Question: 37. Let XI, ,, ,,Xm and lj, ... , y be independent samples from N(tl) and N( 1/,1), and consider the hypothesis H : 1/

37. Let XI, ,, ,,Xm and lj, ... , y" be independent samples from N(tl) and N( 1/,1), and consider the hypothesis H : 1/ S Eagainst K : 1/ > E. There exists a UMP test, and it rejects the hypothesis when Y- Xis too large. [If EI < 1/1 is a particular alternative, the distribution assigning probability 1 to the point 1/ = E= (mEl + n1/I)/(m + n) is least favorable.]

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