Construct a 90% confidence interval. what is the upper and lower limit? Actuarie
ID: 3172579 • Letter: C
Question
Construct a 90% confidence interval. what is the upper and lower limit?
Actuaries use various parameters when evaluating the cost of a life insurance policy. The variance of the life spans of a population is one of the parameters used for the evaluation. Each year, the actuaries at a particular insurance company randomly sample 25 people who died during the year (with the samples chosen independently from year to year) to see whether the variance of life spans has changed. The life span data from this year and from last year are summarized below:
Carry your intermediate computations to at least three decimal places. Write your final responses to at least two decimal places. (If necessary, consult a list of formulas.)
What is the lower limit of the 90% confidence interval? ______
What is the upper limit of the 90% confidence interval? ______
Construct a 90% confidence interval. what is the upper and lower limit?
Actuaries use various parameters when evaluating the cost of a life insurance policy. The variance of the life spans of a population is one of the parameters used for the evaluation. Each year, the actuaries at a particular insurance company randomly sample 25 people who died during the year (with the samples chosen independently from year to year) to see whether the variance of life spans has changed. The life span data from this year and from last year are summarized below:
Current Year Last Year (The first row gives the sample means, and the second row gives the sample variances.)Assuming that life spans are approximately normally distributed for each of the populations of people who died this year and people who died last year, construct a confidence interval for , the ratio of the variance of the life span for the current year to the variance of the life span for last year. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Write your final responses to at least two decimal places. (If necessary, consult a list of formulas.)
What is the lower limit of the 90% confidence interval? ______
= 76.2Explanation / Answer
Answer to the question:
In order to find the confidence intervals we need to find the two F values
Since we find the 90% confidence interval , so the area under each tail would be 0.05
So we find the F value for 0.05 with df n = df d = 25-1=24
We get the F(0.05) = 1.98376
Similarly F value for 0.95 with df n = df d = 24 will be
F(0.95) = 0.504093
.
Thus the confidence limit is :
0.504093 * (57.8 / 53.3) < Variance < 1.98376 * (57.8 / 53.3)
0.546653 < Variance < 2.151244
.
Thus the lower confidence limit is : 0.546653
The upper confidence limit is 2.151244