The Power of the Test A $\bar { Y }$ Or $\bar { Y } ^ { 2 }$

Short Answer

The power of the test a. is the probability that the test actually incorrectly rejects the null hypothesis when the null is true.
b. depends on whether you use $\bar { Y }$ or $\bar { Y } ^ { 2 }$ for the $t$ -statistic.
c. is one minus the size of the test.
d. is the probability that the test correctly rejects the null when the alternative is true.