In an observational study, researchers compare habits people already have instead of assigning a treatment. Check who joined the study, who formed the groups, and what the averages measure. Volunteers aren't a random sample of all adults, and a difference between existing groups doesn't prove what caused it. Keep the conclusion with the people and results actually measured.
Hints
- Hint 1
A random sample uses chance to select people from a larger group. These adults volunteered instead. How far can the conclusion reach beyond the people who took part?
- Hint 2
An observational study records what people already do. The researcher didn't decide who would take vitamins, so other differences between the groups might explain their sleep habits.
- Hint 3
A group average describes a group, not what will happen to each person. Subtract the nonusers' average from the users' average, then ask whether that gap describes the volunteers or predicts a change from starting vitamins.
Step-by-step
Check the study design and the measured difference
Step 1Limit who the result describes
No Desmos needed. The study design determines what the averages support, and finding their gap takes one subtraction. The 600 adults volunteered. A random sample would use chance to select people from all adults, so keep the conclusion to these volunteers rather than extending it to all adults.
- Step 2
Check how the groups were formed
The researcher asked whether volunteers already took the supplement; no one was assigned to take it. This is an observational study, which compares existing groups. A difference between those groups shows an association, not what caused it. Other habits could affect both vitamin use and sleep.
- Step 3
Find the difference between the averages
Subtract the nonusers' 6.8 hours from the supplement users' 7.2 hours:
The 0.4-hour gap is between two group averages. It doesn't tell you how much a nonuser's sleep would change by starting vitamins.
- Step 4
State only what the study supports
Among the 600 volunteers, those who reported taking vitamins slept, on average, 0.4 hour longer per night than those who didn't. That describes the measured groups without claiming a cause or a result for all adults. Choice D.