A randomized experiment uses chance to assign people to treatment and comparison groups, which can support a cause-and-effect conclusion. To decide how widely the result applies, check whether participants were also chosen at random from the larger population. The key trap is treating random assignment to groups as though it were random selection of participants.
Hints
- Hint 1
In a randomized experiment, chance decides who receives the treatment. That makes the treatment, rather than the participants’ own choices, a credible explanation for a difference between groups. Who decided which runners got the gel?
- Hint 2
A placebo looks like the treatment but does not contain the treatment being tested. It gives the researchers a comparison group. What can they compare when both groups consume something that looks and tastes the same?
- Hint 3
A random sample uses chance to select people from a larger population. These runners volunteered from one club. Could they differ from other runners, even though their treatment groups were formed at random?
Step-by-step
Separate assignment from selection
Step 1Decide whether the design supports cause
No Desmos needed. This question asks how the study was designed, not for a calculation. The nutritionist randomly assigns runners to the two groups, so this is a randomized experiment: chance, not a runner’s preference or ability, decides who gets the gel. If the groups’ finish times differ, the design supports attributing that difference to the gel for these runners.
- Step 2
Identify what the gel is compared with
The other group consumes a placebo, something that looks and tastes like the gel but does not contain the treatment being tested. This gives the gel group a comparison under similar conditions, helping separate the gel’s effect from the effect of expecting to take it. A placebo alone would not establish cause without random assignment.
- Step 3
Limit who the conclusion covers
The runners are volunteers from one local club, not a random sample chosen from all runners. They may differ from runners elsewhere, so the result cannot necessarily be generalized to all runners. Random assignment supports cause; random sampling supports generalization. The study can support a cause-and-effect conclusion about 5K times for its runners, but not necessarily for all runners. Choice D.