Question

Hurricane Andrew swept through southern Florida causing billions of dollars of damage, Because of the severity of the storm and the type of residential construction used in this semitropical area, there was some concern that the average claim size would be greater than the historical average hurricane claim of $25,500. Several insurance companies collaborated in a data gathering experiment. They randomly selected 22 homes and sent adjusters to settle the claims. In the sample of 22 homes, the average claim was $27,000 with a population standard deviation of $4300. Is there sufficient evidence at a 0.02 significance level to support the claim that the home damage is greater than the historical average? Assume the population of insurance claims is approximately normally distributec.

Answer 1

The null hypothesis is that the average claim size is equal to the historical average of $25,500, whereas the alternative hypothesis is that the average claim size is greater than $25,500. Using a one-sample t-test, the calculated t-value is less than the critical t-value, indicating insufficient evidence to support the claim.

Step-by-step explanation:

To test whether the home damage is greater than the historical average, we can use a one-sample t-test.

The null hypothesis is that the average claim size is equal to the historical average of $25,500, and the alternative hypothesis is that the average claim size is greater than $25,500.

Using the given information, we can calculate the t-statistic as follows:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Plugging in the values, we get t = (27,000 - 25,500) / (4,300 / sqrt(22)) ≈ 1.692.

With 21 degrees of freedom (sample size - 1), the critical t-value for a one-tailed test at a 0.02 significance level is about 2.5181.

Since the calculated t-value is less than the critical t-value, we fail to reject the null hypothesis. There is insufficient evidence to support the claim that the home damage is greater than the historical average.