In a test of the hypothesis H_{0}: p = 0.8 against H_{a}: p > 0.8, the power of the test when p = 0.9 is greatest for which of the following? (4 points)
n = 70, α = 0.10 

n = 75, α = 0.10 

n = 70, α = 0.05 

n = 75, α = 0.05 

There is not enough information given to draw a conclusion. 
We know, higher sample size gives more information about the population and so the probability of rejecting the null hypothesis when the null hypothesis is false increases as the sample size increases i.e. the power of a test increases with increase in sample size.
Changing the significance level from 0.05 to 0.10 makes the region of acceptance smaller, which ensures increase in the probability of rejecting the null hypothesis, thus increasing the power of the test.
So, the power of the test is greatest when n = 75, = 0.10
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