A college admissions officer will draw a simple random sample of 100 mathematics SAT scores from the entering freshman class. The admissions officer will perform a test of the hypotheses H0: μ = 500 versus H1: μ > 500 at the

α = 0.05 level of significance. Assume the population standard deviation is σ = 116.

a. Find the power of the test against the alternative

μ1 = 520.

b. Find the power of the test against the alternative

μ1 = 550.

c. Find the power of the test against the alternative μ1 = 520 if the test is made at level

α = 0.01.

d. Find the power of the test against the alternative μ1 = 550 if the test is made at level

α = 0.01.