An auditor for a government agency needs to evaluate payments for doctors' office visits paid by Medicare in a small regional town during the month of June. A total of 25,056 visits occurred during June in this small regional town. The auditor wants to estimate the total amount paid by Medicare to within ± $5 with 95% confidence. On the basis of past experience, she believes that the standard  deviation is approximately $30.

(a) What sample size should she select?

Using the sample size selected in (a), an audit was conducted and it was found that the sample mean amount of reimbursement was $93.70 and the sample standard deviation was $34.55. In 12 of the office visits, an incorrect amount of reimbursement was provided. For the 12 office visits in which there was an incorrect reimbursement, the differences between the amount reimbursed and the amount that the auditor determined should have been reimbursed were as follows

$17 $25 $14 -$10 $20 $40 $35 $30 $28 $22 $15 $5

(b) Construct a 90% confidence interval estimate of the population proportion of reimbursements that contain errors.

(c) Construct a 95% confidence interval estimate of the population mean reimbursement per office visit.

(d) Construct a 95% confidence interval estimate of the population total amount of reimbursements for this small regional town.

(e) Construct a 95% confidence interval estimate of the total difference between the amount reimbursed and the amount that the auditor determined should have been reimbursed.