I almost assigned that problem two weeks ago.
I can work it out, but it's a lot of typing.
Basically, and I'm sure you'll keep asking me the same question repeatedly, the
MLEs of populations means under BOTH hypotheses are the sample means.
The estimates of the population variances are of the form
for each of these sets.
UNDER the null hypothesis we have as the estimate of the COMMOM variance as the pooled estimator.
JUST like in the two sample t case, giving us...
You reject the null hypothesis when the ensuing ratio is large...