Question 20·Medium·Evaluate Statistical Claims: Observational Studies and Experiments
A botanist wants to know whether a new fertilizer increases the growth of tomato plants under greenhouse conditions. She randomly assigned 120 identical seedlings to two groups of 60: one group received the fertilizer weekly, while the other group received only water. Eight weeks later, the average height of the fertilized group was 18.3 cm, and the average height of the non-fertilized group was 16.2 cm. The difference of 2.1 cm is statistically significant at the 5% level.
Which conclusion is best supported by these results?
For questions about statistical conclusions, first identify whether the study is an experiment with random assignment or an observational study; only experiments justify causal language like “causes” or “increases.” Next, interpret terms like “statistically significant at the 5% level” correctly—as evidence that the observed effect is unlikely due to chance, not as a guarantee for every individual or a 95% range. Then check each answer for scope: eliminate options that overgeneralize beyond the setting studied (e.g., “any environment,” outdoor gardens when only greenhouses were used) or that claim exact effects (“exactly 2.1 cm”). Choose the option that accurately reflects a likely effect on the average outcome within conditions similar to those in the experiment.
Hints
Identify the study design
Ask yourself: Did the botanist just observe plants, or did she randomly assign some plants to get the fertilizer and others not to? This affects whether we can talk about cause and effect.
Interpret “statistically significant at the 5% level”
Think about what it means that the 2.1 cm difference is statistically significant at the 5% level. Does it guarantee a result for every plant, or does it tell you something about how likely the observed difference is if there were no real effect?
Watch for overgeneralization
Look for choices that go beyond the situation actually tested. Did the experiment include outdoor gardens, all possible environments, or just certain greenhouse conditions?
Be careful with exact numbers and 95% statements
Ask whether we can truly say plants will grow exactly 2.1 cm taller, and whether “5% level” really tells us that 95% of individual plants fall in a certain height range.
Step-by-step Explanation
Identify the type of study
The botanist randomly assigned 120 identical seedlings to a fertilizer group and a control (water-only) group, then compared their heights.
Random assignment to treatments makes this a controlled experiment, not just an observational study. That means we can talk about cause and effect for the conditions actually used (this greenhouse setup).
Interpret “statistically significant at the 5% level”
The mean heights after 8 weeks were:
- Fertilizer group: 18.3 cm
- No-fertilizer group: 16.2 cm
- Difference in means: 2.1 cm
“Statistically significant at the 5% level” means that if the fertilizer truly had no effect, a difference this large (2.1 cm) would be very unlikely to happen just by random assignment (probability less than about ).
So the data provide strong evidence that the fertilizer does affect average height (and here, increases it) under these greenhouse conditions.
Think about the limits of the conclusion
Even with statistical significance, we must be careful about how far we generalize:
- We can make a causal statement (fertilizer affects growth) only for similar greenhouse conditions to those in the experiment.
- We cannot claim the exact size of the effect for every plant (it will vary, and 2.1 cm is an average difference in this sample).
- We cannot make claims about other environments (like all outdoor gardens) that were not part of the study.
- The 5% level does not mean “95% of all plants fall in a certain height range.” It’s about the chance of seeing such a difference if there were no true effect.
Match each choice to the evidence and scope
Now compare the answer choices to what the study does and does not justify:
- Any claim that says “in any environment” is too broad; the study used only one type of greenhouse setup.
- Any claim that says plants will grow “exactly 2.1 cm taller” is too precise; 2.1 cm is a sample mean difference, not a guarantee for every plant.
- Any claim about outdoor gardens goes beyond the data (no gardens were studied).
- Any claim that interprets “5% level” as a 95% range of individual plant heights misunderstands statistical significance.
The only choice that stays within these limits and reflects a likely increase in average height under similar greenhouse conditions is:
A) Under similar greenhouse conditions, using the fertilizer is likely to increase the average height of tomato plants compared with not using the fertilizer.