Ultimate Inference Guide

One-sample z-interval for a proportion

Uses statistic p̂ and parameter p with conditions of random sample, sample size constraints, and formula p̂±z∗√(p̂(1−p̂)/n).

Two-sample z-interval for difference in proportions

Uses statistic p̂₁ − p̂₂ and parameter p₁ − p₂ with conditions for independent random samples and formula (p̂₁−p̂₂)±z∗√(p̂₁(1−p̂₁)/n₁ + p̂₂(1−p̂₂)/n₂).

One-sample t-interval

Uses statistic x̄ and parameter μ with conditions of random sample or experiment, size constraints, and formula x̄±t∗(s/√n).

Two-sample t-interval for difference in means

Uses statistic x̄₁ − x̄₂ and parameter μ₁ − μ₂ with conditions for independent samples and formula (x̄₁−x̄₂)±t∗√(s₁²/n₁ + s₂²/n₂).

t-interval for slope

Uses statistic b and parameter β with conditions on linear relationship, normal residuals, and formula b±t∗SEb.

One-sample z-test for a proportion

Hypothesis test with H₀: p = p₀, random sample conditions, and formula z=(p̂−p₀)/√(p₀(1−p₀)/n).

Two-sample z-test for difference in proportions

Tests H₀: p₁ − p₂ = 0 with conditions of independent samples and formula z=(p̂₁−p̂₂)/√(p̂(1−p̂)(1/n₁ + 1/n₂)).

One-sample t-test

Tests H₀: μ = μ₀ with assumptions of random sample, normality, and formula t=(x̄−μ₀)/(s/√n).

Two-sample t-test for difference in means

Tests H₀: μ₁ − μ₂ = 0 with conditions of independent samples and formula t=(x̄₁−x̄₂)/√(s₁²/n₁ + s₂²/n₂).

Goodness-of-fit test

Tests H₀: Distribution is correct using the formula χ²=∑((O−E)²/E) and conditions for expected counts.

Homogeneity test

Tests H₀: No difference across groups using the same formula χ²=∑((O−E)²/E) and conditions for expected counts.

Independence test

Tests H₀: Variables are independent also using χ²=∑((O−E)²/E) with conditions on expected counts.