statistics
posted by Lezlie .
The researcher wanted to test the hypothesis that Ho: μ=3, knowing the population, which was normal, had a variance of 1.00.

How powerful would this test be against the alternative hypothesis that
Ha: μ=4, given that n=15, α = .05

The probability of making a Type II error is equal to beta. A Type II error is failure to reject the null when it is false. The power of the test is 1beta and is the correct decision of rejecting the null when it is false. The alpha level directly affects the power of a test. The higher the level, the more powerful the test. Sample size also affects power. I'm not sure if your question is asking to calculate the actual power of the test or just determine if the test itself is powerful. If I'm interpreting the question correctly, then the test has power at alpha .05.
I hope this will be some help to you.