Problem 3. Suppose each X; for i = 1, 2,... is independently drawn from the same normal distribution with unknown mean and unknown variance. In this problem, we are going to do hypothesis testing for the variance of a normal random variable. Suppose we have n = 6 data points, with values: X = 1 X2=2 X3 = 4 X = 0 X5 = 2.5 X6 = 10 (Note these are the same values as from the previous problem, so you should have already calculated X and s.) (a) Consider the null hypothesis Ho: 0 = 4, and the alternative hypothesis H: 0 4. Suppose we have desired confidence level of 95%. Can we reject the null hypothesis, or will we fail to reject it? (b) This time, let's consider a different alternative hypothesis. Consider the null hypothesis Ho = 4, and the alternative hypothesis H < 4. Note the difference in H compared to the previous problem. Suppose we have desired confidence level of 95%. Can we reject the null hypothesis, or will we fail to reject it? Remark: Recall this test involves a x (chi-squared) distribution. You can type 'chi-squared table' into a search engine to find an appropriate table.