An auditor for a government agency is assigned the task f evaluation reimbursement for office visits to physicians paid by Medicare. The audit was conducted on a sample of 75 of the reimbursements, with the following results:

• In 12 of the office visits, an incorrect amount of reimbursement was provided
• The amount of reimbursement was X* = $39.70, 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 your answer to (a) if the sample mean equals $90?

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