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

Free

60.1K

Verified Solution

Question

Basic Math

In New York State, savings banks are permitted to sell a form oflife insurance called savings bank life insurance (SBLI). Theapproval process consists of underwriting, which includes a reviewof the application, a medical information bureau check, possiblerequests for additional medical information and medical exams, anda policy compilation stage in which the policy pages are generatedand sent to the bank for delivery. The ability to deliver approvedpolicies to customers in a timely manner is critical to theprofitability of this service to the bank. During a period of onemonth, a random sample of 27 approved policies was selected, andthe total processing time, in days, was as shown below and storedin the file 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. Construct and interpret a 95% confidence interval estimate ofthe population mean processing time. Use Minitab. (Don'tworry about this one.)
b. What assumption must you make about the populationdistribution in order to construct the confidence interval in(a)?
c. Do you think that the assumption needed in order to constructthe confidence interval estimate in (a) is valid? Explain.

Answer & Explanation Solved by verified expert

3.6 Ratings (436 Votes)

Part a

Required 95% confidence interval by using Minitab is given as below:

VariableÂ Â Â Â Â Â Â Â Â NÂ Â Â Â Â MeanÂ Â Â Â StDevÂ Â SE Mean

TimeÂ Â Â Â Â Â Â Â Â Â Â Â 27Â Â Â Â 43.89Â Â Â Â 25.28Â Â Â Â Â 4.87

VariableÂ Â Â Â Â Â Â Â Â Â Â Â 95.0% CIÂ Â Â Â Â Â Â Â Â Â Â

TimeÂ Â Â Â Â Â Â Â Â (Â Â 33.89,Â Â 53.89)Â Â Â Â

Confidence interval = (33.89, 53.89)

Part b

The assumption of normality we must make about the population distribution in order to construct the above confidence interval.

Part c

Yes, assumption needed in order to construct the confidence interval is valid because the variable total processing time is approximately normally distributed.

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member