2. In the situation of the previous problem there exists no test for testing H: = 0 at level a , which for all 0 has power P> a against the alternatives

a, 0) with = ~l > O. [Let P( ~l' 0) be the power of any level a test of H, and let P( 0) denote the power of the most powerful test for testing = 0 against = ~l when 0 is known. Then infopal ' o):s; infoP(o) = a.]