Question

4. Cluster sampling: The registrar of a university with a population of N=4000 full-time students is asked by the president to conduct a survey to measure satisfaction with the quality of life on campus. The registrar intends to take a probability sample of n=200 students and project the results from the sample to the entire population. Suppose that each of the n=4000 registered full-time students lived in one of the 10 campus dormitories. Each dormitory can accommodate 400 students. It is the college policy to fully integrate students by gender and class designation in each dormitory - 50 essentially each dormitory can be considered a "mini-population" or in other words, representative of the overall student population. Explain how you would collect a cluster sample.

Answer 1

In cluster sampling, the population within a cluster should be heterogeneous, while there should be homogeneity between clusters. In the question, as each dormitory of the university is a heterogeneous mix of genders, and also every dormitory is similar to the other, we can treat a dormitory as a clustered sample. The registrar can randomly pick any dormitory of the university, and out of the 400 students in the university, he can randomly select 200 students for his survey. Therefore, the results from the clustered sample can be projected to the entire university population, as a random clustered sample is a good representation of the university population.