13.9 Suppose there are three test statistic, T1, T2, and T3, each of which can be used to test a null hypothesis H0 against an alternative hypothesis H1.

Show that for any pair of tests, say T1 and T3, when the relevant ARE’s exist, ARE(T1, T3) ¼ ARE(T1, T2) ARE(T2, T3) ¼ ½ARE(T3, T1)1 where we take 1=1 to be 0 and 1=0 to be 1.