ANOVA.

6. Goodness of fit tests
6.1. Introduction
6.2. Chi-square tests
6.3. Kolmogorov-Smirnov test
6.4. Graphical tools