An auditor for a government agency was assigned the task of evaluating reimbursement for office visits to physicians paid by Medicare. The audit was conducted on a sample of 75 reimbursements, with the following results: In 12 of the office visits, there was an incorrect amount of reimbursement. The amount of reimbursement was X = $93.70, S = $34.55.

a. At the 0.05 level of significance, is there evidence that the population mean reimbursement was less than $100?

b. At the 0.05 level of significance, is there evidence that the proportion of incorrect reimbursements in the population was greater than 0.10?

c. Discuss the underlying assumptions of the test used in (a).

d. What is the answer to (a) if the sample mean equals $90?

e. What is the answer to (b) if 15 office visits had incorrect reimbursements?