Chapter 3, Problem 51P

Obstetrics

The following data are derived from the Monthly Vital Statistics Report (October 1999) issued by the National Center for Health Statistics [10]. These data are pertinent to livebirths only.

Suppose that infants are classified as low birthweight if they have a birthweight <2500 g and as normal birthweight if they have a birthweight ≥2500 g. Suppose that infants are also classified by length of gestation in the following five categories: <28 weeks, 28–31 weeks, 32–35 weeks, 36 weeks, and ≥37 weeks. Assume the probabilities of the different periods of gestation are as given in Table 3.8.

Also assume that the probability of low birthweight is .949 given a gestation of <28 weeks, .702 given a gestation of 28–31 weeks, .434 given a gestation of 32–35 weeks, .201 given a gestation of 36 weeks, and .029 given a gestation of ≥37 weeks.

Table 3.8 Distribution of length of gestation

Show that the events {length of gestation ≤ 31 weeks} and {low birthweight} are not independent.