Question: Problem 4) In New York State, savings banks are permitted to sell a form of life insurance called Savings Bank Life Insurance. The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation state where the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service. During a period of one month, a random sample of 27 approved policies and selected insurance and the total processing time in days recorded:

73, 19, 16, 64, 28, 28, 31, 90, 60, 56, 31, 56, 22, 18, 45, 48, 17, 17, 17, 91, 92, 63, 50, 51, 69, 16, 17

In the past the mean processing time averaged 45 days. At the 0.05 level of significance, is there evidence that the mean processing time has changed from 45 days.