A random sample can help you generalize a survey result, but only to the group from which people were picked. Find that group before using the reported percentage. Keep random selection apart from random assignment: choosing respondents at random does not show that a habit caused an outcome.
Hints
- Hint 1
A random sample picks people by chance from a particular list. It can help represent people on that list, but not people who had no chance of being picked. Who was on this list?
- Hint 2
Randomly selecting respondents is different from randomly assigning a treatment. The researcher asked about sleep but did not decide who drank energy drinks. Can the survey show what caused the sleep difficulty?
- Hint 3
The word most means more than half. Compare the reported percentage with , then keep the conclusion about the group from which the teenagers were selected.
Step-by-step
Limit the conclusion to the sampled group
Step 1Identify who the sample can represent
No Desmos needed. This depends on who could be selected, not on a calculation. A random sample is picked by chance from a specified group. These teenagers came from a list of teenagers who reported drinking at least one energy drink daily. So the result can speak for that group, not all teenagers or adults.
- Step 2
Separate the survey from a cause-and-effect test
The researcher asked about sleep but did not assign teenagers to drink energy drinks or compare assigned groups. This observational study records what people report, so it cannot show that an energy drink caused difficulty falling asleep.
- Step 3
Use the percentage to make a supported inference
The who answered yes are more than half of those surveyed, so “most” fits. The supported inference is that most teenagers who drink at least one energy drink daily experience difficulty falling asleep at least three nights per week. It stays within the sampled group and makes no claim about cause. Choice C.