Question 51·Hard·Evaluate Statistical Claims: Observational Studies and Experiments
A botanist is studying whether a new liquid fertilizer increases the mass of a certain variety of basil plants. Out of 240 identical seedlings growing in one greenhouse, she randomly selects 120 to receive weekly applications of the fertilizer and 120 to receive only water. After 8 weeks, the basil plants in the fertilizer group have a statistically significantly greater mean mass than those in the water-only group.
Based on the design of the study, which statement is best supported by the results?
On SAT statistics questions about studies, first decide whether it is an observational study or a randomized experiment by checking if the researcher actively assigns treatments. If there is random assignment and a statistically significant difference, you can usually support a cause-and-effect conclusion, but only for the group actually studied. Next, look for any mention of random sampling from a larger population; without it, you cannot generalize the result beyond the specific group in the study. Finally, eliminate answer choices that either weaken causality when an experiment justifies it or overgeneralize to “all people/plants/etc.” when the sample does not support such a broad claim.
Hints
Identify the type of study
Ask yourself: Does the botanist just observe which plants get fertilizer, or does she actively decide (and randomly assign) which plants get fertilizer and which do not?
Think about what random assignment lets you conclude
When subjects are randomly assigned to treatment and control groups, what kind of relationship (association vs. cause-and-effect) can a strong, statistically significant difference support?
Consider the population you can talk about
All the seedlings are from one greenhouse. Were they randomly selected from all basil plants of this variety or from all basil plants anywhere? Based on that, how far can you reasonably extend the conclusion?
Step-by-step Explanation
Understand the study setup
The botanist has 240 identical basil seedlings in one greenhouse. She randomly chooses 120 to get weekly fertilizer and 120 to get only water. After 8 weeks, the fertilizer group has a statistically significantly greater mean mass than the water-only group.
Key details:
- Same greenhouse, same variety, identical seedlings.
- Random assignment to fertilizer vs. water.
- Statistically significant difference in mean mass.
Decide if this is an experiment or observational study
In an observational study, the researcher just observes what is already happening. In an experiment, the researcher assigns treatments to subjects.
Here, the botanist chooses which plants get fertilizer and which get only water, and she does this randomly. That means this is a randomized experiment.
In a well-designed randomized experiment, if there is a statistically significant difference between groups, it supports a cause-and-effect conclusion (for the units that were studied).
Figure out how far the results can be generalized
To generalize results to a larger population, the subjects must be randomly selected from that population.
Here, all 240 plants are described as seedlings already growing in one greenhouse. There is no indication they were randomly sampled from all basil plants of this variety or from all basil plants everywhere.
So:
- We can talk about cause and effect, because of random assignment.
- We cannot safely extend the conclusion beyond the basil plants in this greenhouse, because there was no random sampling from a broader population.
Match the reasoning to the answer choices
We need the choice that:
- Uses causal language (because this is a randomized experiment with a significant result), and
- Limits the claim to the basil plants in this greenhouse (because there was no random sampling from a wider population).
Only choice A) For the basil plants in this greenhouse, weekly use of the fertilizer causes an increase in mean plant mass. makes both of these restrictions correctly, so it is the best-supported statement.