We test the hypothesis that p = 35% versus p

Question

We test the hypothesis that p = 35% versus p < 35%. We don't know it but actually p = 26%. With which sample size and significance level will our test have the greatest power?
A) a = 0.03, n = 250
B) a = 0.01, n = 250
C) The power will be the same as long as the true proportion p remains 26%
D) a = 0.01, n = 400
E) a = 0.03, n = 400

Quizplus · Accepted Answer

The power of a test increases with larger sample sizes and higher significance levels (i.e., a larger alpha). Thus, a combination of a larger sample size (n = 400) and a higher significance level (alpha = 0.03) will yield the greatest power.

We Test the Hypothesis That P = 35% Versus P