I'm trying to re-learn statistics but the terminology used in my class is different than what I'm used to. Can somebody tell me if I'm on the right track?

Suppose units per day has a normal distribution with unknown mean and standard deviation .

I want to test vs. .

Suppose days and will be rejected if the sample mean daily units satisfies . What is the value of the power function if ?

My work:

So,

Am I understanding this "power function" thing correctly?