Indiana audits nursing homes to see whether and how much the nursing home has overbilled Medicaid. Here is how they do it. Nurseco has 70 homes in Indiana. The state randomly samples one invoice per nursing home and determines Nurseco’s liability as follows. Suppose nursing home 1 has billed Medicaid $100,000. If the one surveyed invoice at nursing home 1 indicates Nurseco has overbilled by 40%, then Nurseco would have to return 40% (or $40,000) that it has collected from the state. What is wrong with this approach? Assuming all nursing homes have overbilled at a similar rate, can you suggest a better plan to determine how much money should be returned to the state?