Mean and standard deviation of difference of sample proportions

An educational researcher is studying two similar high schools in different states. Suppose that

50 %

of all

425

students at high school A have taken a college-level course, while

40 %

of all

525

students from high school B have taken such a course. The researcher plans on taking separate random samples of

50

students from each high school to look at the difference

(A - B)

between the proportions of students who have taken a college-level course in each sample.

Consider the formula:

σ_{{\hat{p}}_{A} - {\hat{p}}_{B}} = \sqrt{\frac{p_{A} (1 - p_{A})}{n_{A}} + \frac{p_{B} (1 - p_{B})}{n_{B}}}

Why is it not appropriate for the researcher to use this formula for the standard deviation of ${\hat{p}}_{A} - {\hat{p}}_{B}$ ‍?

AP®︎/College Statistics