Other Sampling Methods

Question 4 • VA-Probability and Statistics

Race organizers want to survey the participating runners on the difficulty of the running course. Which of the following most effectively uses cluster sampling?

Answer

Separate the runners into men and women, then randomly select 20 men and 20 women.

Organize the runners into groups (elite runners, fast runners, moderate runners, and walkers). Randomly select a group, and survey all the runners in that group.

Put the same number of marbles as runners into a bag, with 20 of the marbles being red. Have each runner select a marble from a bag at the finish line. If they choose a red marble, they take the survey.

Place the runners into groups based on the seconds part of their finishing time (0:00–0:05, 0:06–0:10, etc.). Randomly select 2 of these groups, and survey every runner within the chosen groups.

Explanation

In cluster sampling, the population is divided into groups, some groups are randomly selected, and everyone in the selected groups is surveyed. Choice D does exactly this by grouping runners according to the seconds portion of their finishing time, randomly choosing two groups, and surveying every runner in them. Choice B also surveys an entire selected group, but the groups are based on running ability and may not represent all participants as effectively.

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