30. Suppose in Problem 29(i) the variance 0 2 is unknown and that the data consist of XI"'" Xn together with an independent random variable S2 for which S2/02 has a X2-distribution.1f K is replaced by EO?/02 = r2, then (i) the confidence sets E(O; - XY/S2 .::;; C are uniformly most accurate equivariant under the group generated by the n-dimensional generalization of the group Go of Example 17 of Chapter 6, and the scale changes X: = cX;, S,2 = c2 S2. (ii) The confidence sets of (i) are minimax with respect to the measure p. given by 1 p.[ C( X , S2)] = 2" [volume of C( X, S2)] . o [Use polar coordinates with 02 = EO?,]