# Multi-parameter likelihood ratio tests

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6.5.3(b) Lex X1,...Xn and Y1,..Ym are independent random samples from N( Î¸1, Î¸3) and

N( Î¸2, Î¸4), respectively. Show that the likelihood ratio test for testing H0: Î¸3= Î¸4, Î¸1 and Î¸2 unspecified, against H1: Î¸3 ^= Î¸4, Î¸1 and Î¸2 unspecified, can be based on the random variable

F= Sum from 1 to n (Xi-Xbar)^2/(n-1)

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Sum from 1 to m (Yi-Ybar)^2/(m-1).

https://brainmass.com/statistics/sampling/multi-parameter-likelihood-ratio-tests-35383

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The solution uses proof and a step-by-step equation to answer the question in an attachment.

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