# Dec 1 - 12/1/10 Posted before class. EXAMPLE INVESTIGATION...

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1 12/1/10 Posted before class. EXAMPLE INVESTIGATION of COVERAGE PROBABILITY Application to Auditing 1. INTRODUCTION. Suppose that over the course of three years, a medical care provider has submitted N = 200,000 bills for reimbursement under the government’s Medicaid Program and received \$5,000,000 from Medicaid as reimbursement. Naturally, the government is concerned that the billings were accurate and reflected the correct amount due to the provider for the services rendered. After all, the provider enrolled in the Medicaid system and thereby agreed to abide by certain rules and regulations. These rules and regulations concern fair costs for services and assurances that unnecessary medical procedures are not billed to Medicaid. Moreover, the government, as the guardian of the taxpayer’s money, is responsible for its efficient use in providing for the general welfare of the citizenry. How is one to determine if the provider has complied with the rules and regulations in billing Medicaid during the three year period? How is one to determine the average error 1 in the billing amount? How is one to determine what percentage of the billings are in error? As with business in general, an audit 2 is required. It is neither possible nor practical to conduct a complete audit of all N = 200,000 billings. It would be prohibitively expensive, and it would be impossible to maintain consistent and accurate evaluation of the N = 200,000 billings. This is where statistical sampling and estimation come into the picture . Using statistical methods, we can work with a relatively small sample of billings, carefully evaluate them and project the results to the entire population. Using the sample information, we are able to say with some degree of confidence what would be found were a complete audit to be accomplished with the same care and auditing rules that were operating in processing the sample. In this paper we will illustrate the ideas by using examples involving simple random sampling and the large sample 95% confidence interval estimates that are covered in class. In practice, experts will design a sampling plan from many possibilities including the use of stratified random sampling and multi-stage random sampling. The expert may employ ratio, regression and bootstrap estimates. Generally, the sampling plan and estimation method are chosen in the given application to produce appropriate margins of error for the application at the smallest possible cost to the auditors. If the results are expected to be controversial and challenged, extreme care and control must be exercised in carrying-out the audit and there must be documentation of the entire audit process. Example 1.Auditing Charges to Medicaid.

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## This note was uploaded on 02/01/2011 for the course STAT 315 taught by Professor Dennisgilliland during the Summer '10 term at Michigan State University.

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Dec 1 - 12/1/10 Posted before class. EXAMPLE INVESTIGATION...

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