In a randomized experiment, chance decides which group receives a treatment, so a significant difference between group averages can support a causal conclusion. Check what each group received, then limit your conclusion to the outcome and setting tested. A 5% significance level does not mean that 95% of individual results fall in a particular range.
Hints
- Hint 1
With random assignment, chance decides which seedlings receive fertilizer. That makes the groups more comparable before treatment. What does the water-only group help you judge about the difference afterward?
- Hint 2
Statistical significance at the 5% level concerns how surprising the measured difference would be if the fertilizer had no effect. It does not tell you what fraction of plants have heights in a particular range.
- Hint 3
An average describes a group, not every plant. Keep the conclusion within the greenhouse setting that was tested. Were any outdoor plants studied?
Step-by-step
Check cause, then check scope
Step 1Use the random assignment to judge cause
No Desmos needed. The question asks what the study supports, not for a calculation.
The botanist randomly assigned identical seedlings, so chance decided which plants received fertilizer. This random assignment makes preexisting differences between the groups less likely to explain a later height difference.
- Step 2
Identify the comparison
The water-only group is the control group, the baseline used to judge what happens without fertilizer. The other group received fertilizer weekly, so comparing the groups tests the fertilizer's effect under the conditions of this experiment.
- Step 3
Interpret the significant difference
Statistical significance at the 5% level means that, if fertilizer had no effect, a difference at least as large as the reported cm would be unlikely from chance under the test. That supports a difference between the group averages. It says nothing about the heights of 95% of individual plants.
- Step 4
Keep the setting within the evidence
A generalization extends a result beyond what was studied. These plants grew under greenhouse conditions, and no outdoor group was tested. Random assignment supports cause, not claims about untested settings. You can't conclude that the fertilizer works everywhere or that it fails outdoors.
- Step 5
Choose a conclusion about the average
An average describes the group, not every plant. The cm gap doesn't promise an exact gain for each seedling. Under similar greenhouse conditions, using the fertilizer is likely to increase tomato plants' average height compared with using only water. Choice D.