4
QuizMultiple Choice

Considerations When Sampling

Question 4 • NC-Math 4 CR

A large retirement community provides many activities for its residents. The activity director is considering adding a trivia night on Tuesday evenings if there is enough interest from the residents. To measure interest in the trivia night, the activity director leaves a printed survey in residents’ mailboxes, on which the resident can express whether they are interested. Of the 68 surveys returned, 55 expressed interest. Which of these describes the type of bias in this survey and a likely direction of the bias in estimating overall community support for the trivia night?

Answer
A
This is nonresponse bias. The result overestimates support for trivia night.
B
This is nonresponse bias. The result underestimates support for trivia night.
C
This is undercoverage bias. The result overestimates support for trivia night.
D
This is undercoverage bias. The result underestimates support for trivia night.

Explanation

Residents chose whether to return the survey, so those who did not respond may differ from those who did. That creates nonresponse bias, not undercoverage, because the survey was distributed to residents through their mailboxes. Residents who are interested in trivia are more likely to return the survey, so the 55 interested responses out of 68 likely overestimate support in the whole community.

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