In a randomized experiment, keep two jobs of chance separate. Random assignment decides who gets a treatment and lets you judge cause; random sampling decides who enters a study and lets you extend results to a larger population. Check how participants entered, then how the groups were formed. Don't mistake randomly assigned volunteers for a random sample of all students.
Hints
- Hint 1
A volunteer sample is made up of people who chose to join. Who entered the study here? Unless students were randomly selected from a larger population, keep the conclusion with the people studied.
- Hint 2
In random assignment, chance decides who receives the course. That's different from randomly selecting students to enter the study. Which job did chance do here, and what does it let you say about cause?
- Hint 3
A control group gives the course group students to compare against. The reported result compares group averages; it doesn't say every student who took the course scored higher.
Step-by-step
Check who joined and who got the course
Step 1Set the limit on who the result describes
No Desmos needed. The question asks what the study design supports, not for a calculation. The 60 eleventh-grade volunteers chose to join; they weren't randomly sampled from a larger population. A sample is the people studied, so keep the conclusion with these volunteers rather than extending it to students elsewhere.
- Step 2
Decide whether the study supports cause
The volunteers were randomly assigned, meaning chance picked who took the course and who entered the control group, which did not take it. Students didn't choose their own groups based on motivation or another trait. Random assignment lets a difference in group results support cause; it does not turn volunteers into a random sample.
- Step 3
Match the conclusion to the measured result
The significantly higher average means the score difference between groups is unlikely to be a chance fluctuation. It doesn't mean every volunteer who took the course scored higher. So, for the eleventh-grade volunteers in this study, taking the review course caused an increase in SAT Math scores on average. Choice D.