11. Consider two experiments with observations (Xl" '" Xn ) and (YI , · .. , Y,,) respectively, where the X; and Y; are independent normal with variance a2 = 1 and means E(X;) = c;8;, E(Y;) = 8;. Then the experiment based on the Y; is more informative than that based on the Xj if and only if Ic;1 1 for all i.

[If l/c; = 1 +

d, with

d, > 0, let Y,' = Y, + Vi, where Vi is N(O, d;) and independent of Y,. Then c,Y,' has the same distribution as X;. Conversely, if

c, > 1, the UMP unbiased test of H: 8; = 8 against 8; > ° based on ( XI , , X,,) is more powerful than the corresponding test based on (YI , , Y" ).]