# One simple multiple choice question

• Apr 26th 2013, 07:36 PM
therexists
One simple multiple choice question
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.)
• Apr 26th 2013, 07:47 PM
chiro
Re: One simple multiple choice question
Hey therexists.

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?
• Apr 26th 2013, 08:09 PM
therexists
Re: One simple multiple choice question
I don't know exactly what the power represents in terms of H0 and H1.
• Apr 26th 2013, 08:10 PM
therexists
Re: One simple multiple choice question
According to your hint, I guess the answer is C, but I'm not sure of "least likely".
• Apr 26th 2013, 08:16 PM
chiro
Re: One simple multiple choice question
The definition of power is given by P(H1 rejected|H1 false) = 1 - B where B = P(H1 rejected|H1 is true).

Your Type I and Type II errors are Type I = P(H0 rejected|H0 true) and Type II = B = P(H1 rejected|H1 true)
• Apr 26th 2013, 08:23 PM
therexists
Re: One simple multiple choice question
so then the answer is B?
• Apr 26th 2013, 08:31 PM
chiro
Re: One simple multiple choice question
No it's the opposite: You want to reduce a Type II error which means you want B to be as small as possible and therefore 1 - B to be as large as possible.
• Apr 26th 2013, 08:36 PM
therexists
Re: One simple multiple choice question
The answer is C or D. You said the power of a test measures the "ability" to reject and C said "fail to reject". So then answer is D?
• Apr 26th 2013, 08:50 PM
chiro
Re: One simple multiple choice question
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.
• Apr 26th 2013, 08:53 PM
therexists
Re: One simple multiple choice question
Yes, the answer is C. I was doing online homework. Thank you very much Chiro, and your explanations are really good. I will read it again before exam.