A study was recently conducted at a major university to estimate the difference in the proportion of business school and non-business school graduates who go on to a higher degree program within five years of graduation A random sample of 400 business school graduates showed that 75 had gone to graduate school, while in a random sample of 500 non-business graduates, 137 had done so. The standard error for the difference in the proportions of the two groups is
A) 0.0279.
B) 0.
C) 0.0008.
D) 0.0865.
E) 0.1875.

Question

Quizplus · Accepted Answer

The standard error for the difference in 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, and $n_1$ and $n_2$ are the sample sizes for the two groups. For business school graduates, $p_1 = \frac{75}{400}$, and for non-business graduates, $p_2 = \frac{137}{500}$. Plugging these values into the formula gives a standard error of approximately 0.0279.

A Study Was Recently Conducted at a Major University to Estimate