Question

Sampling Dorm Residents. Students in the dormitories of a university in the state of New York live in clusters of four double rooms, called suites. There are 48 suites, with eight students per suite.

(a) Describe a cluster sampling procedure for obtaining a sample of 24 dormitory residents.

(b) Students typically choose friends from their classes as suitemates. With that in mind, do you think cluster sampling is a good procedure for obtaining a representative sample of dormitory residents? Explain your answer.

(c) The university housing office has separate lists of dormitory residents by class level. The number of dormitory residents in each class level is as follows. Use the table to design a procedure for obtaining a stratified sample ( with proportional allocation ) of 24 dormitory residents.

Short answer

Part (a) Used cluster sampling procedure.

Part (b) No. Cluster sampling is not a representative sample.

Part (c) Used table for obtaining a stratified sample.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

Students in the dormitories of a university in the state of New York live in clusters of four double rooms, called suites. There are 48 suites, with eight students per suite.

Part (a) Step 2. Describe a cluster sampling procedure for obtaining a sample of 24 dormitory residents.

First of all, number the suites from 1 to 48.

After that use a table of random numbers to select three of the 48 suites at random.

At last, utilize the 24 dormitory occupants who live in the three suites as the sample.

Part (b) Step 1. Identify if cluster sampling is a good procedure for obtaining a representative sample of dormitory residents or not.

Due to the fact that students usually choose buddies from their classrooms to be their suitemates.

Cluster sampling would almost certainly not be a representative sample in this situation.

This is due to the fact that suitemates and friends frequently have similar viewpoints.

Part (c) Step 1. Use the table to design a procedure for obtaining a stratified sample of 24 dormitory residents.

According to proportional allocation, the number of freshmen, sophomores, juniors, and seniors chosen should be 8, 7, 6, and 3 accordingly.

Using a table of random numbers, 8 of the 128 freshmen dormitory inhabitants were randomly selected from a stratified sample of 24 dormitory occupants ranging from 1 to 128.

Now to select 7 of the 112 sophomore dormitory occupants at random, number the inhabitants from 1 to 112 and utilize a table of random numbers:

Number the juniors dormitory occupants from 1 to 96, then use a table of random numbers to choose 6 of the 96 residents at random.

Then number the senior dormitory residents from 1 to 48, then choose three at random from a table of random numbers.