Oh I did that before, went to an English day there.
Catch any bus in the city (from Central or Town Hall station too)
that says Moore Park (its right across the road) or catch a general UNSW bus (but NOT one of the express UNSW ones) and get off at Moore Park and cross the road.
The STAT is a test that students need to do if they are considering courses at some unis like pharmacy at usyd. not all unis need STAT.
its pretty much just an iq-style test.