A random sample's sample mean estimates the mean for the whole population. Its margin of error gives a plausible interval: subtract the margin for the low end and add it for the high end. Look for a cautious claim about the population mean. The interval doesn't describe where individual students' study times fall.
Hints
- Hint 1
A mean is an average for a group, not a value each person has. Since the students were chosen at random, their sample mean can estimate an average for which larger group?
- Hint 2
A margin of error extends equally below and above an estimate. Subtract it for the low end and add it for the high end. What single average do those endpoints describe?
Step-by-step
Interpret the margin of error
Step 1Identify the average being estimated
No Desmos needed. Each endpoint takes one operation; the key is what the interval describes.
The sample mean is the average for the surveyed students. Because they were selected at random from college students, their -hour mean estimates the population mean, the average for all college students. It doesn't describe any one student's time.
- Step 2
Find the low end
The margin of error tells you how far below or above the estimate the population mean could plausibly be. Subtract hours from the -hour estimate for the low end:
- Step 3
Find the high end
Add the same margin to the estimate for the high end:
- Step 4
Match the interval to the claim
The interval describes the population mean, not individual students' study times. So it is plausible that the mean weekly study time for all college students is between and hours. Choice D.