Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. The insurance company knows that, last year, the life expectancy of its policyholders was 77 years. They want to know if their clients this year have a longer life expectancy, on average, so the company randomly samples some of the recently paid policies to see if the mean life expectancy of policyholders has increased. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. Here are the data: 86 75 83 84 81 77 78 79 79 81 76 85 70 76 79 81 73 74 72 83 Which method will you use here to perform the statistical inference? 1-sample T 2-sample T 1-sample Z 1-proportion Z Does this sample indicate that the insurance company should change its premiums because life expectancy has increased? Test an appropriate hypothesis and state your conclusion at 5% significance level. State the null and alternative hypothesis: a Which distribution will you use here? If you use t distribution, give the degree of freedom. If you use z or normal, give the mean and standard deviation. b Give the test statistic: Find the P-value: Decision: Conclusion: Find a 95% confidence interval for the mean life expectancy of policyholder, and interpret your interval with the context.

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Description: Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. The insurance company knows that, last year, the life expectancy of its policyholders was 77 years. They want to know if their clients

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. The insurance company knows that, last year, the life expectancy of its policyholders was 77 years. They want to know if their clients this year have a longer life expectancy, on average, so the company randomly samples some of the recently paid policies to see if the mean life expectancy of policyholders has increased. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. Here are the data:

86 75 83 84 81 77 78 79 79 81 76 85 70 76 79 81 73 74 72 83

Which method will you use here to perform the statistical inference?

1-sample T
2-sample T
1-sample Z
1-proportion Z

Does this sample indicate that the insurance company should change its premiums because life expectancy has increased? Test an appropriate hypothesis and state your conclusion at 5% significance level.

State the null and alternative hypothesis:

a Which distribution will you use here? If you use t distribution, give the degree of freedom. If you use z or normal, give the mean and standard deviation.

b Give the test statistic:

Find the P-value:

Decision:

Conclusion:

Find a 95% confidence interval for the mean life expectancy of policyholder, and interpret your interval with the context.

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