Two-sample t test
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.
Conditions for conducting two sample t-test for means:
1.) Parent populations from which samples are drawn are normally distributed.
2.) The two samples are random and independent of each other.
3.) Population variances are equal and unknown.
For validity of t-test we should check the equality of variances with the help of F-test for equality of variances. If the hypothesis is rejected then we cannot apply t-test. In such cases we apply Behren's d-test.
But for practical problems the assumptions 1.) and 3.) are taken to be true.