If we assume normality I am told I should be able to write the likelihood ratio test

λ1 = $\displaystyle 2[ln\hat{L} - ln\hat{L_R}]$

as

λ2 = $\displaystyle T[ln\hat{σ_R^2} - ln\hat{σ^2}]$

provided we assume normality.

How would I do this?

(my equations don't look right they should be

λ1 = 2[ln(L-hat) - ln(L-hat-restricted)]

as

λ2 = T[ln(σ^2_R) - ln(σ^2)] )