A study claiming a program caused higher scores is asking about causation, not the size of the score gap. First check who formed the groups: chance or the students themselves. Then ask whether the groups could have differed before the program began. A comparison group lets you measure a difference, but it cannot, by itself, show what caused it.
Hints
- Hint 1
To judge whether tutoring caused higher scores, check how students got into the tutoring group. Random assignment means chance decides who attends. Did chance decide here, or did the students?
- Hint 2
A confounding variable is another factor that may affect math scores alongside tutoring. What other influences could make the groups’ scores differ even if the school program made no difference?
Step-by-step
Check how the groups were formed
Step 1Check who decided which students attended
No Desmos needed. This question turns on the study's design, not a calculation. Random assignment means chance decides who gets tutoring. Here, students chose whether to attend, so chance did not form the two groups.
- Step 2
Look for a difference that came before tutoring
A confounding variable is something besides tutoring that could affect scores. Students who chose to attend might already have been more motivated or stronger at math. They might have scored higher even without the sessions, so the comparison cannot separate that starting difference from tutoring's effect.
- Step 3
Decide what the score gap supports
The 15-point gap shows an association: attending tutoring and earning a higher average score went together. It does not establish that tutoring caused the gap. When students choose their own groups, a preexisting difference may explain the result. So the best explanation points to students' possible motivation or achievement before the semester. Choice D.