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.