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    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( θ1, θ3) and
    N( θ2, θ4), respectively. Show that the likelihood ratio test for testing H0: θ3= θ4, θ1 and θ2 unspecified, against H1: θ3 ^= θ4, θ1 and θ2 unspecified, can be based on the random variable

    F= Sum from 1 to n (Xi-Xbar)^2/(n-1)
    _____________________________
    Sum from 1 to m (Yi-Ybar)^2/(m-1).

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

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