A medical experiment compared zinc supplements with a placeb

A medical experiment compared zinc supplements with a placebo for reducing the duration of colds. Let denote the mean decrease, in days, in the duration of a cold. A decrease to = 1 is a practically important decrease. The power of the test against the specific alternative = 1 is defined as

Solution

Power of a test defintion:

The power of a hypothesis test is actually the probability of making the correct decision if the alternate hypothesis is true. Here it is the probability of taking the corerct decision when mu = 1 is true.

In other words,