Question

An insurance company has business objectives of reducing the amount of time it takes to approve applications for life insurance. During a period of one month, you collect a random sample of 27 approved policies and the total processing time, in days, stored in insurance are: 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. On 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? 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

Answer 1

(A) Mean = 43.88889 ... S.DE" = 25.28352 , 79=27 Test stal Hoi u=45 ......... Hai l 745 .. ... Test statistica ......... t X- M 43-88889-45 Blvñ 35 25.28352) 127 --------- = -0.2283504 D-value = P(>0.2283504)...totype = 0.8211603 .x=0.05. As petraluce >xz0.05 then we can conclude that to connot be rejected. This mean has not changed from 45 days.................................................... (B) The population is assumed to follow ------- normal distribution ... ---------

C.)

Normal Q-Q Plot o We 80 Sample Quantiles 40 60 20 TTTT 70 0 0 0 0 0 0 Boo Theoretical Quantiles

D.)

Many points are off the line, thus there is a doubt that the assumption of normality may not be valid.