Question:
Frank wants to know the percent of the 900 seniors at his high school who plan to attend college. He selects 40 of the seniors at random and asks each student if he or she plans to attend college. What is the population for Frank’s study?
(A) All students in Frank’s math class
(B) All students at Frank’s high school
(C) The 900 seniors at Frank’s high school
(D) The 40 students that Frank interviewed
Level:
Intermediate
Standards
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
Student performance
The correct answer for this question is option C. The use of random samples to make claims about a population is a common statistical activity. Random samples are useful when collecting data from the entire group of interest is not practical (or even impossible). The larger group that is represented by the random sample is called the population. In this question, a random sample of 40 seniors is taken from the entire group of 900 seniors at Frank’s high school.The random sample is not representative of all students at Frank’s high school, nor is it representative of seniors at other high schools. Therefore, the group of 900 seniors is the population.
The most common incorrect answer was option D). An important learning outcome for students in any statistics course is knowing - and believing - that valid claims about a larger group (population) are possible using a smaller group of randomly-selected individuals from that population. Because Frank randomly selected students, sample data can be used to make valid claims about the entire group of 900 seniors not just the 40 seniors that Frank interviewed. There is a degree of uncertainty in claims about the population, of course, but this uncertainty is quantifiable and does not render the claims invalid.