Estimation of Population Mean Using Cluster Sampling Provided the sample size is large, a 100(1 - a)% confidence interval estimation of the population mean using cluster sampling is as follows: T 2a/2= Similarly, confidence intervals for the population proportion based on cluster sam- pling are established Estimation of Population Proportion Using Cluster Sampling Provided the sample size is large, a 100(1 a)% confidence interval estimation of the population proportion using cluster sampling is as follows: Det zagn V3 Notice that inferences can be made with relatively little prior information about the population. All that is required is a breakdown into identifiable clusters. It is not necessary to know the total number of population members. It is sufficient to know the numbers in each of the sampled clusters, and these can be determined during the course of the survey, since a full census is taken in each cluster in the sample. In addition, since sample members will be geographically close to one another within clusters, their contact by interviewers is relatively inexpensive. Example 17.5 Cluster Sampling for Family Incomes (Estimation) A simple random sample of 20 blocks is taken from a residential area containing a total of 1,000 blocks. Each household in the sampled blocks is then contacted, and informa- tion is obtained about family incomes. The mean annual incomes and the proportion of families with incomes below $15,000 per year in the sampled blocks are contained in the data file Income Clusters. For this residential area estimate the mean family income and the proportion of families with incomes below $15,000 per year