Let X1,...,Xm; Y1,...,Yn be independently normally distributed with common variance 2 and means E(Xi) = +

Let X1,...,Xm; Y1,...,Yn be independently normally distributed with common variance σ2 and means E(Xi) = α + β(ui − u¯), E(Yj ) =

γ + δ(vj − v¯), where the u’s and v’s are known numbers. Determine the UMP invariant tests of the linear hypotheses H : β = δ and H : α = γ, β = δ.