Chapter 4.1, Problem 21E

(a)

To determine

To find: The strata recommendation based on the stratified random sampling.

Answer to Problem 21E

Sideline, Corner and End zone

Explanation of Solution

Given information:

The University of Michigan athletic department plans to conduct a survey about concessions that are sold during games. Tickets are most expensive for seats near the field and on the sideline.

The Stratified random sampling draws simple random samples from independent subgroups. The independent subgroups are called the strata.

Given is that trickery prices are the same for each of the sections: Sideline, Corner and End zone.

Moreover every individual will be in exactly one section.

Thus it is best to use the strata: Sideline, Corner and End zone.

(b)

To determine

To find: The recommendation of the clusters based on cluster sample.

Answer to Problem 21E

The single people in the simple random samples as they are spread over randomly overall boxes.

Explanation of Solution

The Stratified random sampling draws simple random samples from independent subgroups.

The Cluster sampling divides the population into non-overlapping subgroups and some of these subgroups are then in the sample.

All the seating boxes (1-44) as the subgroups, of which the some subgroups are selected.

It will then be easier to select the individuals, because all individuals of a few boxes will be in the sample and thus we could just place individuals at the entrance of those boxes to take the surveys of the people in that box.

The stratified random sampling from part (a) will be much more difficult, because we need to draw a simple random sample from the sideline / corner / end zone strata and it will be a lot more difficult to find and interview all the single people in the simple random samples as they are spread over randomly overall boxes.