As in Example 3.9.2, suppose X is multivariate normal with unknown mean = (1,..., k )

As in Example 3.9.2, suppose X is multivariate normal with unknown mean ξ = (ξ1,..., ξk ) and known positive definite covariance matrix . Assume a = (a1,..., ak ) is a fixed vector. The problem is to test H :

k i=1 ai ξi = δ vs. K :

k i=1 ak ξi = δ .

Find a UMPU level α test. Hint: First consider  = Ik , the identity matrix.