High intraocular pressure is considered to be a risk factor for glaucoma. A new drug has been proposed for reducing intraocular pressure, and hence glaucoma risk. A (nonrandomized) experiment is planned, under which patients with high intraocular pressure are to be given the drug for one month. The reduction in intraocular pressure in mm Hg is to be measured following treatment. A review of the literature suggests that = 10 mm Hg. Consider testing H0 : = 0 against Ha : < 0

a. Determine how many subjects are required to achieve 90% power for an 0. 05 level test of the null hypothesis, when we wish to be able to detect an effect of size a 5?

b. Suppose that only 80% power is desired. What is the required sample size? What is the effect of the power setting on the required sample size?

c. Determine how many subjects are required to achieve 90% power for an 0. 05 level test of the null hypothesis, when we wish to be able to detect an effect of size a 10? What is the effect of choice of an on the required sample size?