I keep reading that in order for a t-test to be valid the data need to be normal. I have distributions which are clearly skewed to the right (long right tails) so they are not normal. However I have a sample of of n>100 in both bases so the sampling distributions are essentially normal.

My question therefore is: does the t-test requirement for normality refer to the original distributions for the raw data, or for the sampling distributions for the sample means?

Thanks