I was studying on this subject and I got some questions. Lets take the test $$H_0:\theta\in\Theta_0 \space vs\space H_1:\theta\in\Theta_0^c$$ where $\Theta$ is the parametric space and $$\lambda(x)=\frac{\sup_{\Theta_0}L(\theta|x)}{\sup_{\Theta^c}L(\theta|x)}$$ and the critical region is:Reject $H_0$ if {$\lambda(x)\leq c$} where $0\leq c\leq 1$
No matter what the hypotheses, the critical region is always that way?
I choose $c$ such that $P_\theta(\lambda(x)\leq c)=\alpha$? Where $\alpha$ is the size of test.