5. For any xed a 6 (0,1), a fact is that 20/\" = t/2logn(l + 0(1)) where 0(1) l- 0 as n > oo (which you can use). (a) Suppose that pr 2 2 log n (1 +5) for a constant .5 > 0. Show that the power of Bonferroni's test converges to 1 as n > 00. (b) Suppose that ,u. 5 #2 log an (15) for a constant a > 0. Show that the power of Bonferroni's test converges to 1 exp(a) g a as n > oo. (The power is even smaller than the signicance level, so we say that the test is powerless and it is not useful in this situation.) The two parts together characterize the phase transition from full power to powerlessness of Bonferroni's test. It can be shown that, below the threshold ./2 log n, no test works better than random guess, so Bonferroni's test is in fact optimal for this