PSAT Math Multiple-Choice Question 400: Answer and Explanation

Question: 400

A psychology professor at a large university is conducting a research project on pre-law students' study habits for courses required for their majors versus their study habits for strictly elective courses. His original plan was to randomly select 250 third-year pre-law students and 250 fourth-year pre-law students and ask them to estimate the amount of time they spend studying for the two course types. Due to a printing error, only 200 survey copies were made; 50 of these went to third-years and 150 went to fourth-years. Assuming 100% of the surveys are returned, what effect(s) will the printing error have on the data collected?

• A. The mean study times will be skewed toward third-year students and the margins of error will increase.
• B. The mean study times will be skewed toward fourth-year students and the margins of error will increase.
• C. The mean study times will be skewed toward third-year students and the margins of error will decrease.
• D. The mean study times will be skewed toward fourth-year students and the margins of error will decrease.

Correct Answer: B

Explanation:

B

Difficulty: Hard

Getting to the Answer: Fewer surveys than planned means a larger margin of error, so eliminate (C) and (D). And surveying significantly more fourth-year students than third-year students means the data will be skewed toward fourth-year students. Choice (B) is the only choice that specifies both effects.