Chapter 4.1, Problem 22E

(a)

To determine

To describe how to obtain a sample using stratified random sampling and explain your choice of strata and why this method might be preferred to SRS.

Explanation of Solution

The university of Michigan athletics department wants to survey fans about concession that are sold during games.

Now, we need to obtain a sample using stratified random sampling method. For this we need to find the population we need to study that is the athletics department in the university.

Then we will decide the strata. The stratas will be the Sideline, Corner and Endzone. This is chosen because stratas should be homogeneous within themselves and heterogeneous among themselves. So these are most preferred strata.

The stratified random sampling is preferred over the SRS as this method gives an equal chance to every individual to be the part of the survey. Whereas in SRS method it does not give the same. Thus, the result of the stratified random sampling is more accurate than SRS.

(b)

To determine

To describe how to obtain a sample using cluster random sampling and explain your choice of clusters and why this method might be preferred to SRS.

Explanation of Solution

The university of Michigan athletics department wants to survey fans about concession that are sold during games.

Now, we need to obtain a sample using cluster sampling method. For this we need to find the population we need to study that is the athletics department in the university.

Then, we need to decide the clusters used in the sampling. Here, cluster sampling might be easier as we can divide whole stadium in two clusters by dividing the clusters into two equal parts by horizontal or vertical line.

Then select one of the cluster and do complete enumeration of selected cluster. Also we can use two stage sampling method by selecting units from selected clusters.

The cluster sampling is preferred over SRS 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 SRS method.