Consider the hypothesis test h 0 : μ 1 = μ 2 against h 1 : μ 1 > μ 2 . suppose that sample sizes are n 1 = 15 and n 2 = 15 , that x1 = 7.7 and x 2 = 5.7 and that s12 = 4 and s 22 = 9 . assume that σ 1 2 = σ 2 2 and that the data are drawn from normal distributions. use α = 0.05.
(a) test the hypothesis and find the p-value.
(b) what is the power of the test in part (a) if μ 1 is 3 units greater than μ2 ?
(c) assuming equal sample sizes, what sample size should be used to obtain β = 0.05 if μ 1 is 3.0 units greater than μ 2 ? assume that α = 0.05.