Assume that we want to test a null hypothesis about a single mean at a 5 .05, one-tailed. Further assume that all necessary assumptions are met. Could there be a case in which we would be more likely...

Assume that we want to test a null hypothesis about a single mean at a 5 .05, one-tailed. Further assume that all necessary assumptions are met. Could there be a case in which we would be more likely to reject a true than to reject a false one? (In other words, can power ever be less than a?)