Actuaries use various parameters when evaluating the cost used for the evaluatio

Question

Actuaries use various parameters when evaluating the cost used for the evaluation. Each year, the actuaries at a particular insurance co of a life insurance policy. The variance of the life spans of a population is one of the parameters mpany 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: Cu x, = 76.8 75.6 = 51.8 -60.8 (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 95% confidence interval for-T, the ratio of the variance of the life span for the current year to the variance of the life span for last year. Then 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 what is the upper limit of the 95% confidence interval,

Explanation / Answer

The statistical software output for this problem is:

Two sample variance summary confidence interval:
?12 : Variance of population 1
?22 : Variance of population 2
?12/?22 : Ratio of two variances

95% confidence interval results:

Hence,

Lower limit = 0.375

Upper limit = 1.933

Ratio Num. DF Den. DF Sample Ratio L. Limit U. Limit ?12/?22 24 24 0.85197368 0.37543834 1.9333645

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