Chapter 4.1, Problem 24E

(a)

To determine

To find out the name of this kind of sampling method used in the question.

Answer to Problem 24E

It is cluster sampling.

Explanation of Solution

A lumber company wants to estimate the proportion of trees in a large forest that are ready to be cut down. They choose a random sample of twenty rectangles and examine every tree that is in one of those rectangles.

Thus, we can say that the given sample is a random sample of twenty rectangles and every tree in those rectangles are in the sample.

Therefore, we note that the subgroups are the rectangles while the entire selected rectangle is in the sample and thus they are forming clusters. Thus the sample has to be a cluster sample.

(b)

To determine

To give a possible reason why the lumber company chose this method.

Explanation of Solution

The cluster sampling is preferred because this method contains mutually exclusive clusters and also this method is more practical and economical and also reduces time of the survey than the other methods. Thus there is a large groups of sample to be surveyed and we cannot use stratified sampling as the stratas formed cannot be more. Therefore the cluster sampling is used for better results.