48. (i) If Xl' . . . ' Xn ; Y1, ••. , y" are independent normal variables with common variance a2 and means E(X;) = Ci' E(Y;) = t + l1, the UMP unbiased test of l1 = 0 against l1 > 0 is given by (59). (ii) Determine the most accurate unbiased confidence intervals for l1. [(i): The structure of the problem becomes clear if one makes the orthogonal transformation X: = (Y; - X;)/fi, Y;' = (X; + y;)/fi.]