Problem 1. Assume we have a random sample of points (x1, Y),..., (x20, Y20) where Xi Yi = = i for all i. = a + xi + are random variables where &; ~N (0,02) and the e; are i.i.d. a, , are unknown constants. We run the experiment once and obtain the sample data Yobs (see the homework12. R file): where Yobs (0.36, 4.55, 2.92, 7.34, 7.54, 7.81, 11.43, 10.23, 14.06, 11.33, 12.97 = , 15.36, 10.27, 20.58, 15.88, 19.52, 21.24, 19.57, 18.47, 22.22) 1. Test against the null hypothesis Ho: B = 0 and give the (2-sided) p-value. Then find the 95% confidence interval for B. 2. Test against the null hypothesis Ho: a = 1 and give the (2-sided) p-value. Then find the 95% confidence interval for a.