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Difficulty: Hard

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

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.

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

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

The $55$ trivia teams in the sample

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

All trivia teams in the tournament

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Explanation

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.