JMP notes that the F distribution is used as the basis of the calculations for the one sample and two sample means tests in this document. https://www.jmp.com/content/dam/jmp/documents/en/white-papers/wp-jmp-powersample-104887.pdf

But I had previously assumed that JMP would make its power calcs using the T-distribution since the T distribution is basis of the one and two-sample tests typically. Nevertheless, I would expect power calculations to give the same answer either way (using F or T appropriately). But I can't seem to obtain the same results as JMP when I use a T-distribution for my own power calcs.

So my questions are: (1) Why does JMP use the F statistic and F-distribution for power calcs? (2) In theory, should it result in the same answer as doing power calculations using a t statistic and T distribution?