In a sleep study, exercise reduces the proportion with difficulty sleeping: 23/100 in exercise vs 31/100 in non-exercise. Which test assesses statistically significant difference in proportions?

In a sleep study, exercise reduces the proportion with difficulty sleeping: 23/100 in exercise vs 31/100 in non-exercise. Which test assesses statistically significant difference in proportions?

• A. 2-proportion z-test
• B. 1-proportion z-test
• C. Paired t-test
• D. Chi-square test

Answer: (A)

This question tests comparing two independent groups on a binary outcome. Here, the outcome is whether someone has difficulty sleeping (yes or no) in two groups: those who exercise and those who don’t. To judge if the observed difference—23% vs 31%—is statistically meaningful, the two-proportion z-test is used. It directly assesses whether the true proportions differ between the two independent samples by comparing the observed difference to what would be expected if both groups had the same underlying proportion. With 100 participants per group, the normal approximation is appropriate, making this test reliable. A chi-square test on a 2x2 table would also be valid and often yields similar results in large samples, but the two-proportion z-test is the most direct way to compare two proportions. The other options don’t fit: a one-proportion z-test is for a single proportion against a known value, a paired t-test is for continuous outcomes in matched pairs, and the chi-square test isn’t specifically about differences in two proportions in independent groups.

This question tests comparing two independent groups on a binary outcome. Here, the outcome is whether someone has difficulty sleeping (yes or no) in two groups: those who exercise and those who don’t. To judge if the observed difference—23% vs 31%—is statistically meaningful, the two-proportion z-test is used. It directly assesses whether the true proportions differ between the two independent samples by comparing the observed difference to what would be expected if both groups had the same underlying proportion. With 100 participants per group, the normal approximation is appropriate, making this test reliable. A chi-square test on a 2x2 table would also be valid and often yields similar results in large samples, but the two-proportion z-test is the most direct way to compare two proportions. The other options don’t fit: a one-proportion z-test is for a single proportion against a known value, a paired t-test is for continuous outcomes in matched pairs, and the chi-square test isn’t specifically about differences in two proportions in independent groups.