We consider automobile injury claims data using data from the Insurance Research Council (IRC), a division of the American Institute for Chartered Property Casualty Underwriters and the Insurance Institute of America. The data, collected in 2002, contain information on demographic information about the claimant, attorney involvement, and economic loss (LOSS, in thousands), among other variables.

We consider here a sample of n = 1,340 losses from a single state.

The full 2002 study contains more than 70,000 closed claims based on data from 32 insurers. The IRC conducted similar studies in 1977, 1987, 1992, and 1997.

a. Compute descriptive statistics for the total economic loss (LOSS). What is the typical loss?

b. Compute a histogram and (normal) qq plot for LOSS. Comment on the shape of the distribution.

c. Partition the dataset into two subsamples, one corresponding to those claims that involved an ATTORNEY (=1) and the other to those in which an ATTORNEY was not involved (=2).

c(i) For each subsample, compute the typical loss. Does there appear to be a difference in the typical losses by attorney involvement?

c(ii) To compare the distributions, compute a box plot by level of attorney involvement.

c(iii) For each subsample, compute a histogram and qq plot. Compare the two distributions.