At one SAT test site students taking a second test inhaled supplemental oxygen for 10 minutes before the test. Some received oxygen, others did not. Which procedure should we use to test whether breathing extra oxygen improves test performance?

At one SAT test site students taking a second test inhaled supplemental oxygen for 10 minutes before the test. Some received oxygen, others did not. Which procedure should we use to test whether breathing extra oxygen improves test performance?

• A. 2-proportion z-test
• B. Matched-pairs t-test
• C. 1-proportion z-test
• D. Paired t-test

Answer: (A)

This question is about comparing two independent groups on a binary outcome. When you have two separate groups (one that received oxygen and one that did not) and the outcome is yes/no (for example, whether a student met a performance criterion), the appropriate test is a two-proportion z-test. It looks at whether the proportion achieving success in the oxygen group differs from the proportion in the non-oxygen group, under the null that the two proportions are the same. The reasoning is that you’re not measuring a continuous score here but a count of successes vs. failures in each group. The two-proportion test uses a pooled proportion to estimate variability under the null and yields a z-statistic to assess whether the observed difference in proportions is likely to occur by chance. Conditions to keep in mind: you need sufficiently large samples in both groups so the normal approximation is valid, and observations should be independent within and between groups. If the outcome were a continuous test score, a two-sample t-test would be more natural, but with a binary outcome across two independent groups, the two-proportion z-test is the best fit.

This question is about comparing two independent groups on a binary outcome. When you have two separate groups (one that received oxygen and one that did not) and the outcome is yes/no (for example, whether a student met a performance criterion), the appropriate test is a two-proportion z-test. It looks at whether the proportion achieving success in the oxygen group differs from the proportion in the non-oxygen group, under the null that the two proportions are the same.

The reasoning is that you’re not measuring a continuous score here but a count of successes vs. failures in each group. The two-proportion test uses a pooled proportion to estimate variability under the null and yields a z-statistic to assess whether the observed difference in proportions is likely to occur by chance.

Conditions to keep in mind: you need sufficiently large samples in both groups so the normal approximation is valid, and observations should be independent within and between groups.

If the outcome were a continuous test score, a two-sample t-test would be more natural, but with a binary outcome across two independent groups, the two-proportion z-test is the best fit.