Two-Proportion Test Examples

Statistics · Axiom Academy

EXAMPLE Two Proportion Examples Three worked examples demonstrating hypothesis testing for comparing two proportions Example 1: Comparing Treatment Success Rates A medical study compares two treatments for a condition. Treatment A had 84 successes out of 120 patients, while Treatment B had 72 successes out of 100 patients. Test at α = 0.05 if there is a significant difference. Excellent work! You've completed three comprehensive two-proportion examples. Here's what we learned: Pooled Proportion: When testing H₀: p₁ = p₂, we combine both samples to estimate the common proportion: p̂ = (x₁ + x₂)/(n₁ + n₂) Standard Error: The SE for two proportions is √[p̂(1-p̂)(1/n₁ + 1/n₂)], which accounts for variability in both samples Test Statistic: The z-statistic measures how many standard errors the difference (p̂₁ - p̂₂) is from zero under H₀ Two-Tailed Test: For α = 0.05, critical values are ±1.96. Reject H₀ if |z| > 1.96 Practical Applications: Two-proportion tests are used in medical trials, political polling, and A/B testing to compare success rates between groups Interpretation: "Fail to reject H₀" means insufficient evidence of a difference, while "Reject H₀" indicates statistically significant difference These three examples demonstrate the complete process for testing differences between proportions in diverse contexts. Practice identifying when to use this test and interpreting results in context!

This is the written version of the interactive lesson above. See the full Statistics course.