PROBLEM 2 (19 points) The ElecMart file contains data on 400 customers' orders from ElecMart, a company that sells electronic appliances by mail order. The ElecMart wants to know the effect of ElecMart credit cards. In the data, we assume card type = ElecMart presents customers who use ElecMart credit card when they make payment and Other presents customers who don't use ElecMart credit card. a. (2 points) Compute the sample proportion of customers who use ElecMart credit cards. Hint: You can use pivot table. b. (3 points) By hand calculations (use only Excel, do not use StatTools), calculate a 95% confidence interval for the proportion of customers who use ElecMart credit cards. - Provide the value of the appropriate Z multiple. Use Excel function or the following Z values: z0.9 =1.282,z0.95=1.645,z0.975=1.960,z0.99=2.326,z0.995=2.576 - Compute the confidence interval in the form point estimate \pm margin of error. Show your work. - Interpret the confidence interval within the context of the problem. c. (3 points) In part b, the MOE exceeds the target level of 3%. How large should the sample be if they would like to ensure that MOE is no larger than 0.03 or 3% at 95% confidence? credit card. For the purpose of this exercise, we will assume that total cost is, in general, normally distributed. d. (2 points) Using Excel, calculate the sample mean and sample standard deviation for the total cost of customers who use ElecMart credit card and don't use ElecMart credit card. Hint: Use the pivot table to analyze the total cost variable for two categories: "Card Type" = ElecMart and "Card Type" = Other e. ( 3 points) By hand calculation, construct a 95% confidence interval for the average total cost of customers who use ElecMart credit card. State the confidence interval in the two forms: point estimate \pm margin of error and [lower limit, upper limit]. Interpret the confidence interval within the context of the problem. f. (3 points) By hand calculation, construct a 95% confidence interval for the average total cost of customers who don't use ElecMart credit card. State the confidence interval in the two forms: point estimate \pm margin of error and [lower limit, upper limit]. Interpret the confidence interval within the context of the problem. g. (3 points) Discuss the comparison between the total costs of customers who use an ElecMart credit card and those who do not use one