Unit 3: Inference for Categorical Data: Proportions

Sampling distribution of the sample proportion guide with center, standard error, conditions, examples, probability, and practice.

Estimate one population proportion from a random sample, check the conditions that justify a normal interval, calculate the margin of error, and interpret the confidence statement in context.

Estimate the difference between two population proportions while preserving group order, using separate sample proportions in the standard error and interpreting the interval in context.

Connect decisions in a significance test to their possible consequences: a Type I error rejects a true null, a Type II error fails to reject a false null, and power is the probability of detecting a specified real effect.

Test a claim about one population proportion using the null value in the standard error, match the p-value tail to the alternative hypothesis, and state the conclusion about the population parameter.

Use a two proportion z test when two independent groups produce binary outcomes and the question asks whether their population proportions differ or differ in a specified direction. The equality null pools the two samples because the null model treats them as sharing one population proportion.

Chi-square tests of homogeneity and independence use the same expected-count formula and chi-square statistic but begin from different data-collection stories. Homogeneity compares categorical distributions across populations or treatments; independence asks whether two categorical variables are associated within one population.

Chi-square calculator with expected counts, df, critical values, p-value logic, worked cases, MCQs, FRQs, and a 20-method statistics engine.

Chi-square assumptions and expected-count diagnostics with design checks, 20 cases, focused MCQs, FRQs, and interpretation guidance.