Question 1 (50 points) Solve the question manually, show detailed calculations: The marketers of shampoo products know that customers like their product to have a lot of foam. A random sample of products was observed and foam heights were observed. The data are as follows (in mm): 225.1 222.4 230.2 226.4 224.1 219.5 227.8 223.5 226.5 227.9 221.4 232.5 233.6 228.5 227.4 226.3 226.6 229.8 3 225.4 221.5 Assume that the foam height is normally distributed with a population variance of 12.6025. a) Calculate the sample mean. (5 points) b) Construct a 99% confidence interval for the mean foam heights. State your comment. (15 points) c) Find a 95% upper confidence bound for the population mean. State your comment. (10 points) d) If we decrease the sample size, how does this change affect the length of 99% confidence interval? Discuss. (10 points) e) How large sample size must be if the length of a 99% two sided confidence interval is to be 3.8? (10 points)Question 2 (50 points) Solve the question using the Minitab: Instead of A you should write the number that is given as the first 3 digits of your AUM ID number. Instead of B you should write the number that is given as the last 3 digits of your AUM ID number. For example, for a student with ID number 57325, A=573 and B=325 A= B= The numbers of advertisements seen or heard in one week for 20 randomly selected people in the Kuwait are listed below. 598 494 441 595 728 690 684 486 735 A 481 298 135 846 764 317 649 732 582 B a) If you are asked to calculate confidence interval for the population mean, which formula would you use? Assume that the population distribution is normal. (10 points) b) Write the appropriate steps for Minitab to calculate a confidence interval. (5 points) c) In Minitab, construct a 90% confidence interval for the true mean number of wins in a season. Copy the Minitab output here. (10 points) d) Interpret the result you got in part c). (5 points) e) Construct a 99% confidence interval for the true mean number of wins in a season. Copy the Minitab output here. (10 points) f) Interpret the result you got in part e). (5 points) g) How answers in c) and e) question are different from each other. Explain the difference. (5 points)