Consider the hypothesis test h0: μ1 = μ2 against h1: μ1 ≠ μ2 with known variances σ1 = 10 and σ2 = 5. suppose that sample sizes n1 = 10 and n2 = 15 and that x1 = 4.7 and x2 = 7.8. use α = 0.05. a. test the hypothesis and find the p-value. b. explain how the test could be conducted with a confidence interval. c. what is the power of the test in part (a) for a true difference in means of 3? d. assume that sample sizes are equal. what sample size should be used to obtain β = 0.05 if the true difference in means is 3? assume that α = 0.05.