Let $X\sim \Gamma(p,\lambda)$, i. e. we have the density:$$f_{p,\lambda}(x)=\frac{\lambda^p}{\Gamma(p)}x^{p-1}\exp(-\lambda x)$$ where $p=2$ and $H_0: \lambda=1$ or $H_1: \lambda=2$. What is the test of $H_0$ against $H_1$ with maximum test power at level $\alpha= 0.05$?
What test should I use here? A Likelihood-ratio test?