I know that t tests are primarily used when n<=30 and/or sigma is unknown.

Which statistics should be used if n>30 or sigma is known.

E.g. which statistics I should use to assess the effect of a medication on 45 patients

when week-1: received the medication, week-2 received a Placibo.

Applying a measurement scale, we know mean of general pop. is 30 and Std-dev=10.

Would a correlation statistics between the two sets of results be the correct way to go?

appreciate your earliest response

Shemtov