At one SAT test site students taking the test for a second time volunteered to inhale supplemental oxygen for 10 minutes before the test. In fact, some received oxygen, but others (randomly assigned) were given just normal air. Test results showed that 42 of 66 students who breathed
Oxygen improved their SAT scores, compared to only 35 of 63 students who did not get the oxygen. Which procedure should we use to see if there is evidence that breathing extra oxygen can help
Test-takers think more clearly?
A) matched pairs t-test
B) 2-sample t-test
C) 2-proportion z-test
D) 1-proportion z-test
E) 1-sample t-test

Question

Quizplus · Accepted Answer

We should use a 2-proportion z-test to compare the proportions of students who improved their scores in the group that received oxygen versus the group that did not. This is because we are comparing two independent groups and looking at the proportion of successes (students who improved their scores) in each group. The matched pairs t-test would be used if we were comparing scores of the same group of students before and after receiving oxygen. The 2-sample t-test would be used if we were comparing means of a continuous variable between two independent groups. The 1-proportion z-test would be used if we were comparing a proportion within a single group to a known population proportion. The 1-sample t-test would be used if we were comparing the mean of a single group to a known population mean.

At One SAT Test Site Students Taking the Test for a Second