A question about what a study supports calls for checking both sampling and study design. In an observational study, researchers record what people do rather than assign them to groups. A random sample can support a conclusion about the population it came from, but random assignment is what supports a cause-and-effect claim. A difference between sample averages is not an exact population difference.
Hints
- Hint 1
A simple random sample uses chance to choose students from a population. It can help the results speak about seniors at the school. Does choosing students at random also decide which sleep group each student enters?
- Hint 2
Random assignment means chance decides each person’s group. Here the students reported how much they slept. Could another difference between the groups, such as study habits, also help explain their scores?
Step-by-step
Check sampling, then assignment
Step 1Identify whom the sample can represent
No Desmos needed. A calculator can’t tell who was sampled or assigned. The researchers took a simple random sample of River City High seniors. A sample is the smaller group measured, so the results can support a conclusion about seniors at that school, not seniors everywhere.
- Step 2
Check how the sleep groups formed
Random assignment would use chance to decide which sleep group each student entered. Instead, researchers recorded the students’ reported sleep. So they cannot say sleep caused a score change: another difference between the groups, such as study habits, could also affect scores. Random sampling helps you generalize; random assignment supports a claim about cause.
- Step 3
Describe what the means support
The sample mean ACT score was for students reporting at least hours of sleep and for those reporting fewer than hours. An association means the two measurements go together, without showing that one causes the other. So the study supports an association among River City High seniors, not an exact difference in the whole school’s averages. Choice C.