Question

Before a researcher tries to prove her alternative hypothesis, she wants to plan her experiment so that the resulting hypothesis test is "powerful". What does this mean?

a. She wants to make sure that if the alternative hypothesis is true, there is a high probability that she will reject the null hypothesis.

b. She wants to make sure that the probability of a type I error is small.

c. She wants to make sure that if the null hypothesis is true, there is a high probability that she won't reject it.

d. None of these choices are really describes what power is all about.

Answer 1

The power of the statistical test is the probability of rejecting a null hypothesis when it is false.

Therefore if the hypothesis test is powerful which means there is a high probability that we reject the null hypothesis when it is not true. Hence the statistical we draw from this test will be good.

Therefore the meaning of powerful test is:

a. She wants to make sure that if the alternative hypothesis is true, there is a high probability that she will reject the null hypothesis.