A recent survey reported that in a sample of 300 students who attend two-year colleges, 105 work at least 20 hours per week. Additionally, in a sample of 225 students attending private four-year universities, only 20 students work at least 20 hours per week. What is the test value for a test of the difference between these two population proportions?
A) 6.95
B) 7.61
C) 2.38
D) 4.18

Question

Quizplus · Accepted Answer

The test value for a test of the difference between two population proportions is given by:z = (p1 - p2) / sqrt(p(1-p)(1/n1 + 1/n2))where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and p is the pooled proportion.In this case, p1 = 105/300 = 0.35, p2 = 20/225 = 0.089, n1 = 300, n2 = 225, and p = (105 + 20) / (300 + 225) = 0.222.Plugging these values into the formula, we get:z = (0.35 - 0.089) / sqrt(0.222(1-0.222)(1/300 + 1/225)) = 6.95Therefore, the test value is 6.95, which corresponds to choice A.

A Recent Survey Reported That in a Sample of 300