In teaching my classes, I've always stressed that under the usual assumptions with variance unknown, the t-test is appropriate and should always be used; however, a student recently posed a question which I could not answer. If doing a C.I. on proportions you don't know p, then you also don't know the variance. The question the students asked was Why don't we use the t-value when we form a C.I. on a proportion?
There is a great deal of logic to their question since clearly p is not normal. Anyone with any ideas?