An observational study compares groups without assigning people to them. If a question asks whether a program caused a difference, first check who chose the groups. Random assignment helps separate the program’s effect from differences students already had. A higher group average shows an association, but even a large sample or a shared school cannot establish the cause.
Hints
- Hint 1
To test a claim of cause, look for random assignment: chance puts students into the tutoring and no-tutoring groups. Who made that choice in this study?
- Hint 2
A confounding variable is a difference between groups besides the program that can affect scores. Could students who sought tutoring have scored differently even without it?
Step-by-step
Check who formed the groups
Step 1Identify the study design
No Desmos needed. This question is about how groups formed, not a calculation.
The program was optional, and students chose whether to attend, so chance did not put them in groups. This is an observational study: the school compared groups students formed themselves.
- Step 2
Check what else could explain the score gap
The attendees’ higher average does not tell us what raised their scores. Students who chose tutoring might also have been more motivated or had stronger math skills beforehand. Either difference could affect scores without tutoring causing the gap. Such an outside influence is a confounding variable, so self-selected groups show an association, not proof of cause. The school cannot conclude that tutoring caused the higher scores. Choice C.