67. (i) Let X;j (j = 1, . . . , n; i = 1, .. . , s) be independent N( t, 02), 0 2 unknown. Then the problem of obtaining simultaneous confidence intervals for all differences - ~i is invariant under Go, G2 , and the scale changes G3• (ii) The only equivariant confidence bounds based on the sufficientstatistics X" and S2 = Et( X;j - X;.)2 and satisfying the condition corresponding to (117) are those given by

(122) (123) ti S(x) = {x: x.i. - x;.- S::; -~; vn - s ti ::;xj.-x;. + ---S for all i *j} with ti determined by the null distribution of the Studentized range P. { max IX,.- X;.I } o S/~