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 hig
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:
OPA-js =
PA (1 - PA) PB (1 - PB)
+
ПА
NB
Why is it not appropriate for the researcher to use this formula for the standard deviation of PA - PB?
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