A randomized experiment uses chance to form treatment groups, so a difference in outcomes can provide evidence of cause and effect. Look for random assignment before judging a causal claim. Then check whether a statement turns a difference between group averages into an exact promise. Volunteers also limit how broadly the result can be applied.
Hints
- Hint 1
In a randomized experiment, chance decides which treatment each participant receives. Does random assignment make the difference between these groups evidence of an effect, rather than only a relationship?
- Hint 2
A sample average describes a group, not a guaranteed change for each person. Subtract the two averages, then ask whether that difference establishes an exact effect for college students.
- Hint 3
A volunteer sample consists of people who chose to participate. That limits how broadly a finding applies, but it does not undo the random assignment that happened after they joined.
Step-by-step
Check the design, then the claims
Step 1Identify what random assignment supports
No Desmos needed. This decision depends on the study design, not a calculation. The students were randomly assigned, meaning chance decided who studied with music. The silent group is a comparison group, a baseline for judging the music group. Because chance formed the groups, their different results provide evidence about the effect of the assigned study condition.
- Step 2
Check the claim of an exact gain
Subtract the silent group's average from the music group's average:
That is the difference between these groups' sample averages. It does not establish an exact -point effect for every student or for college students generally. So statement I goes beyond the evidence.
- Step 3
Keep the conclusion within reach of the study
The students were volunteers, not a random sample selected from all college students. That limits how far the result can be generalized, or extended to a larger population. It does not erase the causal evidence from the random assignment. Random assignment supports causation; random sampling supports generalization. Statement II makes the cautious claim that the experiment provides evidence of improvement for similar students. So II is supported, but I is not. Choice C.