To compare the proportions between two independent groups, which test would you use?

To compare the proportions between two independent groups, which test would you use?

• A. 1-Proportion Z-Test
• B. 1-Proportion T-Test
• C. 2-Proportion Z-Test
• D. Chi-Square Test of Independence

Answer: (C)

When you want to compare the proportions from two independent groups, you use a two-proportion z-test. This test specifically looks at the difference between two population proportions (p1 and p2) and asks whether they are equal. It relies on the normal approximation to the distribution of the difference between sample proportions, provided the samples are large enough. You set up H0: p1 = p2 (no difference in proportions) and compute the test statistic as z = (p1_hat − p2_hat) / SE, where SE is based on the pooled proportion under the null. The pooled proportion is p_hat = (x1 + x2) / (n1 + n2), and SE = sqrt[ p_hat(1 − p_hat) (1/n1 + 1/n2) ]. If the p-values or z-value exceed your alpha threshold, you conclude there is a real difference between the groups. Key conditions to meet: large enough sample sizes so the normal approximation holds (typically n1 p_hat ≥ 5, n1(1 − p_hat) ≥ 5, and the same for n2). If those conditions aren’t met, an exact method like Fisher’s test would be more appropriate. Why this fits best: it directly assesses whether two independent samples differ in their proportions, rather than testing a single proportion against a fixed value or examining association in a contingency table.

When you want to compare the proportions from two independent groups, you use a two-proportion z-test. This test specifically looks at the difference between two population proportions (p1 and p2) and asks whether they are equal. It relies on the normal approximation to the distribution of the difference between sample proportions, provided the samples are large enough.

You set up H0: p1 = p2 (no difference in proportions) and compute the test statistic as z = (p1_hat − p2_hat) / SE, where SE is based on the pooled proportion under the null. The pooled proportion is p_hat = (x1 + x2) / (n1 + n2), and SE = sqrt[ p_hat(1 − p_hat) (1/n1 + 1/n2) ]. If the p-values or z-value exceed your alpha threshold, you conclude there is a real difference between the groups.

Key conditions to meet: large enough sample sizes so the normal approximation holds (typically n1 p_hat ≥ 5, n1(1 − p_hat) ≥ 5, and the same for n2). If those conditions aren’t met, an exact method like Fisher’s test would be more appropriate.

Why this fits best: it directly assesses whether two independent samples differ in their proportions, rather than testing a single proportion against a fixed value or examining association in a contingency table.