Question 44·Medium·Evaluate Statistical Claims: Observational Studies and Experiments
A pharmaceutical company conducted a clinical experiment with 200 adult volunteers who suffer from seasonal allergies. The volunteers were randomly assigned to two equal groups: one group received the company’s new allergy drug, and the other group received a placebo pill that looked identical. After 4 weeks, 72 percent of the volunteers who took the new drug reported a reduction in symptoms, compared with 45 percent of the volunteers who took the placebo.
Based on the design and the results of the experiment, which of the following statements are supported?
I. For the volunteers in this experiment, taking the new drug caused a greater reduction of symptoms than taking the placebo.
II. The results can be generalized to all adults with seasonal allergies in the country.
III. The difference in the percentages proves that the placebo had no effect on any of the volunteers.
For experiment-and-survey questions, first identify whether the study is an experiment with random assignment or an observational study, and whether participants were randomly selected from a larger population. Use this to decide two things separately: (1) Does the design support causal conclusions (yes if it’s a well-designed experiment with random assignment)? (2) Can the results be generalized to a wide population (yes only if there was random sampling from that population). Finally, be skeptical of extreme wording like "all," "any," or "proves"—on the SAT, such statements are usually not fully justified by typical study designs.
Hints
Think about the type of study
Ask yourself: Is this an observational study or an experiment? Does the way participants were assigned to groups allow us to talk about cause and effect?
Focus on who the conclusion is about
Some statements talk specifically about "volunteers in this experiment," and others talk about "all adults" in the country. Which kind of conclusion does this study design actually justify?
Look closely at the placebo group results
Notice the percentage of people in the placebo group who reported reduced symptoms. Does that percentage support the idea that the placebo had no effect on anyone?
Watch for extreme words
Be careful with words like "all," "any," and "proves." Ask whether the data and design are strong enough to justify such absolute claims.
Step-by-step Explanation
Identify what the study design allows us to conclude
This was a clinical experiment with random assignment to two groups: new drug vs placebo. Random assignment makes the two groups similar on average, except for the treatment. That means differences in outcomes between the groups can reasonably be attributed to the treatment for the volunteers in this experiment.
So the design supports causal conclusions about these 200 volunteers, but says nothing yet about people who were not in the study.
Evaluate Statement I (causal conclusion for the volunteers)
Statement I: "For the volunteers in this experiment, taking the new drug caused a greater reduction of symptoms than taking the placebo."
- In the new drug group, reported symptom reduction.
- In the placebo group, reported symptom reduction.
Because the volunteers were randomly assigned to groups in an experiment, the difference in percentages can be interpreted as the effect of the drug vs. the placebo for the participants.
Therefore, the design and results support Statement I.
Evaluate Statement II (generalizing to all adults in the country)
Statement II: "The results can be generalized to all adults with seasonal allergies in the country."
To generalize results to a larger population, you usually need a random sample from that population. The problem only says "200 adult volunteers"—it does not say they were randomly selected from all adults with seasonal allergies.
Because these are volunteers (not a random national sample), we cannot confidently extend the results to all adults with seasonal allergies in the country.
So Statement II is not supported.
Evaluate Statement III (placebo had no effect on any volunteer) and decide the answer
Statement III: "The difference in the percentages proves that the placebo had no effect on any of the volunteers."
- In the placebo group, reported a reduction in symptoms.
- That means many placebo-group volunteers did report improvement.
We cannot say the placebo had no effect on any volunteer. Also, in statistics, we almost never say results prove something that strong; the data only show a difference between the groups, not that the placebo was completely ineffective for every person.
So Statement III is not supported.
Only Statement I is supported, so the correct answer choice is D) I only.