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Test
Math
Domain
Problem-Solving and Data Analysis
Skill
Evaluating statistical claims: Observational studies and experiments
Difficulty
Hard
ID: 7d68096f
Modded SAT Question Bank by Abdullah Mallik

A trivia tournament organizer wanted to study the relationship between the number of points a team scores in a trivia round and the number of hours that a team practices each week. For the study, the organizer selected 55 teams at random from all trivia teams in a certain tournament. The table displays the information for the 40 teams in the sample that practiced for at least 3 hours per week.

Hours practiced Number of points per round
6 to 13 points 14 or more points Total
3 to 5 hours 6 4 10
More than 5 hours 4 26 30
Total 10 30 40

Which of the following is the largest population to which the results of the study can be generalized?

  1. All trivia teams in the tournament that scored 14 or more points in the round

  2. The 55 trivia teams in the sample

  3. The 40 trivia teams in the sample that practiced for at least 3 hours per week

  4. All trivia teams in the tournament

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Correct Answer: D
Rationale

Choice D is correct. It's given that the organizer selected 55 teams at random from all trivia teams in the tournament. A table is also given displaying the information for the 40 teams in the sample that practiced for at least 3 hours per week. Selecting a sample of a reasonable size at random to use for a survey allows the results from that survey to be applied to the population from which the sample was selected, but not beyond this population. Thus, only the sampling method information is necessary to determine the largest population to which the results of the study can be generalized. Since the organizer selected the sample at random from all trivia teams in the tournament, the largest population to which the results of the study can be generalized is all trivia teams in the tournament.

Choice A is incorrect. The sample was selected at random from all trivia teams in the tournament, not just from the teams that scored an average of 14 or more points per round.

Choice B is incorrect. If a study uses a sample selected at random from a population, the results of the study can be generalized to the population, not just the sample.

Choice C is incorrect. If a study uses a sample selected at random from a population, the results of the study can be generalized to the population, not just a subset of the sample.

Question Difficulty: Hard
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