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: X₁ = 1 X2=2 X3 = 4 X₁ = 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 s².) (a) Consider the null hypothesis Ho: 0² = 4, and the alternative hypothesis H₁: 0² 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 Hoσ² = 4, and the alternative hypothesis H₁² < 4. Note the difference in H₁ 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 x² (chi-squared) distribution. You can type 'chi-squared table' into a search engine to find an appropriate table.

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