Question: help with this previous year question? Problem 5: [20pts] Let X1, . . . ,X,L be an i.i.d. sample from N(0, 02) and we consider

help with this previous year question?

Problem 5: [20pts] Let X1, . . . ,X,L be an i.i.d. sample from N(0, 02) and we consider testing H0 : (72 = 1 vs H A : a2 a 1. Dene g(t) = t 1 log(t), T = zz-"=1 9:2. A statistician has programmed the following testing procedure: Step 1. Given a and sample size n, compute two constants a, b by solving g(a) = g(b) and 1 a = P(na 3 xi S nb) where xi is Chi-square distribution with 11 degrees of freedom. Step 2: then rejects H0 if and only if mlc 2 b or 9mm 5 a Show that the above test is indeed the Likelihood ratio test of EXACT size a

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