4
QuizMultiple Choice

Simple Random Sample

Question 4 • VA-Probability and Statistics

Several members of a running club would like to survey the rest of the members to determine which 5K race the club should enter. They decide to sample 10 of the 78 members and have them fill out a survey about their race preference. Which of the following would be a simple random sample?

Answer
W
Write each member’s name on an equal-sized slip of paper. Place the slips of paper in a bag and shake. Draw 10 slips of paper and survey the members selected.
W
Write each member’s name on an equal-sized slip of paper. Place the slips of paper in a bag. Draw 10 slips of paper off the top and survey the members selected.
W
Write each member’s name on a scrap of paper. Fold the pieces of paper and place them in a bag. Draw 10 slips of paper off the top and survey the members selected.
W
Write each member’s name on a scrap of paper. Fold the pieces of paper, place them in a bag, and shake the bag. Draw 10 slips of paper and survey the members selected.

Explanation

A simple random sample gives every group of 10 members an equal chance of being selected. In choice A, all names are written on equal-sized slips, mixed by shaking, and then 10 are drawn, so the selection is random and each slip has an equal chance. Drawing slips from the top, as in B and C, may favor slips in particular positions; D mixes the slips but uses scraps of potentially different sizes.

AI-written and checked against the verified answer.

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