Distinguishes paired from independent sample designs and shows why pairing reduces noise and produces a more powerful test. Students calculate paired differences and the paired t-statistic, construct confidence intervals for the mean difference, and apply the CI-hypothesis test duality to before/after and matched business comparisons.

Covers the two-proportion Z-test for comparing two independent proportions, including the pooled standard error used for testing and the unpooled standard error used for confidence intervals. Students apply proportion tests to ad-channel comparisons, send-time optimization, and defect-rate analysis, learning when a statistically significant difference is too small to matter.

Builds a contingency table from two categorical variables and calculates expected frequencies under independence, then the chi-square test of independence for detecting association. Students calculate Cramér's V to measure association strength separately from statistical significance, applying both to customer churn and survey-association questions.

Explains why running multiple pairwise t-tests inflates the Type I error rate and introduces one-way ANOVA as the corrective F-test comparing between-group and within-group variance. Students construct the ANOVA table, run Tukey's HSD post-hoc test to identify which specific group pairs differ, and calculate eta-squared as an effect size, applying the full pipeline to a real four-region sales comparison.