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AP®︎/College Statistics

Lesson 5: Sampling distributions for differences in sample proportions

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 ${\hat{p}}_{A} - {\hat{p}}_{B}$ ‍?

Stuck?