Question

1. Along with interest rates, life expectancy is a component in pricing financial annuities. Suppose that you know that last year average life expectancy was 77 years for your annuity holders. Now you want to know if your clients this year have a longer life expectancy, on average, so you randomly sample n=20 of your recently deceased annuity holders to see actual age at death. Using a 5% level of significance, test whether or not the new data shows evidence of your annuity holders now live longer than 77 years, on average. The data below are the sample data (in years of life): (USE R)

(78,75,83,81,81,77,78,79,79,81,76,79,77,76,79,81,73,74,78,79)

1. Does this sample indicate that life expectancy has increased? Test an appropriate hypothesis and state your conclusion (use a 5% level of significance). Be sure to check the necessary assumptions and conditions before conducting your test.

                      

2. Construct A 90% confidence interval for the true average age of death for the population of your annuity holders. Explain why your confidence interval agrees or not statistically with your hypothesis testing decision in part a).

3. Suppose that you want to construct 90% confidence interval that has a margin of error of one half of a year. What size sample would you need at a minimum?

Answer 1

Answer:-

Given That:-

Along with interest rates, life expectancy is a component in pricing financial annuities. Suppose that you know that last year average life expectancy was 77 years for your annuity holders. Now you want to know if your clients this year have a longer life expectancy, on average, so you randomly sample n=20 of your recently deceased annuity holders to see actual age at death. Using a 5% level of significance, test whether or not the new data shows evidence of your annuity holders now live longer than 77 years, on average. The data below are the sample data

1. (USE R)

(78,75,83,81,81,77,78,79,79,81,76,79,77,76,79,81,73,74,78,79)

claim : The Average life expectancy increase number of sample

sample mean

Standard deviation

a)this sample indicate that life expectancy has increased

Null and Alternative Hypothesis :-

  

(i) Test statistics :-

(ii) P - value

Since P - value is less than SO, we reset the null hypothesis So there is sufficient to confidence conclude the Average life expectancy increase this year.

(b)Construct A 90% confidence interval for the true average age of death for the population of your annuity holders.

90% confidence interval :-

Since

CI =

we are 90% confident that the Average value lies in that range

yes, confidence interval agrees the decision.

c)Since   and

Margin error =