Consider the hypothesis test H0: μ1= μ2 against H1: μ1Image for Consider the hypothesis test H0: mu1= mu2 against H1:mu1mu2. Suppose that the sample sizes aren1 = 15 and n2 =μ2. Suppose that the sample sizes aren1 = 15 and n2 = 15, that Image for Consider the hypothesis test H0: mu1= mu2 against H1:mu1mu2. Suppose that the sample sizes aren1 = 15 and n2 = = 4.7 and Image for Consider the hypothesis test H0: mu1= mu2 against H1:mu1mu2. Suppose that the sample sizes aren1 = 15 and n2 = = 7.8 and that s21 = 4 ands22 = 6.25. Assume thatσ21 = σ22 andthat the data are drawn from normal distributions. Use α =0.05.
(a) Test the hypothesis and find the P-value.
(b) Explain how the test could be conducted with a confidenceinterval.
(c) What is the power of the test in part (a) for a truedifference in means of 3?
(d) Assuming equal sample sizes, what sample size should beused to obtain β = 0.05 if the true difference in means is -2?Assume that α = 0.05.