A 2013 Gallup poll asked randomly selected U.S. adults about staying at their current weight. Among 562 men, 242 wanted to stay; among 477 women, 172 wanted to stay. Which test should be used to compare these two proportions?

A 2013 Gallup poll asked randomly selected U.S. adults about staying at their current weight. Among 562 men, 242 wanted to stay; among 477 women, 172 wanted to stay. Which test should be used to compare these two proportions?

• A. 2-proportion z-test
• B. Chi-square test of homogeneity
• C. Fisher's exact test
• D. Z-test for proportions

Answer: (B)

When you want to compare proportions across two independent groups, think in terms of a 2x2 table: group by outcome (stay vs not stay). The chi-square test of homogeneity asks whether the distribution of the outcome is the same across groups. It uses all four counts and compares observed counts to what would be expected if the two groups shared the same proportion. With large samples in both groups, the chi-square approximation is reliable, making this a natural choice for testing whether staying at current weight differs between men and women. A two-proportion z-test would also assess the difference in proportions and is closely related, but the chi-square test of homogeneity is the standard contingency-table approach used for this kind of comparison. Fisher’s exact test isn’t needed here because all expected counts are well above five, and a Z-test for proportions is suited to testing a single proportion rather than comparing two groups.

When you want to compare proportions across two independent groups, think in terms of a 2x2 table: group by outcome (stay vs not stay). The chi-square test of homogeneity asks whether the distribution of the outcome is the same across groups. It uses all four counts and compares observed counts to what would be expected if the two groups shared the same proportion. With large samples in both groups, the chi-square approximation is reliable, making this a natural choice for testing whether staying at current weight differs between men and women. A two-proportion z-test would also assess the difference in proportions and is closely related, but the chi-square test of homogeneity is the standard contingency-table approach used for this kind of comparison. Fisher’s exact test isn’t needed here because all expected counts are well above five, and a Z-test for proportions is suited to testing a single proportion rather than comparing two groups.