Number 7 and 8

A statistics professor thinks their students have too much time on their hands while learning from home. That professor makes their students roll an unfair die 400 times. One roll of the die has a standard deviation of 1.5. According to the professor, one roll of the die has a mean value of 3.3. Suppose a student finds the average value of their 400 rolls is 3.45. In the following, you MUST construct the confidence interval and test the hypothesis by hand. Round your numerical answers to FOUR decimal places. 7. (a) (1 pt) Find the lower bound of a 90% confidence interval for the true mean value of one roll of the die. (b) (1 pt) Find the upper bound of a 90% confidence interval for the true mean value of one roll of the die. (c) (1 pt) Using the confidence interval you found in parts (a) and (b), can we say the mean value of one roll of the die is 3.3? JUSTIFY your answer using complete sentences in plain language. 8. The student suspects the actual average value for one roll of the die is greater than 3.3. (a) (1 pt) Identify the hypotheses: i. What is the value of Mo in the null hypothesis Ho? ii. Using math symbols, write the alternative hypothesis Ha. iii. Is Ha right-tailed, left-tailed, or two-tailed? (b) (1 pt) Conduct the hypothesis test: i. Find the test statistic and p-value AND say if the distribution was z or t. ii. Is the result significant at the a = .01 level? At the a = .05 level? iii. What do you do with the null hypothesis Ho? JUSTIFY your answer. (c) (1 pt) Using complete sentences, state the "real-world" conclusion in context