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Let X1, X2, ..., Xn be random sample from normal population N(H,σ2) with unknown mean and variance. With the parameters represented as θ = (θ1, θ2) = (H,σ2), use the likelihood ratio technique to construct the hypothesis test for 2 2H0 :σ  =σ 0. First obtain the likelihood ratio Λ and then show that instead of Λ, the test statistic Λ' (n-1)S(squared)  /  σ squared))  must be used, where S2 is sample variance. Hence, establish that the likelihood ratio test for variance of the single normal population is identical to the result obtained for null hypothesis significance testing of single variance.

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