Problem V. (9 points) Answer following questions. 1. (2 points) Suppose we construct a 90%-confidence interval [Oz, Ou] for (*, that is, P(0* E [OL, Ou]) =90%, which one is/ are random? O Only * is random. O Only Oz and Ou are random. O (*, Or and Oy are random. 2. (3 points) Assume that X ~ N(#1, 01), and Y ~ N(#2, 02), where X and Y may be dependent, of and oz are unknown. Now, we have paired samples D; = X; - Yi, i = 1, . .. ,n with n = 20. Consider the hypothesis testing, Ho : #1 = /2 VS Ho : #1 # #2, which test you want to conduct? O T-test O Z-test. O T-test or Z-test. O need further investigation about the data assumption 3. (4 points) Let X ~ N(#, ) and X be sample mean from 25 random samples, then we construct an interval a to where o is the population standard deviation of X. Compute the confidence level of this interval estimator, that is, P(X - o S A X +0)