An auditor for a government agency needs to evaluate payments for doctors' office visits paid by Medicare in a particular zip code during the month of June. A total of 25,056 visits occurred during June in this area. The auditor wants to estimate the total amount paid by Medicare to within 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 is conducted, with the following results:
Amount of Reimbursement
 = $93.70............S = $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 (and stored in Medicare):
$17 $25 $14 - $10 $20 $40 $35 $30 $28 $22 $15 $5
b. Construct a 90% confidence interval estimate for the population proportion of reimbursements that contain errors.
c. Construct a 95% confidence interval estimate for the population mean reimbursement per office visit.
d. Construct a 95% confidence interval estimate for the population total amount of reimbursements for this geographic area in June.
e. Construct a 95% confidence interval estimate for the total difference between the amount reimbursed and the amount that the auditor determined should have been reimbursed.