I have found a nice example for you to check out on the Penn State web page.
With the final notice saying:
“Comparing two proportions – For proportions there consideration to using “pooled” or “unpooled” is based on the hypothesis: if testing “no difference” between the two proportions then we will pool the variance, however, if testing for a specific difference (e.g. the difference between two proportions is 0.1, 0.02, etc — i.e. the value in Ho is a number other than 0) then unpooled will be used.”
as a quick sum up.
here is a link to a detailed description, if you would like some more detail as to why this is.
https://onlinecourses.science.psu.edu/stat200/node/60
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