Math-Statistice

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In New York State, savings banks are permitted to sell a form of life insurance (SBLI). 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 stage in which 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. In the past, the actual mean processing time was 45 days. During a period of one month, a sample of approved policies is selected, and the total processing time was 45 days. During a period of one month, a sample of approved policies is selected, and the total processing time in days, is 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, and 17

a) At 5% level of significance, is there sufficient evidence to conclude that the actual mean processing time differs from the past? (Your conclusion must be in terms of the P-value as well as setting up a Rejection Region)
b)Which statistical distribution should be applied and why?
c) what type of error is possible and describe this error in terms of the problem.
d) Based on a 95% confidence level, estimate the actual mean processing time.
e)Carefully interpret the interval estimation
f) Explain carefully whether or not there is sufficient evidence to conclude that the actual mean processing time differs from the past using the estimation in part (d)

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