How was your stay? 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 survey $120$ guests who stayed at the hotel during a convention about their overall satisfaction with the property.

(a) Explain why choosing a stratified random sample might be preferable to an SRS in this case. What would you use as strata?

(b) Why might a cluster sample be a simpler option? What would you use as clusters?

A hotel has $30$ floors, each with $40$ rooms. On one side of the hotel, accommodations overlook the ocean, while on the other, rooms overlook a golf course. The accommodations with a view of the water are more expensive. The hotel manager wishes to poll $120$ convention attendees about their overall satisfaction with the property.

Divide the population into groups, or clusters, to select a cluster sample. Pick a few of these clusters at random. The sample includes all of the people in the chosen clusters.

In this case, a stratified random sample rather than an SRS might be preferable. Simple random samples are obtained from independent subgroups using stratified random sampling. Simple random sampling involves selecting a sample from which each person has an equal probability of being chosen. A simple random sample requires us to choose $120$people from 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). Thus, a stratified random sample is preferable since it allows us to consider opinions based on room type if the strata are room types.

Simple random samples are obtained from independent subgroups using stratified random sampling. A cluster sample would be straightforward since, if the subgroups are the floors, only a few floors need to be chosen rather than the entire hotel. Divide the population into groups, or clusters, to select a cluster sample. Pick a few of these clusters at random. The sample includes all of the people in the chosen clusters.