Health care fraud. Most errors in billing insurance providers for health care services involve honest mistakes by patients, physicians, or others involved in the health care system. However, fraud is a serious problem. The National Health Care Anti-fraud Association estimates that approximately $68 billion is lost to health care fraud each year.7 When fraud is suspected, an audit of randomly selected billings is often conducted. The selected claims are then reviewed by experts, and each claim is classified as allowed or not allowed. The distributions of the amounts of claims are frequently highly skewed, with a large number of small claims and a small number of large claims. Since simple random sampling would likely be overwhelmed by small claims and would tend to miss the large claims, stratification is often used. See the section on stratified sampling in Chapter 2 (page 59). Here are data from an audit that used three strata based on the sizes of the claims (small, medium, and large):

(a) Construct the 3 × 2 table of counts for these data and include the marginal totals.

(b) Find the percents of claims that were not allowed in each of the three strata.

(c) To perform a significance test, combine the medium and large strata. Explain why we do this.

(d) State an appropriate null hypothesis to be tested for these data.

(e) Perform the significance test and report your test statistic with its degrees of freedom, and the P-value. State your conclusion.