Assume that as part of a consulting project, you need to work
on a paired data analysis, with data (xi, yi), i = 1, · · · , 18. The purpose is test
H0 : θD = 0 versus H1 : θD > 0, where θD is the location parameter of the
distribution of differences Di = Yi − Xi for i = 1, · · · , n. Using the power of
the t-test as the criterion, explictly write down the steps you will use to assess
whether the paired t-test procedure is robust to departures from assumptions,
and the data is actually from a considerably heavier-tailed (than the normal)
distribution.

I will highly appreciate your help.