Suppose X1 and X2 are iid samples and consider the null hypothesis H0 : Xi ∼ N(0, 1) versus the alternative H1 : Xi ∼ U[

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Suppose X1 and X2 are iid samples and consider the null
hypothesis H0 : Xi ∼ N(0, 1) versus the
alternative H1 : Xi ∼ U[0, 2] for i = 1,
2.
(a) Show that the critical region of a likelihood ratio test is
of the form S \ C, where S is a square and C is a circle.
(b) Determine the size and power of the test φ for which the
radius of the circle equals the side length of the square.
(c) Determine the power of the test ψ for which the size is
0.05.