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In a study of human mortality rate, an Actuary estimated that in US and Canada, about 78% (fictional figures) of life insurance claims resulted from accidental deaths. Suppose a study is being planned to estimate the relative frequency of claims in Canada, and it is desired that the standard error of the esrimated relative frequency should be 0.013. How many claims should be included in the study.
To determine the number of claims that should be included in the study, we need to use the normal distribution and the concept of standard error.
The formula to calculate the standard error (SE) is:
SE = sqrt(p * (1 - p) / n)
where:
- p is the estimated proportion (in this case, the estimated relative frequency of claims)
- n is the sample size (number of claims)
In this case, the standard error is given as 0.013. We need to rearrange the formula to solve for n:
n = p * (1 - p) / SE^2
Given that the estimated relative frequency of claims is 0.78 (78%), and the standard error is 0.013, substitute these values into the formula to calculate the sample size:
n = 0.78 * (1 - 0.78) / 0.013^2
n = 0.78 * 0.22 / 0.000169
n = 0.1716 / 0.000169
n ≈ 1017.75
Therefore, we should include approximately 1018 claims in the study.