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Posts: 199
2 weeks ago
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.



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.
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
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2 weeks ago
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H0: μ = 77 years. The mean life life expectancy of the insurance company's patients is 77
years.
HA: μ > 77 years.  The mean life expectancy of the insurance company's patients is greater
than 77 years.
* Randomization condition: The records from the insurance company were randomly sampled.
* 10% Condition: 20 records represent less than 10% of the company's records.
* Nearly Normal condition: The histogram of the ages at death is unimodal and reasonably symmetric. This is close enough to Normal for our purposes

Under these conditions, the sampling distribution of the mean can be modeled by Student's t with df = n - 1 = 20 - 1 = 19.

We will use a one-sample t-test for the mean.
We know:  n = 20, = 78.6 years , and s = 4.48 years. So, SE() = = = 1.002 years.
t = = = 1.597.  
P = P(t19 > 1.597) = 0.063.

The P-value of 0.063 is fairly high, so we fail to reject the null hypothesis. The insurance company shouldn't need to increase their premiums because there is little evidence to indicate that people who buy their policies are living longer than before.
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