Repeat the experiment described in Exercise 6

Repeat the experiment described in Exercise 6.1, but for Xi, Yi ∼ Gam(3, 2). As our random variables are not normally distributed we have no right to believe in the pvalue for the t-test. Interestingly, the p-value is not a bad estimate of the probability of the t-value occurring. This gives some confidence that even when the data is not exactly normal the p-values of the t-test are not always too misleading. Of course, it is always possible to cook up examples where the p-values are significantly underestimated, particularly for thick-tailed distributions.