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 α

Question

Quizplus · Accepted Answer

To find the z-test statistic, we first need to calculate the proportions of each group:

Proportion of business school seniors pursuing MBA = 26/200 = 0.13
Proportion of arts and sciences seniors pursuing MBA = 120/800 = 0.15

Next, we need to calculate the standard error of the difference between two proportions:

SE = sqrt(p1(1-p1)/n1 + p2(1-p2)/n2)
SE = sqrt(0.13(0.87)/200 + 0.15(0.85)/800)
SE = 0.0287

Finally, we can calculate the z-test statistic:

z = (p1 - p2) / SE
z = (0.13 - 0.15) / 0.0287
z = -0.716

Therefore, the z-test statistic is -0.716, which corresponds to choice letter C.

At Huge University, a Sample of 200 Business School Seniors