Question 2 - Disability Insurance Products (15 Marks) An insurance company that sells different life insurance policies is investigating expanding its "disability insurance" products. To help determine the extent and type of offerings, the company needs to know its target market. A survey of 320 adults was drawn, and each person was asked to choose his/her preferred new policy. The survey results can be found in the dataset insurance. The response codes are: (1) just life insurance with a 2% discount; (2) just disability insurance with a 2% discount; (3) life and disability insurance with a 3% discount; and (4) life and health insurance with a 5% discount. a) Compute the sample target market defined as the sample proportion of adults who chose "disability insurance with a 2% discount" as their preferred new policy. b) Compute the standard error of the target market. c) Test whether the target market is larger than 35%. Use a 10% significance level and the p-value approach. e) Construct the appropriate one-sided approximate 90% confidence interval for the target market. Is this interval consistent with your conclusion in parts c) above? Explain. d) What sample size is needed if the company wishes to be 98% confident that their estimate is within 0.02 of the true target market value? 1 1 2 3 3 4 5 6 7 8 9 10 11 12 Row Labels 1 2 3 4 Grand Total Count of Answer Code 63 125 45 87 320 13 14 Answer Code 2 2 4 4 3 1 2 2 1 4 4 2 1 2 2 2 2 3 4 3 4 4 4 2 2 2 15 16 17 18 19 20 21 22 23 24 25 26 27 Question 2 - Disability Insurance Products (15 Marks) An insurance company that sells different life insurance policies is investigating expanding its "disability insurance" products. To help determine the extent and type of offerings, the company needs to know its target market. A survey of 320 adults was drawn, and each person was asked to choose his/her preferred new policy. The survey results can be found in the dataset insurance. The response codes are: (1) just life insurance with a 2% discount; (2) just disability insurance with a 2% discount; (3) life and disability insurance with a 3% discount; and (4) life and health insurance with a 5% discount. a) Compute the sample target market defined as the sample proportion of adults who chose "disability insurance with a 2% discount" as their preferred new policy. b) Compute the standard error of the target market. c) Test whether the target market is larger than 35%. Use a 10% significance level and the p-value approach. e) Construct the appropriate one-sided approximate 90% confidence interval for the target market. Is this interval consistent with your conclusion in parts c) above? Explain. d) What sample size is needed if the company wishes to be 98% confident that their estimate is within 0.02 of the true target market value? 1 1 2 3 3 4 5 6 7 8 9 10 11 12 Row Labels 1 2 3 4 Grand Total Count of Answer Code 63 125 45 87 320 13 14 Answer Code 2 2 4 4 3 1 2 2 1 4 4 2 1 2 2 2 2 3 4 3 4 4 4 2 2 2 15 16 17 18 19 20 21 22 23 24 25 26 27
