A margin of error question gives a sample estimate and asks what is reasonable for the whole population. Check that the sample was randomly chosen from that population, then subtract and add the margin to build an interval for its mean. The tempting reversal is to choose values outside the endpoints instead of between them.
Hints
- Hint 1
A sample mean is the average for the people surveyed; it estimates the population mean, the average for the whole group. Because the seniors were randomly selected, which group can this estimate reasonably describe?
- Hint 2
A margin of error gives a distance from the estimate in both directions. Use the sample mean as the center: what do you get when you subtract that distance, and when you add it?
Step-by-step
Build the margin-of-error interval
Step 1Identify the mean being estimated
Because the seniors were randomly selected, their sample mean of messages estimates the population mean, the average for all high school seniors. It doesn't tell you how many messages each senior sends.
- Step 2
Find the lower end
The margin of error is the distance to go below or above the estimate. Subtract it for the lower end and add it for the upper end. Type in Desmos; it shows . So messages is the lower end.
- Step 3
Find the upper end and choose the statement
For the upper end, type on the next Desmos line; it shows . So the plausible interval for the mean of all high school seniors is to messages per day. Values outside that interval aren't supported by this estimate. Choice D.