An experiment gives different treatments to groups and compares their results. For a study-design question, check who assigned the groups: random assignment supports a causal claim, while a placebo provides a comparison. Then check how people entered the study before extending the claim beyond them. Random assignment supports cause; random sampling supports a wider population claim. A difference in averages doesn't mean everyone improved.
Hints
- Hint 1
A randomized experiment uses chance to decide who gets each treatment. That helps separate the treatment's effect from differences people already had. Who chose the groups in this study: the volunteers or chance?
- Hint 2
A placebo is a comparison treatment without the supplement. Compare how much sleep changed on average in the two groups. What does random assignment let you say about the difference?
- Hint 3
A random sample uses chance to select people from a larger group. These participants volunteered, so random assignment doesn't make them representative of everyone with insomnia. Does a result about averages promise that each person improved?
Step-by-step
Check cause, then check who the result covers
Step 1Use assignment to judge causation
No Desmos needed. This asks what the study design supports, not for a calculation. Randomly assigned means chance chose who received the supplement and who received the placebo. Because volunteers didn't choose their groups, this experiment can support a cause-and-effect conclusion for its participants.
- Step 2
Compare the two groups
The placebo group received a comparison treatment without the supplement. The supplement group's average sleep duration increased significantly more, so the evidence supports a greater average gain caused by the supplement than by the placebo.
- Step 3
Limit the claim to the participants
The researchers recruited volunteers, not a random sample picked from everyone with chronic insomnia. So even though treatment was assigned at random, the result can't be extended to all people with chronic insomnia.
- Step 4
Keep the average in the conclusion
The result compares group averages; it doesn't say every volunteer slept longer. For the volunteers in this study, the supplement caused a greater increase in average nightly sleep than the placebo. Choice B.