Question

The sampling examples below use either the stratified or the cluster method of sampling. Select the examples that use the stratified method.
a. A questionnaire is created to gauge student opinion on a new university cafeteria. A sample of 40 freshmen, 50 sophomores, 60 juniors, and 50 seniors is selected to fill out the questionnaire.
b. A city council wants to know if elementary students in its city are meeting national standards. Eight schools are selected from the city's 30 total elementary schools, and the test scores of all students in the selected schools are evaluated.
c. A potato field is believed to be infected with a plant disease. The field is divided into 10 equal areas, and 25 potatoes are selected from each area to be tested for the disease.
d. A landlord wants to know the average income of his tenants. He selects three of his eight apartment complexes and collects income information from several randomly chosen tenants within the selected complexes.
e. A health agency needs to assess the performance of hospitals in a region but does not have the resources to evaluate each hospital. To reduce costs, the agency selects 5 of the 23 hospitals in the region and samples data related to performance from randomly chosen days and times.

Answer 1

A landlord wants to know the average income of his tenants. He selects three of his eight apartment complexes and collects income information from several randomly chosen tenants within the selected complexes.

A health agency needs to assess the performance of hospitals in a region but does not have the resources to evaluate each hospital. To reduce costs, the agency selects 5 of the 23 hospitals in the region and samples data related to performance from randomly chosen days and times.

Answer: Options D and E.

Explanation:

Cluster sampling is a sampling plan used when mutually homogeneous yet internally heterogeneous groupings are evident in a statistical population. It is often used in marketing research. In this sampling plan, the total population is divided into these groups and a simple random sample of the groups is selected.

Stratified sampling is a probability sampling technique wherein the researcher divides the entire population into different subgroups or strata, then selects the final subjects proportionally from the different strata.