A study compares pass rates for two teaching methods with binary outcomes. Which test should be used?

A study compares pass rates for two teaching methods with binary outcomes. Which test should be used?

• A. One-Proportion Z-Test
• B. Paired T-Test
• C. Two-Proportion Z-Test
• D. Chi-Square Test of Independence

Answer: (C)

When you’re comparing success rates (binary outcomes) between two independent groups, you want to know if the difference in proportions is due to chance or reflects a real effect. The two-proportion z-test does exactly this by comparing the two observed pass rates and using a pooled estimate of the proportion under the assumption that there is no real difference. It provides a z-score to assess whether the difference in proportions is statistically significant, assuming a large-sample normal approximation. This approach is appropriate here because the data are counts of passes and fails in two independent groups, and the goal is to test a difference in proportions, not a single proportion or a mean. A one-proportion z-test would only test against a fixed value for one group. A paired t-test is for continuous data in matched pairs, which doesn’t fit binary outcomes. The chi-square test of independence could be used on a 2x2 table, but the two-proportion z-test is the direct and typical method for testing a difference in two proportions with large samples.

When you’re comparing success rates (binary outcomes) between two independent groups, you want to know if the difference in proportions is due to chance or reflects a real effect. The two-proportion z-test does exactly this by comparing the two observed pass rates and using a pooled estimate of the proportion under the assumption that there is no real difference. It provides a z-score to assess whether the difference in proportions is statistically significant, assuming a large-sample normal approximation.

This approach is appropriate here because the data are counts of passes and fails in two independent groups, and the goal is to test a difference in proportions, not a single proportion or a mean. A one-proportion z-test would only test against a fixed value for one group. A paired t-test is for continuous data in matched pairs, which doesn’t fit binary outcomes. The chi-square test of independence could be used on a 2x2 table, but the two-proportion z-test is the direct and typical method for testing a difference in two proportions with large samples.