Suppose we have paired data (Xi,Yi), 1i10,Xiarei.i.drandom variables with distributionN(1,12) andYiarei.i.drandom variables with distributionN(2,2), where1,2,1,2are unknown, the observed values are:

X: 2.2 1.9 0.7 4.2 2.9 5.1 2.7 3.5 4.3 3.8Y: 4.0 1.9 2.8 6.4 2.4 5.3 3.9 4.6 4.7 3.9

1. (a)ConsiderH0:12= 0 v.s.H1:21>0, and we would like to conduct a paired test. Please formulate a hypothesis testing procedure using the p-value approach at level of significance= 0.05.
2. (b)ConsiderH0:12= 0 v.s.H1:21>0, and we would like to conduct a paired test. Please formulate a hypothesis testing procedure using the rejection region approach at level of significance
3. = 0.05. Do you get the same conclusion as in (a)?
4. (c)Construct a 95% confidence interval for12