The U.S. government authorizes private contractors to audit bills paid by Medicare and Medicaid. The contractor audits a random sample of paid claims and judges each claim to be either fully justified or an over payment. Here is a 2 × 2 table that summarizes data from one such audit. (One of the authors served as a statistical consultant in connection with this audit. For reasons of confidentiality we cannot identify the health care provider.) For this audit, all claims were divided into two sub-populations according to amount of the claim, small or medium. Two simple random samples were chosen, 30 small claims and 30 medium claims. We want to answer the question, €œDoes the chance that a claim is judged to be an over payment depend on the size of the claim?€

a. What is the response variable? What is the explanatory variable?
b. What are the observational units for this study?
c. As for any 2 × 2 table, there are two pairs of conditional proportions. For this table, the two pairs are 14/30 versus 8/30 and 16/38 versus 14/22. Which pair corresponds to the question of interest?

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Small Total Medium Fully justified Overpayment Total 38 16 22 22 14 30 60