A survey question about a larger group calls for statistical inference: using a sample to estimate a value for the whole group. First ask who could have been selected, because random selection supports conclusions only about that group. Then treat the sample mean as an estimate, not an exact population mean. A random pick cannot extend a conclusion to people who were never eligible.
Hints
- Hint 1
A random sample is a group chosen by chance from a larger group. Ask who was eligible for selection here. Could a part-time student or a student at another university have been picked?
- Hint 2
A sample mean is the average among the people surveyed. It estimates the average for the eligible group, but doesn't establish the exact average for everyone in that group. Which conclusion leaves room for a difference?
Step-by-step
Match the estimate to the sampled group
Step 1Identify the group the sample can represent
No Desmos needed. This asks who the data describe, not for arithmetic. A random sample uses chance to select people. The students were picked from full-time undergraduates at this university, so the results can reasonably represent that group. Part-time students and students elsewhere weren't eligible. Random selection supports conclusions only about the group from which people were picked.
- Step 2
Treat the reported mean as an estimate
The sample mean is the average for the surveyed students: hours. Most of the university's full-time undergraduates weren't surveyed, so their overall mean need not equal . A margin of error accounts for a possible difference between the estimate and the true mean; no numerical margin is given to calculate.
- Step 3
Choose the supported conclusion
So the average studying time for all full-time undergraduates at this university is likely close to hours, though its exact value may differ by some margin of error. Choice B.