Estimation of True Mean with 98 Percent Confidence

Question

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies.  Last year the average life expectancy of all policy holders that were paid out was 77 years.  ABI Insurance wants to determine of their clients now have a longer life expectancy on average, so they randomly sample 101 of their recently paid policies.  The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before.  The sample has a mean of 78.6 years and a standard deviation of 4.48 years.  Use a 1% significance level to answer the following.

• Construct a 95% confidence interval for what the true mean life expectancy is located. Round your final answer to the nearest 0.1 years.
• If the company wants to estimate the true mean to within 1 year with 98% confidence, what sample size should they take? Round your answer to the nearest person. Was their original sample of 101 sufficient to meet their desired margin of error?

Summary

This question belongs to statistics and discusses about insurance companies tracking life expectancy information to assist in determining the cost of life insurance policies.

Word count: NA