Hint: The power of a test measures the ability to reject the null hypothesis when it is not true. Do you know what the power represents in terms of probability regarding H0 and H1?
Hi, I have one multiple choice question.
When you are designing a research study and considering what hypothesis test you might use, a common rule of thumb is to select the most powerful test. Why is this a good idea?
a. The most powerful test is the test most likely to get the right answer.
b. The most powerful test is the test most likely to result in a type II error.
c. The most powerful test is the test least likely to fail to reject the null hypothesis when it is false.
d. The most powerful test is the most likely to not reject the null hypothesis when it is true.
Thanks! (Brief explanation will be very helpful to me.)
It can't be b) because you want to minimize the Type II error.
It can't be d) because the power looks at the alternative hypothesis.
In terms of a) we would be tempted to say yes but it is not completely true.
The reason why I think the answer is c) is because being least likely to reject H0 when H0 is false means that it is most likely to fail to reject H0 when H0 is false and thus accept H1 when H1 is true which is the definition of power.
Remember that Power = P(H1 accepted|H1 true) and so you want to maximize this probability to maximize the power of your test.