In New York State, savings banks are permitted to sell a form of life insurance called savings bank 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 polices to customers in a timely manner is critical to the profitability of this services. During a period of one month, a random sample of 27 approved polices is selected, and the total processing time, in days, is recorded (and stored in Insurance):
|
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
|
|
a. In the past, the mean processing time was 45 days. At the 0.05 level of significance, is there evidence that he mean processing tiem has changed from 45 days?
b. What assumption about the population distribution is needed in order to conduct the t test in (a).
c. Construct a boxplot or a normal probability plot to evaluate the assumption made in (b).
d. Do you think that the assumption needed in order to conduct the t test in (a) is valid? Explain.