Suppose the Arizona Department of Health wishes to take a survey of 2-year-olds whose families receive medical assistance, to determine the proportion who have been immunized. The medical care is provided by several different health care organizations, and the state has 15 counties. Table 3.6 shows the population number of 2-year-olds for each county/organization combination. The sample is to be stratified by county and organization. It is desired to select sample sizes for each combination so that
a the margin of error for estimating percentage immunized is 0.05 or less when the data are tabulated for each county (summing over all health care organizations)
b the margin of error for estimating percentage immunized is 0.05 or less when the data are tabulated for each health care organization (summing over all counties)
c at least two children (fewer, of course, if the cell does not have two children) are selected from every cell.
Note that for this problem, as for many survey designs, many different designs would be possible.