In study-design questions, separate random assignment from random selection: the first decides treatments and supports a causal conclusion; the second can help a sample represent a larger group. A randomly chosen school doesn't make its volunteers a random sample of all students. Check that an average difference isn't treated as a promise for each person. Chance must act at the right stage for the claim you make.
Hints
- Hint 1
A random sample uses chance to pick the people whose results are measured. The schools were picked at random, but did chance pick which seventh graders participated? That sets the larger group the results might represent.
- Hint 2
Random assignment means chance decides who gets a treatment after people enter a study. Did students choose whether to use the app, or did chance put them in groups? That decides whether a causal conclusion is supported.
- Hint 3
An average describes a group, not every person in it. Check whether the sleep difference compares two group averages and whether a claim extends it to all district students.
Step-by-step
Separate who joined from who got the app
Step 1Set the limit on who the result describes
No Desmos needed. This depends on who joined and how groups were formed, not on arithmetic.
The researchers randomly selected schools, but students and caregivers then chose whether to participate. A volunteer sample can differ from the district students who didn't join, so the result can't necessarily represent all seventh graders in the district.
- Step 2
Decide whether the app caused the difference
After the students joined, the researchers randomly assigned half to use the app and half not to. This is random assignment: chance, rather than a student's sleep habits or preference, determined their group. Those habits could still differ by chance, but volunteering didn't sort students into the app group. So the comparison supports a causal conclusion for the participants.
- Step 3
Match the claim to the average reported
The 18-minute difference compares group averages; it doesn't say every participant gained 18 minutes of sleep. So the study provides evidence that, among the participating students, assignment to use the app increased mean (average) nightly sleep by about 18 minutes compared with no app. It doesn't necessarily support that claim for all district seventh graders. Choice D.