A simple random sample of 200 students is selected from a large university.In this sample,there are 35 minority students.A simple random sample of 80 students is selected from the community college in the same town.In this sample,there are 28 minority students.What is the standard error of the difference in sample proportions of minority students?
A)0.004
B)0.03
C)0.06
D)0.08

Question

Quizplus · Accepted Answer

The standard error of the difference in sample proportions is calculated using the formula: $\sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}}$, where $p_1$ and $p_2$ are the sample proportions of minority students in the university and community college, respectively, and $n_1$ and $n_2$ are the sample sizes. For the university, $p_1 = \frac{35}{200} = 0.175$ and for the community college, $p_2 = \frac{28}{80} = 0.35$. Plugging these values into the formula gives: $\sqrt{\frac{0.175(1-0.175)}{200} + \frac{0.35(1-0.35)}{80}} \approx 0.06$.

A Simple Random Sample of 200 Students Is Selected from a Large