An article in the International Journal of Clinical Practice described a study in which a sample of 314 patients took a combination of the drugs ezetimibe and simvastatin in order to reduce their total blood cholesterol levels. A test of the hypotheses H0: μ = 1 versus H1: μ > 1 will be made at the α = 0.05 level of significance.

Assume the population standard deviation is σ = 0.2.

a. Find the power of the test against the alternative

μ1 = 1.02.

b. Find the power of the test against the alternative

μ1 = 1.05.

c. Find the power of the test against the alternative μ1 = 1.02 if the test is made at level

α = 0.01.

d. Find the power of the test against the alternative μ1 = 1.05 if the test is made at level

α = 0.01.