E.g. the null hypothesis is $\beta = 0$, while the true value of $\beta$ is 0. What would be the power of the hypothesis test?
My way of thinking is: Since the power of the test is 1- Prob(Type II error) (Type II error is the error to accept the null hypothesis when it is false). However, since the null hypothesis is true here, Prob(Type II error)=0. So the power of the test is 1. Am I correct?