Consider the setting where we have multiple null hypotheses HQ"; for 1' E [n] := {1, . . . ,n}. Suppose that we are interested in testing the global null hypothesis H H0 = n Hos: i=1 which holds if and only if all the individual hypotheses Ho- hold. Moreover, suppose that for each individual HM, we already have a test that produces a pvalue pm- which is a uniform random variable over (0,1) under H0,i- We would like to combine p1, . . . , pn to test the global null hypothesis H0. Suppose that the p-values p1, . . . , pn are independent. 4. Consider the individual Z-test that rejects H03 if K- 2 250, where 2:0I is the (1 a) quantile of N(D,1). Show that Bonferroni's test {based on Ztests) rejects the global null if and only if main 2 2W". I'E[n]