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Math Help - LRT for variance of normal distribution

  1. #1
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    LRT for variance of normal distribution

    Derive a likelihood ratio test for H0: σ = σ0 vs. Ha : σ ≠ σ0 for a sample from a normal distribution with unknown mean.

    I have found the two likelihood functions that make up the ratio, but I am struggling to simplify it into something understandable.
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  2. #2
    MHF Contributor harish21's Avatar
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    What have you found so far? Please write down!
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  3. #3
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    -2log⁡(λ)= nlog(σ0)- n/σhat ̂ - nlog(σhat)+ (nσhat)/(σ0^2)

    This is the simplest I've gotten it, and it doesn't seem very coherent to me.
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