(a) Show that for the t and F distributions, for any v, , and k, tv,/2 ...

(a) Show that for the t and F distributions, for any v, α, and k,
tv,α/2 ≤ √(k - 1)Fk-l,v,α.
(Recall the relationship between the t and the F. This inequality is a consequence of the fact that the distributions kFk,v are stochastically increasing in k for fixed v but is actually a weaker statement. See Exercise 5.19.)
(b) Explain how the above inequality shows that the simultaneous Scheffe intervals are always wider than the single-contrast intervals.
(c) Show that it also follows from the above inequality that Scheffe tests are less powerful than t tests.