In a study, 63 of 211 men and 130 of 651 women prefer cats to dogs. Which test assesses whether women are more likely to prefer cats?

In a study, 63 of 211 men and 130 of 651 women prefer cats to dogs. Which test assesses whether women are more likely to prefer cats?

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

Answer: (C)

When you want to compare the likelihood of a binary outcome between two independent groups, you use a test for two proportions. Here, “prefers cats” is a yes/no outcome, with two independent groups: men and women. The right approach is the two-proportion z-test. Compute the sample proportions: men 63/211 ≈ 0.299, women 130/651 ≈ 0.200. The observed difference (women minus men) is about -0.099, which points in the opposite direction of the stated hypothesis but the test will tell you whether that difference is statistically significant. The two-proportion z-test uses a pooled estimate under the null that the proportions are equal and assesses whether the observed difference could arise by chance given the sample sizes. This test is preferred here because it directly handles comparing two independent proportions from binary data. The other options are for different situations: t-tests compare means of continuous data (not applicable to proportions), a paired t-test is for matched or repeated measurements on the same subjects, and a chi-square test of independence could also be used with a 2x2 table but the direct, conventional choice for comparing two independent proportions is the two-proportion z-test.

When you want to compare the likelihood of a binary outcome between two independent groups, you use a test for two proportions. Here, “prefers cats” is a yes/no outcome, with two independent groups: men and women. The right approach is the two-proportion z-test.

Compute the sample proportions: men 63/211 ≈ 0.299, women 130/651 ≈ 0.200. The observed difference (women minus men) is about -0.099, which points in the opposite direction of the stated hypothesis but the test will tell you whether that difference is statistically significant. The two-proportion z-test uses a pooled estimate under the null that the proportions are equal and assesses whether the observed difference could arise by chance given the sample sizes.

This test is preferred here because it directly handles comparing two independent proportions from binary data. The other options are for different situations: t-tests compare means of continuous data (not applicable to proportions), a paired t-test is for matched or repeated measurements on the same subjects, and a chi-square test of independence could also be used with a 2x2 table but the direct, conventional choice for comparing two independent proportions is the two-proportion z-test.