Let X1,...,Xn be a sample from the normal distribution N(, 2). (i) If = 0 (known),

Let X1,...,Xn be a sample from the normal distribution N(ξ, σ2).

(i) If σ = σ0 (known), there exists a UMP test for testing H : ξ ≤ ξ0 against

ξ>ξ0, which rejects when (Xi − ξ0) is too large.

(ii) If ξ = ξ0 (known), there exists a UMP test for testing H : σ ≤ σ0 against K : σ>σ0, which rejects when (Xi − ξ0)

2 is too large.