Describe the difference that one could draw from a sample T-test when CLT does NOT apply. What could one do instead of a T-test?

Describe the difference in the conclusions that one could draw from a sample T-test when CLT did NOT kick in, as in qqnorm() did not show a normal distribution for the sample size. What could one do instead of a T-test, and what would their test statistic be?

2017-04-11T00:37:33.809Z