Hypothesis test for the difference in the mean processing time.
In New York State, savings banks are permitted to sale a form of life insurance known as savings bank life insurance (SBLI). The approval process consists of underwriting, that includes a review of the application, a medical information bureau check, probable requests for addition medical information and medical exams, and policy compilation stage in which the policy pages are generated and sent to the bank for delivery. The capability to deliver approved policies to customers in a timely manner is critical to the profitability of this service. Throughout a period of one month, a random sample of 27 approved policies is selected, and the total processing time, in days, is recorded (as stored in the insurance.xls file):
73 19 16 64 28 28 31 90 60 56 13 56 22
45 48 17 17 17 91 92 63 50 51 69 16 17
In the past, the mean processing time was 45 days. At the 0.05 level of significance, is there evidence that the mean processing time has changed from 45 days?