and the s are constants adding to zero, determine (with respect to a suitable group leaving the problem invariant) (i) a UMP invariant test of

and the α’s are constants adding to zero, determine (with respect to a suitable group leaving the problem invariant)

(i) a UMP invariant test of H : α1 = ··· = αa;

(ii) a UMP invariant test of H : ξ1 = ··· = ξa =0 (ξi = µ + αi);

(iii) a test of H : σ2 B/σ2 ≤ δ which is both UMP invariant and UMP unbiased.