Find a 95 confidence interval for based on inverting the test statistic statistic .
For our data we have
Therefore it can be proven that the MLE for is given by
To find the confidence interval I should invert the test statistic .
The most powerful unbiased size test for testing
where has acceptance region
Substituting my problem (I think) we get that the most powerful unbiased size test for testing
has acceptance region
Substituting we obtain
This means that my confindence interval is defined to be
But I can't seem to find anything concrete and I feel that I've made mistakes somewhere. What to do?