In New York State, savings banks are permitted to sell a form of life insurance

Question

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 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 is selected, and the total processing time, in days, is recorded (as stored in the “insurance” file): 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 the mean processing time has changed from 45 days? Use the critical value and p value approach. Use Minitab.

b. What assumption about the population distribution is needed in order to conduct the t test in (a)?

c. Do you think that the assumption needed in order to conduct the t test in (a) is needed? Explain.

Explanation / Answer

a. Level of significance = 0.05

xbar = 43.89 and standard deviation s= 25.28

Level of significance = 0.05

Here hypothesis are

Null Hypothesis : H0 : = 45

Alternative Hypothesis : H1 : 45

Test statistic : t = (xbar - 45)/ (s/n) = (43.89 - 45)/(25.28 /27) = (-1.11)/ 4.86 = - 0.23

tcritical for dF = 26 and alpha = 0.05 => tcritical = 2.056

P- value for t - value = 0.8198 > 0.05 so not significant results

so t < tcritical , so we can not reject the null hypothesis and we can conclude that there is no significnat difference betwen mean processing time and it is 45 days.

(b) Assumption in order to conduct t- test

(i) It is the scale of measurement. Scale of measurement applied to the data collected should be a continuous or ordinal scale.

(ii) The data selected must be representative and randomly selected portion of the total population.

(iii) It must be a normal distribution, bell shaped curve.

(iv) Each observation should be independent of each other.

c. Yes, the assumption needed in order to conduct the t- test in patt (a). otherwise we can not use the normal distribution formula or critical t- values and p- values.

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