At Huge University, a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree, compared with 120 of 800 arts and sciences seniors. We want to know if the proportion is higher in the arts and sciences group. For this test, the assumption of normality for the difference of proportions is:
A)clearly unjustified.
B)clearly justified.
C)a borderline call.

Question

Quizplus · Accepted Answer

The assumption of normality for the difference of proportions is justified when both sample sizes are greater than 10 and the expected number of successes and failures in each group is at least 5. In this case, the sample size for the arts and sciences group is 800, which is clearly greater than 10, and the expected number of successes (120*0.15 = 18) and failures (680*0.85 = 578) in this group are both greater than 5. Therefore, we can assume normality for the difference of proportions and use a z-test to compare the proportions between the two groups.

At Huge University, a Sample of 200 Business School Seniors