An insurance company is reviewing its current policy rates. When originally setting the rates, they believed that the average claim amount was $1,800. They are concerned that the true mean is actually higher than this because they could potentially lose a lot of money.
d) Suppose they randomly select 40 claims and calculate a sample mean of $1,950. Assuming that the population standard deviation of claims is $500 and the significance level is set to 0.05, test to see if the insurance company should be concerned. What would the p-value be? (Show your work.)
e) Provide an interpretation of what the p-value means in the context of the problem.
f) If the significance level is 0.05, state a conclusion.