Question

At one ACT test location students taking the test for a second time volunteered to inhale supplemental oxygen for 5 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 ACT 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?
2-sample t-test

matched pairs t-test

1-proportion z-test

2-proportion z-test

1-sample t-test

Answer 1

Answer:

2-proportion z test

Step-by-step explanation:

2-sample t-test: tests the differences between two population means (tests if means are equal). This won't be the best fit for our procedure.

Matched pairs t-test: this is similar to the 2-sample t-test except it compares the means for a significance difference of paired data. This won't be the best fit for our procedure.

1-proportion z-test: is used to test the outcome of one proportion in a population. Since we have two proportions this procedure won't be a best fit.

1-sample t-test: it tests or compares your sample mean to a known value or population mean. Generally, t-tests are used to compare means and are not bests fits to test if two proportions are the same.

2-proportion z-test is to compare two proportions (independent of each other) to see if they are the same.

Here we are comparing to independent proportions of oxygen (supplemental oxygen and normal air). Since we are testing the claims about the inferences for both proportions,  2-proportion z-test is best procedure to use.