Case 1: small sample, from normal population of known
variance—> z-test
Case 2: SMALL sample, normal population of
unknown variance, variance estimated—> t-test
Case 3: LARGE sample, normal population of
unknown variance, variance estimated—> z-test
Here is a full summary for you:
1. Population distribution known to be normal.
1.1 population variance known(large/small sample size):
z-test.
1.2 population variance unknown(large sample size): z-test.(t(n-1)
is very close to N(0,1) when n is large).
1.3 population variance unknown(small sample size): t-test.
2. Population distribution unknown.
Large samples, we can assume a normal distribution by
CLT. z-test regardless of variance.