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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 30 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 Last Year Year x1= 75.8 | x2= 76.2 s1= 47.61 s= 92.16 (The first row gives the sample means and the second row gives the sample variances.) Assume that life spans are approximately normally distributed for each of the populations of people who died this year and people who died last year. Can we conclude, at the 0.05 significance level, that the variance of the life span for the current year, of, differs from the variance of the life span for last year, o,? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. Ho : of = o (b) Determine the type of test statistic to use. D=D OSO Degrees of freedom: dfn: O dfd: 0 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0.517 (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) 0.476 and 2.101 (e) Can we conclude that the variance of the life span for the current year differs from the variance of the life span for last year? Yes oNo olo

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 30 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 Last Year Year x1= 75.8 | x2= 76.2 s1= 47.61 s= 92.16 (The first row gives the sample means and the second row gives the sample variances.) Assume that life spans are approximately normally distributed for each of the populations of people who died this year and people who died last year. Can we conclude, at the 0.05 significance level, that the variance of the life span for the current year, of, differs from the variance of the life span for last year, o,? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. Ho : of = o (b) Determine the type of test statistic to use. D=D OSO Degrees of freedom: dfn: O dfd: 0 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0.517 (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) 0.476 and 2.101 (e) Can we conclude that the variance of the life span for the current year differs from the variance of the life span for last year? Yes oNo olo

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 30 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 Last Year Year x1 = 75.8 | x,= 76.2 si= 47.61 s3= = 92.16 (The first row gives the sample means and the second row gives the sample variances.) Assume that life spans are approximately normally distributed for each of the populations of people who died this year and people who died last year. Can we conclude, at the 0.05 significance level, that the variance of the life span for the current year, of, differs from the variance of the life span for last year, o,? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. Ho : H1 : (b) Determine the type of test statistic to use. D=0 OSO F Degrees of freedom: dfn: I dfd: 1 O<O O>O (c) Find the value of the test statistic. (Round to three or more decimal places.) 0.517 (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) 0.476 and 2.101 |(e) Can we conclude that the variance of the life span for the current year differs from the variance of the life span for last year? Yes oNo
Transcribed Image Text: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 30 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 Last Year Year x1 = 75.8 | x,= 76.2 si= 47.61 s3= = 92.16 (The first row gives the sample means and the second row gives the sample variances.) Assume that life spans are approximately normally distributed for each of the populations of people who died this year and people who died last year. Can we conclude, at the 0.05 significance level, that the variance of the life span for the current year, of, differs from the variance of the life span for last year, o,? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. Ho : H1 : (b) Determine the type of test statistic to use. D=0 OSO F Degrees of freedom: dfn: I dfd: 1 O<O O>O (c) Find the value of the test statistic. (Round to three or more decimal places.) 0.517 (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) 0.476 and 2.101 |(e) Can we conclude that the variance of the life span for the current year differs from the variance of the life span for last year? Yes oNo
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