Suppose X1,..., Xn are i.i.d. N(, 2) with both parameters unknown. Consider testing = 0 versus

Suppose X1,..., Xn are i.i.d. N(μ, σ2) with both parameters unknown. Consider testing μ = 0 versus μ = 0. Find the likelihood ratio test statistic, and determine its limiting distribution under the null hypothesis. Calculate the limiting power of the test against the sequence of alternatives (μ, σ2) =

(h1n−1/2, σ2 + h2n−1/2).