Chapter 4.1, Problem 21E

(a)

To determine

To describe how to obtain a sample of $120$ rooms using stratified random sampling and explain your choice of strata and why this method might be preferred to SRS.

Explanation of Solution

A hotel room has $30$ floors with $40$ rooms per floor. Then, we have,

Total rooms in the hotel be:

  $\begin{array}{l}=30\times 40\\ =1200\end{array}$

Thus, there are $1200$ rooms in total in the hotel. The rooms on one side of the hotel face the water while rooms on the other side face a golf course. We need to obtain a sample of $120$ rooms using stratified random sampling method.

Thus, we know that the population to be examined are the customers in the $1200$ rooms of the hotel. Now, we have to divide the population into the strata. The rooms facing the water will be the one group and the rooms facing a golf course will be the other group. So the strata will be the rooms facing the water and the rooms facing a golf course. Now, the population will be divided into the sample so that every individual have equal chance of participating the survey. Then we randomly divide the rooms into half i.e. $60$ rooms each of the rooms facing the water and the rooms facing a golf course so that each individual have equal number of chance to be the part of the survey. Thus, this is the strata used in the sampling.

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 of $120$ rooms using cluster random sampling and explain your choice of clusters and why this method might be preferred to SRS.

Explanation of Solution

A hotel room has $30$ floors with $40$ rooms per floor. Then, we have,

Total rooms in the hotel be:

  $\begin{array}{l}=30\times 40\\ =1200\end{array}$

Thus, there are $1200$ rooms in total in the hotel. The rooms on one side of the hotel face the water while rooms on the other side face a golf course. We need to obtain a sample of $120$ rooms using cluster sampling method.

Thus, we know that the population to be examined are the customers in the $1200$ rooms of the hotel. Now, we have to divide the population into the clusters. The rooms facing the water will be the one group and the rooms facing a golf course will be the other group. So the clusters will be the rooms facing the water and the rooms facing a golf course. Now, the rule of the cluster sampling method is that each group should be mutually exclusive. So, the sample from the rooms facing the water and the rooms facing a golf course should be mutually exclusive. Then we will divide $120$ rooms into the clusters and they need not be necessary same and they should be representative of the population. Thus the cluster sampling is used.

The cluster sampling is preferred over SRS because this method contains mutually exclusive clusters and also this method is more practical and economical than the SRS method.