# Contrasting answers on problem on populations and samples

I recently received this question in my homework assignment:

A sociologist wants to study the attitudes of American male college students toward marriage and husband-wife relations. She gives a questionnaire to 25 of the men enrolled in Sociology 101 at her college. All 25 complete and return the questionnaire. What is the sample and population?

I indicated that the sample was the 25 men who completed the questionnaire, which the assignment's answer key agreed with me on. However, I indicated that the population was American male college students, as this was the group the sociologist was studying, but the answer key stated that the population was the Sociology 101 class at her college, because this is the group that the sample was selected from.

My question is: who is correct and why?

This is an interesting one. You're both correct... in a sense. The assignment is poorly worded though.

In survey design, there are actually two populations. There's the target population, which is the set of units we want to studying. Then there is also the sample population, which is the set of units that we could study. Ideally, the study is designed such that the sample and target populations match closely.

In this case, you have answered with the target population, while your homework says it's the sample population.

A sociologist wants to study the attitudes of American male college students toward marriage and husband-wife relations.

The population of interest is "American male college students", because that is how the research topic is worded.

"American male college students" appear to be the population of interest, but "the men enrolled in Sociology 101 at her college" was the sampling frame---the actual list of available units that was used to take your sample.

Ideally, the frame would match the population perfectly. For example, if your target population is all the students currently enrolled at your college, the Registrar's Office has a complete list that (by definition) includes all such students and only such students. They should have no undercoverage (enrolled students who aren't on the list) or overcoverage (people on the list who aren't enrolled students).

When the target population and the frame do not match, we have "frame error". This is common in most real surveys/studies. For example, if your target population is all residents of your city, a possible frame might be all the residential addresses in city limits---but your frame would miss unhoused people, and your frame would mistakenly include out-of-towners who own property here but don't live here.