Question

21 . In New York State, savings banks are permitted to sell a form of life insurance called Savings Bank Life Insurance (SBLI). 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 25 approved policies is selected and the sample average processing time is 40 days and sample standard deviation is 25 days. In the past, the mean processing time average 45 days. At the 0.05 level of significance, is there evidence that the mean processing time has become shorter than 45 days? (Please use both critical value approach and p-value approach to conduct the hypothesis testing, 16 points, without calculation process you will get zero point.)

Answer 1

H0: Null Hypothesis: 45

HA: Alternative Hypothesis: 45

SE = s/

= 25/ = 5

Test statistic is:

t = (40 - 45)/5 = - 1.00

= 0.05

ndf = n - 1 = 25 - 1= 24

From Table, critical value of t = - 1.7109

Since calculated value of t = - 1.00 is greater than critical value of t = - 1.7109, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the mean processing time has become shorter than 45 days.

t score = - 1.00

One Tail - Left Side test

ndf = 24

By Technology, P - Value = 0.1636

Since P - Value = 0.1636 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that the mean processing time has become shorter than 45 days.