Samples from a Partitioned Population
An opinion poll is performed on an upcoming election. In our (artificial1y constructed) example the population is partitioned into three subpopulations, and from each subpopulation a preliminary sample of size 10 is drawn. Each element of the sample can have the values ° (vote for party A) or 1 (vote for party B). The samples are
(a) Use these samples to form an estimator for the result of the election and its variance s2. Does this result show a clear advantage for one party?
(b) Use these samples to determine for a much larger sample of size n the sizes ni of the subsamples in such a way that has the smallest variance (cf. Example 6.6).
Example 6.6
Optimal choice of the sample size for subpopulations