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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 9

Lesson 5: Sampling distributions for differences in sample proportions

# Mean and standard deviation of difference of sample proportions

## Problem

An educational researcher is studying two similar high schools in different states. Suppose that 50, percent of all 425 students at high school A have taken a college-level course, while 40, percent 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 left parenthesis, start text, A, end text, minus, start text, B, end text, right parenthesis between the proportions of students who have taken a college-level course in each sample.
Consider the formula:
sigma, start subscript, p, with, hat, on top, start subscript, start text, A, end text, end subscript, minus, p, with, hat, on top, start subscript, start text, B, end text, end subscript, end subscript, equals, square root of, start fraction, p, start subscript, start text, A, end text, end subscript, left parenthesis, 1, minus, p, start subscript, start text, A, end text, end subscript, right parenthesis, divided by, n, start subscript, start text, A, end text, end subscript, end fraction, plus, start fraction, p, start subscript, start text, B, end text, end subscript, left parenthesis, 1, minus, p, start subscript, start text, B, end text, end subscript, right parenthesis, divided by, n, start subscript, start text, B, end text, end subscript, end fraction, end square root
Why is it not appropriate for the researcher to use this formula for the standard deviation of p, with, hat, on top, start subscript, start text, A, end text, end subscript, minus, p, with, hat, on top, start subscript, start text, B, end text, end subscript?