The proportion of hospitals in Example A of Section 7.2 that had fewer than 1000 dischar...

The proportion of hospitals in Example A of Section 7.2 that had fewer than 1000 discharges is p = .654. Suppose that the total number of hospitals having fewer than 1000 discharges is estimated from a simple random sample of size 25. Use the central limit theorem to sketch the approximate sampling distribution of the estimate.

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.