In George Casella textbook page 383, it said we have: $P_\theta(\textbf{X}\in R) = $ probability of a type I error if $\theta\in \Theta_0$;
= one minus the probability of a Type II error if $\theta\in \Theta_0^c$.
I am confused here. So the sum of type I error and type II error is equal to 1? Please correct my mistakes.