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.What is the z test statistic?
A) -1.322
B) -1.122
C) -0.716
D) We must first know $\alpha$.

Question

Quizplus · Accepted Answer

To test if the proportion is higher in the arts and sciences group, we need to conduct a two-sample proportion z-test. 
The formula for z-test statistic to compare two proportions is: 
z = [(p1 - p2) - 0] / sqrt{p(1-p)[(1/n1) + (1/n2)]}
where p = (x1 + x2) / (n1 + n2), x1 is the number of successes in sample 1, x2 is the number of successes in sample 2, n1 and n2 are the sample sizes, and p1 and p2 are the sample proportions. 
In this case, we have:
n1 = 200, x1 = 26, p1 = 26/200 = 0.13
n2 = 800, x2 = 120, p2 = 120/800 = 0.15
p = (26 + 120) / (200 + 800) = 0.138
z = [(0.13 - 0.15) - 0] / sqrt{0.138(1-0.138)[(1/200) + (1/800)]} = -0.716
Therefore, the z-test statistic is -0.716, and the answer is choice (C).

At Huge University,a Sample of 200 Business School Seniors Showed α\alphaα

At Huge University,a Sample of 200 Business School Seniors Showed $\alpha$