Two well-known aviation training schools are being compared using random samples of their graduates. It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try, compared with 104 of 260 graduates of Blue Yonder Institute. To compare the pass rates, the p-value for a right-tailed test is approximately:
A).054
B).027
C).155
D).013

Question

Quizplus · Accepted Answer

We are conducting a right-tailed test to determine if the pass rate at Blue Yonder Institute is higher than that of Fly-More Academy. We can use a two-sample z-test for proportions to compare the two groups.

The observed proportion of Fly-More Academy graduates passing on the first try is 70/140 = 0.5, and the observed proportion of Blue Yonder Institute graduates passing on the first try is 104/260 = 0.4.

The pooled proportion of passing is (70+104)/(140+260) = 0.43.

The test statistic is:
z = (0.4 - 0.5) / sqrt(0.43(1-0.43)(1/140 + 1/260)) = -2.34

Using a standard normal distribution table or calculator, the p-value for this test is approximately 0.027. This means that there is strong evidence to suggest that the pass rate at Blue Yonder Institute is higher than at Fly-More Academy, with a p-value less than the conventional alpha level of 0.05. Therefore, we reject the null hypothesis and conclude that there is a significant difference in the pass rates between the two schools.

Two Well-Known Aviation Training Schools Are Being Compared Using Random