Attached is a problem I am trying to do for revision
It's mostly bookwork I've done that. What worries me are parts b) (iii) and c).
Could you help me with the interpretation of the likelihood ratio statistic and the graphs? What I know is that $\Lambda$ will converge in distribution to $\chi_{1}^2$ so that we can compare the result with the given values. For part c) we can conclude that both graphs pass through the point $(\lambda_{0},\alpha)$, if we plot the power against the value of $\lambda$. We also have by the NP lemma that $w_{a}(\lambda)> w_{b}(\lambda)$ for $\lambda > \lambda_{0}$