We will test the hypothesis that p = 60% versus p 60%. We don't know it, but actually p is 70%.
With which sample size and significance level will our test have the greatest power?
A) a = 0.05, n = 200
B) a = 0.01, n = 200
C) The power will be the same so long as the true proportion p remains 70%.
D) a = 0.01, n = 500
E) a = 0.05, n = 500

Question

We will test the hypothesis that p = 60% versus p > 60%. We don't know it, but actually p is 70%.
With which sample size and significance level will our test have the greatest power?
A) a = 0.05, n = 200
B) a = 0.01, n = 200
C) The power will be the same so long as the true proportion p remains 70%.
D) a = 0.01, n = 500
E) a = 0.05, n = 500

Quizplus · Accepted Answer

The power of a test increases with larger sample sizes and higher significance levels (lower α means more conservative, so a higher α like 0.05 compared to 0.01 is less conservative and more powerful for detecting an effect if one truly exists). Therefore, a larger sample size (n = 500) and a higher significance level (α = 0.05) will give the greatest power to detect that p > 60% when p is actually 70%.

We Will Test the Hypothesis That P = 60% Versus