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

Section: Chapter Questions

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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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