In a test of the hypothesis H0: p = 0.5 against Ha: p 0.5, the power of the test when p = 0.6 is greatest for which of the following?

n = 40, α = 0.10
n = 40, α = 0.05
n = 35, α = 0.10
n = 35, α = 0.05
There is not enough information given to draw a conclusion.

I'm stuck between A and B. It could be A because as α increases, power of test increases, but at the same time it increases the chance of a Type I error, which why it could be B.

It's definitely not C D or E, I just need some advice on choosing between A and B.

Question

In a test of the hypothesis H0: p = 0.5 against Ha: p > 0.5, the power of the test when p = 0.6 is greatest for which of the following?

n = 40, α = 0.10
 n = 40, α = 0.05
 n = 35, α = 0.10
 n = 35, α = 0.05
 There is not enough information given to draw a conclusion.

I'm stuck between A and B. It could be A because as α increases, power of test increases, but at the same time it increases the chance of a Type I error, which why it could be B.

It's definitely not C D or E, I just need some advice on choosing between A and B.

AGENTJSVSL · Answer

Imma go for A because it's asking about the power of test, not about variability or making a type I/II error.