A margin of error around a sample mean gives a plausible interval for the population mean, the average for the whole group. Subtract the margin to find the low end and add it to find the high end. The sample mean is an estimate, not a guarantee that the population mean is exactly the same.
Hints
- Hint 1
A sample mean describes the students who were surveyed. The question asks about the population mean, the average for all college students. Which given number estimates that average?
- Hint 2
A margin of error gives a distance on both sides of an estimate. Subtract it to find the low end of the plausible interval, then add it to find the high end.
Step-by-step
Build the plausible interval
Step 1Apply the margin of error to the estimate
No Desmos needed. Each endpoint takes one operation. The sample mean of hours estimates the average for all college students. The margin of error puts the plausible population average hour below or above that estimate, so its interval is to hours.
- Step 2
Find the low end
Subtract the margin from the estimate to get the lower endpoint:
- Step 3
Find the high end
Add the margin to the estimate to get the upper endpoint:
- Step 4
State what the interval describes
The population mean is the average for all college students, not the hours studied by each student. The margin of error gives a plausible range, not an exact population average. So it is plausible that the average studied last week was between and hours. Choice D.