A margin of error tells you how far a sample estimate may be from the population mean, the average for the whole group. Subtract the margin from the sample mean for the low endpoint, and add it for the high endpoint. Then check which proposed mean falls in that interval. Don't multiply by the population size: the question asks for an average, not total hours.
Hints
- Hint 1
A sample mean describes the surveyed students. The question asks about the population mean, the average for all students at the university. Which reported number is the estimate of that average?
- Hint 2
The margin of error is a distance from the sample mean, not a range of sleep times for individual students. Subtract and add that distance to find the endpoints of the plausible interval.
Step-by-step
Build the plausible interval
Step 1Translate the margin of error
No Desmos needed. Each endpoint takes one addition or subtraction. The sample mean is the average for the 200 surveyed students. Let be the population mean, the average for all 4,800 students. The margin of error puts within hour of , so subtract and add the margin to find the plausible interval:
- Step 2
Find the low endpoint
Subtract the margin from the sample mean to find the low endpoint:
So the population mean could plausibly be as low as hours.
- Step 3
Find the high endpoint and check the proposed means
Add the margin to the sample mean to find the high endpoint:
So the population mean could plausibly be as high as hours.
The plausible interval runs from through hours. The proposed value is at an endpoint, and endpoints count. So hours is a plausible mean for all 4,800 students. Choice B.