Chapter 5.3, Problem 5.71E

(a)

To determine

To explain why we can say that the sample was taken in several stages.

Explanation of Solution

Given: Sample of $2012$ adults was randomly selected from $520$ randomly selected geographic points.The number of people selected in each geographic point is proportional to the proportion of the population size of the geographic point compared to the entire population.

The population is thus divided in subgroups, which is thus the stratified random sampling method.

The sample drawn from the subgroups are selected such that the sample is proportional to the proportion of the population in the geographic point, thus the samples from each subgroup are not of the same size and this then makes the sample a multistage sample.

(b)

To determine

To explain why it is bad practise to use an SRS from a large number “government points” across the country rather than a stratified sample of such points.

Explanation of Solution

Since some geographic points will have a much larger population than some of the other geographic points, it is very likely that some geographic areas will be over represented when taking a simple random sample, while other geographic areas might not be represented in the sample at all.