We want to test a null hypothesis about a single mean at α = 0.05, one-tailed test assumed. All necessary assumptions are met. Could there be a case where we are more likely to reject a true null...

We want to test a null hypothesis about a single mean at α = 0.05, one-tailed test assumed. All necessary assumptions are met. Could there be a case where we are more likely to reject a true null hypothesis than a false one? In other words, can power ever be less than α?