Hypothesis Testing Using Summations

Question

Assuming that n=12 and $\sum_{i=1}^n Y_i^{2}\tag{} = 42 $ perform a level $\alpha=0.05 $ hypothesis test of the following hypothesis. $$H_o=\theta=\theta_o=2$$ against the alternative $$H_a: \theta >2$$. Explain the rejection region. I know that $Y_i^{2}$ is a chi-squared with 2 degrees of freedom or an exponential with expectation 2. And it is a small sample so it would be a t-test. But am unsure on how to solve the problem.

Answer 1

You need to say something about your model (what is $\theta$). Anyway,

Hint: there are good reasons to take the likelihood-ratio test.