Question: Let X1,..., Xn be a random sample from a n(, 2) population. Consider testing H0: 0 versus H1 : > 0. Let

Let X1,..., Xn be a random sample from a n(θ, σ2) population. Consider testing
H0: θ ≤ θ0 versus H1 : θ > θ0.
Let m denote the sample mean of the first m observations, X1,... ,Xm, for m = l,...,n. If <σ2 is known, show that for each m = 1 ,...,n, the test that rejects H0 when
m > θ0 + zα√σ2/m
is an unbiased size α test. Graph the power function for each of these tests if n = 4.

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