A randomized experiment can support cause and effect when chance puts participants into treatment groups. Check who entered the study to see whose outcomes the conclusion can describe, then compare the group averages. Randomly assigned volunteers are not the same as adults randomly sampled from a population. Statistical significance also says nothing about how many individuals improved.
Hints
- Hint 1
A volunteer sample consists of people who chose to enter the study. Even if their later group assignments were random, were these people randomly chosen from all adults?
- Hint 2
In random assignment, chance decides which treatment each participant gets. That makes preexisting differences less likely to favor one group. What does it let you say about the cause of a difference between groups?
- Hint 3
The mean is a group average, not a count of people who improved. Compare the two group averages. Does their difference tell you what happened to every volunteer?
Step-by-step
Check reach, cause, and averages
Step 1Limit who the conclusion covers
No Desmos needed. This question asks what the study design supports, not for a calculation. The adults volunteered; they weren't randomly selected from all adults. So the conclusion must stay with the volunteers in the study, not extend to all adults.
- Step 2
Check whether the study supports cause
The volunteers were randomly assigned: chance decided who took the supplement and who took the placebo. That makes other differences between the groups less likely to explain their different results, so the comparison can support a causal conclusion for these volunteers. Random assignment supports cause; it does not make the volunteers a random sample of all adults.
- Step 3
Compare what was measured
A mean is a group average. The supplement group's mean LDL decrease was 12 mg/dL, compared with 3 mg/dL for the placebo group. So the supplement group had a larger average decrease. These averages don't tell you what fraction of individual volunteers improved.
- Step 4
Use the significant difference to choose
Statistically significant means the difference between the group averages is unlikely to be due to chance alone. Together with random assignment, that supports the conclusion that, for the volunteers in the study, taking the supplement caused a larger average LDL decrease than taking the placebo. Choice D.