Chapter 8, Problem 64PS

Claims fraud (illegitimate claims) and buildup (exaggerated loss amounts) continue to be issue of concern among automobile insurance companies. Fraud is defined as specific material misrepresentation of the facts of a loss; buildup is defined as the inflation of an otherwise legitimate claim. A recent study examined auto injury claims closed with payment under private passenger coverages. Detailed data on injury, medical treatment, claimed losses, and total payments, as well as claim-handing techniques, were collected. In addition , auditors were asked to review the claim files to indicate whether specific elements of fraud of buildup appeared in the claim and, in the case of buildup to specify the amount of excess payment. The file InsuranceClaims contains data for 90 randomly selected auto injury claims. The following variables are included: CLAIM–Claim ID; BUILDUP–1 if buildup indicated, 0 if not; and EXCESSPAYMENT –excess payment amount, in dollars.

a. Construct a $95\%$ confidence interval for the population proportion of all auto injury files that have exaggerated loss amounts.

b. Construct a $95\%$ confidence interval for the population mean dollar excess payment amount.