Consider the hypothesis test H0: 1 = 2 against H1: 1 < 2 with known variances (1

Question:

Consider the hypothesis test H0: µ1 = µ2 against H1: µ1 < µ2 with known variances (1 = 10 and (2 = 5.Suppose that sample sizes n1 = 10 and n2 = 15 and that x̅1 = 14.2 and x̅2 = 19.7.
Use a = 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) if p1 is 4 units less than P2?
(d) Assume that sample sizes are equal. What sample size should be used to obtain 13 = 0 05 if p1 is 4 units less than P2? Assume that a = 0.05.