Egeland et al. (1995) use capture–recapture to estimate the total number of fetal alcohol syndrome cases among Alaska natives born between 1982 and 1989. Two sources of cases were used: thirteen cases identified by private physicians, and 45 cases identified by the Indian Health Service (IHS). Eight cases were on both lists.

- Estimate the total number of fetal alcohol syndrome cases. Give a 95% CI for your estimate, using either the inverted chi-square test or the bootstrap method.

- The capture–recapture estimate relies on the assumption that the two sources of data are independent—that is, a child on the IHS list has the same probability of appearing on the private physicians list as a child not on the IHS list. Do you think this assumption will hold here? Why or why not? What advice would you give the investigators if they were concerned about independence?

- Suppose that children who are seen by private physicians are less likely to be seen by the IHS. Is ˆN then likely to underestimate or to overestimate the number of children with fetal alcohol syndrome? Explain.