Suppose that the total number of discharges, τ, in Example A of Section 7.2 is estimated...

Suppose that the total number of discharges, τ, in Example A of Section 7.2 is estimated from a simple random sample of size 50. Denoting the estimate by T , use the central limit theorem to sketch the approximate probability density of the error T − τ .

Reference

This is the first of many examples in this chapter in which we will illustrate ideas by using a study by Herkson (1976). The population consists of N = 393 short stay hospitals. We will let xi denote the number of patients discharged from the ith hospital during January 1968. A histogram of the population values is shown in Figure 7.1. The histogram was constructed in the following way: The number of hospitals that discharged 0–200, 201– 400, . . . , 2801–3000 patients were graphed as horizontal lines above the respective intervals. For example, the figure indicates that about

40 hospitals discharged from 601 to 800 patients. The histogram is a convenient graphical representation of the distribution of the values in the population, being more quickly assimilated than would a list of 393 values.