Confidence Interval on the Difference Between Proportions (4 of 4)
Next chapter: Logic of hypothesis testing

lower limit = p_{1}  p_{2}  (z) (estimated)
 upper limit = p_{1}  p_{2} + (z) (estimated)
 Confidence
interval: lower limit ≤ π_{1}  π_{2} ≤ upper
limit.
Assumptions

The two proportions are
independent.
 The adequacy of
the normal approximation depends on the sample size (N) and π. Although
there are no hard and fast rules, the following is a guide to
needed sample size:
If π is between 0.4
and 0.6 then an N of 10 is adequate. If π is as low as
0.2 or as high as 0.8 then N should be at least 25. For π
as low as 0.1 or as high as 0.9, N should be at least 30.
A more conservative rule of thumb that is often recommended is
that Nπ and N(1  π) should both be at least 10.
Click
here for
an interactive demonstration of the normal approximation to the
binomial to explore the validity of these rules of thumb.
Next chapter: Logic of hypothesis testing