The mayor of a large city with over 2 million adult citizens wants to know what percentage of adults in the city support a tax increase to fund a new public library. What is the most appropriate way to learn about the opinions of adult citizens about this issue?

(A) Conduct a census and ask each adult citizen about the tax increase.
(B) Place a notice in the local newspaper asking adult citizens to write letters to the mayor expressing their opinion about the tax increase.
(C) Select a random sample of adult citizens with library cards and ask each member of the sample about the tax increase.
(D) Select a random sample of adult citizens and ask each member of the sample about the tax increase.



7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Correct answer and commentary

The correct answer to this question is Choice (D). In this context, surveying a random sample of adult citizens is the most appropriate way to learn their opinions on an issue. As consumers of statistical information, it is important for students to recognize that survey results are only trustworthy when the sample is representative of a population. When random sampling is used, individuals are included in the sample based on impersonal chance. This ensures that no group is systematically over- or under-represented, resulting in random samples that tend to be representative of the population. 52% of students answered this question correctly.

Choices (B) and (D) exemplify sampling methods that could lead to non-representative samples and biased results. Choice (B) is a voluntary sample, because each citizen would decide for themselves whether to answer the mayor’s call for letters. Results of voluntary samples tend to be biased toward those with the strongest opinions. For example, people who are passionately opposed to a tax increase may write letters to the mayor, while less enthusiastic supporters of the tax increase choose not to, leading to an over-representation of negative opinions. Choice (C) is a random sample drawn from a subset that probably does not represent the population as a whole. The results of a survey of library card holders would almost certainly be biased in favor of a tax increase to fund a new library. Students should recognize that non-random samples may lead to bias and think critically about the direction of bias in a particular context.

The most popular incorrect answer was choice (A). A census is tempting in that it eliminates the variability that comes with random sampling, but this option would require a large amount of time and resources, making it arguably not practical for a population of over 2 million peopleAs students learn to consider how data are produced, it is important to attend to practical concerns as well as theoretical concerns.

Student performance