In a randomized experiment, chance picks who gets each treatment, so you can compare the groups to judge a cause-and-effect claim. Keep the two jobs of chance separate: random assignment supports causation; random sampling supports generalization. Check how participants entered the study before extending a result to a larger population, and don’t assume a placebo proves what happened to every person who received it.
Hints
- Hint 1
In a randomized experiment, chance decides who gets each treatment. Since the volunteers didn’t choose their own pills, what does the difference in reported improvement let you say about cause among these volunteers?
- Hint 2
A random sample uses chance to choose participants from a larger population. Here, chance chose the treatments after people volunteered, not the adults who entered the study. How far can the finding reach?
- Hint 3
A placebo looks like the treatment but lacks the new drug. That doesn’t prove it had no effect on anyone. What do the reports of improvement tell you, and what can’t they prove?
Step-by-step
Check cause, population, and placebo
Step 1Use random assignment to judge cause
No Desmos needed. The question asks what the experiment supports, not for a calculation. Random assignment means chance decided which pill each volunteer got. So a difference between the groups’ results can support a causal comparison of the drug and placebo for these volunteers.
- Step 2
Compare the improvement rates
The drug group had reporting reduced symptoms, compared with of the placebo group. So the drug group had a higher rate of reported improvement. That supports a group-level claim about the volunteers, not a promise that every person improved or that each person’s symptoms fell by a greater amount.
- Step 3
Limit who the result represents
A random sample uses chance to pick people from the larger population. These adults volunteered; chance assigned their pills only after they entered the study. So the result cannot be generalized to all adults with seasonal allergies in the country.
- Step 4
Check the claim about the placebo
A placebo looks like the drug but lacks the new drug. Still, of the placebo group reported improvement. Those reports don’t tell us what caused each person’s relief, so they cannot prove the placebo had no effect on anyone. Statement I is supported for the volunteers; II and III are not. Choice D.