Question 3·Hard·Evaluate Statistical Claims: Observational Studies and Experiments
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 | 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?
For questions about generalizing study results, first find exactly who was randomly selected and from what larger group—that larger group is your candidate population. Ignore the detailed counts in tables unless they change who was randomly selected; subgroups or subsets of the sample usually are not new populations. Then, among the answer choices, pick the largest group that matches the original population from which the random sample was drawn, being careful not to confuse the sample (or parts of it) with the population.
Hints
Locate the random selection
Look for where the problem mentions that teams were chosen "at random." Which group is described as being randomly selected? From what larger group?
Distinguish between sample and population
Ask yourself: Which group is the full group the organizer is interested in, and which groups are just the ones that happened to be in the study or in the table?
Pay attention to the word “largest”
Among the answer choices, find the biggest group that is still consistent with the way the sample was chosen. Don’t pick a group that is only a subset of another reasonable choice if that bigger group is still supported by the random sampling.
Step-by-step Explanation
Understand “population” vs. “sample”
In statistics, the population is the full group you care about, and the sample is the smaller group actually studied. You can generally generalize results only to the population from which you took a random sample.
Identify who was randomly selected
The prompt says the organizer selected 55 teams at random from all trivia teams in a certain tournament. Therefore, the random sample came from the tournament’s full set of teams. Keep that in mind when determining how broadly the results can be generalized.
Interpret the table correctly
The table shows only the 40 teams in the sample that practiced at least 3 hours per week, broken down by points scored and hours practiced. These 40 teams are a subset of the 55 randomly selected teams, but they were not randomly selected from some new, larger population on their own; they came from the original random sample.
Choose the largest valid population
Because the only random selection was from all trivia teams in the tournament, the study’s results can be generalized to that entire group, and no larger group is justified. Therefore, the largest population to which the results can be generalized is all trivia teams in the tournament.