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

As in Example 3.9.2, suppose X is multivariate normal with unknown mean ξ = (ξ1,...,ξk)

T and known positive definite covariance matrix

Σ. Assume a = (a1,...,ak)

T is a fixed vector. The problem is to test H : k i=1 aiξi = δ vs. K : k i=1 akξi = δ .

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