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. They randomly select 40 claims, and calculate a sample mean of $1,950. Assuming that the standard deviation of claims is $500, and set ? =0.05, test to see if the insurance company should be concerned. (One-tailed test)

a. State Null hypothesis

b. State Alternate hypothesis

c. What is the calculated value of t?

d. Determine the t-critical

e. Draw a conclusion