How is your room? A hotel has 30floors with 40rooms 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 120rooms 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 120rooms 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 120rooms using cluster sampling. Explain your choice of clusters and why this method might be preferred to simple random sampling.

Short Answer

Expert verified

(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

01

Part (a) Step 1: Given information

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

02

Part (a) Step 2: Explanation

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

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 60rooms with views of the water and 60rooms with views of the golf course, with rooms chosen at random from all rooms of that type.

03

Part (b) Step 1: Given information

We need to find the cluster of the sample

04

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

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