A private health fund auditor is assigned the task of evaluating benefits paid to members for dental consultation claims. The audit is conducted on a sample of 85 claims.In 10 of the consultations, an incorrect amount of reimbursement was provided. The amount of benefit was: mean = $98.95, S= $34.55.

a) At the 0.05 level of significance, is there a sufficient evidence that the mean benefit is less than $100.

b) At the 0.05 level of significance, is there a sufficient evidence that the proportion of incorrect benefit 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 to $90?

e) What is your answer to (b)if 15 consultations had incorrect reimbursements?