In a study-design question, random assignment determines whether a treatment can be called a cause; random sampling determines who the result can represent. Check how the groups were formed, how participants entered the study, and whether the result describes an average or every person. Volunteers can still be assigned at random: volunteering limits the reach of the conclusion, not the experiment's ability to support causation.
Hints
- Hint 1
An experiment gives groups different treatments. Here, chance chose who played the game. What does that let you say about the difference between the groups' test scores?
- Hint 2
Random sampling uses chance to pick participants from a larger group. These students volunteered instead. Can the result be extended to every student at their school or in the district?
- Hint 3
The reported difference is between group averages, not a record of how each student changed. What can you say about the participants without promising that every one of them improved?
Step-by-step
Check cause, reach, and average
Step 1Use the assignment to judge cause
No Desmos needed. The decision depends on how the study formed its groups, not on a calculation. Random assignment means chance chose whether each volunteer played the game or kept doing usual homework. So this experiment supports a cause-and-effect claim about the difference in the groups' scores, rather than only an association.
- Step 2
Limit who the result covers
The ninth graders volunteered; they weren't a random sample, a group picked by chance from all the students a claim might cover. So the evidence doesn't extend to every ninth grader at their school, much less to district high-school students. Random assignment supports cause; random sampling supports generalization beyond the participants.
- Step 3
Keep the result about averages
The game group's average score was points higher. The difference was statistically significant: a gap that large would be unlikely from random assignment alone if the game had no effect. This supports a higher group average, not a promise that every participant improved.
- Step 4
Choose the conclusion within those limits
The supported conclusion says the game caused higher test scores for the ninth graders who participated, compared with usual homework. Read that as a result about their group average, not a claim about every student's score or students outside the study. Choice D.