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In New York State, savings banks are permitted to sale a form of life insurance called savings bank life insurance (SBLI).  The approval process consists of underwriting, which comprise a review of application, a medical information bureau check, possible requests for the addition medical information and medical exams, and policy compilation phase in which the policy pages are generated and sent to the bank for delivery. The capability to deliver approved policies to customers in timely manner is critical to profitability of this service. During the period of one month, a random sample of 27 approved policies is selected, and 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        18

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?

Statistics and Probability, Statistics

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