The President of a large university with 30,000 students wants to investigate student support for an increase in tuition (the cost to enroll in classes). The President requests a sample of 200 students. Which of the following methods of sample selection would be best?
(A) Select 200 students at random from the list of students currently enrolled at the university.
(B) Select 200 students at random from those in the campus bookstore on the first day of class.
(C) Select 50 students at random from the list of the 10,000 students living in dorms on campus.
(D) Select 50 students at random from each of the first four football games of the season.
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.
S-IC.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Correct answer and commentary
Student performance
The correct answer to this item is option (A). The President of the university aims to use a sample of 200 students to make generalizations about the entire population of students at the university. This can be accomplished with a reasonable degree of accuracy using sound statistical practices. The sampling procedure described in option A is likely to produce a representative sample, because it calls for random selection of students from the population of interest. Thus, option (A) provides the President with the best method of sample selection for investigating student support for the tuition increase among all students who will be affected.
All of the incorrect answer choices contain the phrase “at random,” so the person taking the test must have a deeper understanding of sampling methods to answer correctly. Options B, C, and D are all incorrect, because they describe sampling from subsets of the population, which would result in a sample that is not representative of all students enrolled at the university. For example, Option (B) was the most popular incorrect answer choice selects 200 students at random like option (A), However, selecting students only from the campus bookstore would provide the President with a non-representative convenience sample, leading to results that are biased towards the opinions of students in the bookstore that day.