An auditor for a government agency is assigned the task of evaluating reimbursement for consultations with specialists paid by Medicare. The audit is conducted on a sample of 75 of the reimbursements with the following results:

• In 12 of the consultations, an incorrect amount ofreimbursement was provided.
• The amount of reimbursement was: X = $93.70, S = $34.55.

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

b. At the 0.05 level of significance, is there evidence that the proportion of incorrect reimbursements in the population is 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 consultations had incorrect reimbursements?