A survey that compares groups without assigning their behavior is an observational study. Ask who chose to respond and who determined the groups being compared. Random sampling sets who a result can represent; random assignment sets whether it can show cause. An open invitation is not random sampling, and an average gap alone doesn't prove cause.
Hints
- Hint 1
A voluntary-response sample contains people who choose to answer. Even if a survey is offered to everyone, does that mean the people who completed it were picked by chance?
- Hint 2
Random assignment means chance chooses who gets a treatment. Here, students already had their own social media habits. Could another difference between the groups, such as study time, help explain their scores?
Step-by-step
Check the respondents and the group comparison
Step 1Limit who the result describes
No Desmos needed. This question is about how the study was conducted, not a calculation. The students voluntarily completed the questionnaire. That's a voluntary-response sample: students chose whether to answer. Posting it for all district students to see didn't make the respondents a random sample, so the result can't be extended to all high-school students nationwide.
- Step 2
Check whether the difference proves cause
The students reported their own social media use; the researcher didn't randomly assign them different amounts of time online. That makes this an observational study. Students in the two groups might also differ in study time, so their score difference doesn't establish that social media use caused it.
- Step 3
Describe what the comparison shows
The reported lower average scores show an association: among the respondents, social media use and math exam scores went together in the observed comparison. Keep the claim about those students, not a larger population or a proven cause. Choice D.