To compare adoption rates between men and women using two proportions, which test is appropriate?

To compare adoption rates between men and women using two proportions, which test is appropriate?

• A. ANOVA
• B. Paired t-test
• C. 2-proportion z-test
• D. Chi-square test of independence

Answer: (C)

You're looking at two independent groups (men and women) with a binary outcome (adopted: yes or no). The goal is to determine if the adoption rates differ between these two groups, which means you’re comparing two population proportions. The two-proportion z-test does exactly that: it tests whether the difference between the observed proportions from the two samples is large enough to conclude that the true population proportions are not equal. It uses the normal approximation to the distribution of the difference in proportions and provides a z statistic (or a p-value) to decide about the null hypothesis p1 = p2. ANOVA is for comparing means across groups, not binary proportions. A paired t-test is for related or matched samples, not two independent groups. A chi-square test of independence could also assess association between gender and adoption in a 2x2 table, but the two-proportion z-test is the direct method designed specifically for comparing two independent proportions.

You're looking at two independent groups (men and women) with a binary outcome (adopted: yes or no). The goal is to determine if the adoption rates differ between these two groups, which means you’re comparing two population proportions. The two-proportion z-test does exactly that: it tests whether the difference between the observed proportions from the two samples is large enough to conclude that the true population proportions are not equal. It uses the normal approximation to the distribution of the difference in proportions and provides a z statistic (or a p-value) to decide about the null hypothesis p1 = p2.

ANOVA is for comparing means across groups, not binary proportions. A paired t-test is for related or matched samples, not two independent groups. A chi-square test of independence could also assess association between gender and adoption in a 2x2 table, but the two-proportion z-test is the direct method designed specifically for comparing two independent proportions.