Question

How is your room? A hotel has $30$floors with $40$rooms per floor. The rooms on one side of the hotel face the water, while rooms on the other side face a golf course. There is an extra charge for the rooms with a water view. The hotel manager wants to select $120$rooms and survey the registered guest in each of the selected rooms about his or her overall satisfaction with the property.

a. Describe how to obtain a sample of $120$rooms using stratified random sampling. Explain your choice of strata and why this method might be preferred to simple random sampling.

b. Describe how to obtain a sample of $120$rooms using cluster sampling. Explain your choice of clusters and why this method might be preferred to simple random sampling.

Short answer

(a) The strata is a type of room and SRS is preferred because it takes account of opinions on types of rooms.

(b) The cluster is floors and SRS is preferred because we only need to select some floors rather than the rooms.

Step-by-step solution

Part (a) Step 1: Given information

We need to find the strata and the reason for SRS being a better option

Part (a) Step 2: Explanation

A basic random sample requires us to choose $120$people from a group of over $1200$people.

A stratified random sample will necessitate taking smaller samples from distinct subgroups, allowing us to account for a new variable (on which the different subgroups are based).

If the strata are the types of rooms, a stratified random sample is better since it allows us to take into consideration the viewpoint based on the type of room.

Our stratified random sample would then include $60$rooms with views of the water and $60$rooms with views of the golf course, with rooms chosen at random from all rooms of that type.

Part (b) Step 1: Given information

We need to find the cluster of the sample

Part (b) Step 2: Explanation

Cluster sampling separates the population into non-overlapping subgroups, which are subsequently included in the sample.

A cluster sample may be easier to administer than a random sample since, if the subgroups are the floors, we only need to select a few floors rather than the entire hotel (which will make it easier to collect the data).

Because we require $120$rooms and each floor has $40$rooms, we'd have to pick three of the $30$floors at random, and all of the rooms on those three floors would be included in the sample.