A margin of error beside a sample mean signals a plausible range for the population mean. The sample mean is the center, so subtract the margin for the lower end and add it for the upper end. Type each endpoint calculation in Desmos, then match the range to the choices. Don’t center a new range on an endpoint instead of on the sample mean.
Hints
- Hint 1
A sample mean is the average for the students surveyed; is the mean for all district high school students. The sample’s average estimates , but the two numbers need not match exactly.
- Hint 2
A margin of error measures how far below or above the sample estimate the population mean could plausibly be. To find both endpoints, what do you get when you subtract from and when you add it?
Step-by-step
Build the margin-of-error interval
Step 1Turn the margin into two limits
The surveyed students are the sample; is the population mean, the average for all district high school students. A margin of error puts the plausible population mean up to hour on either side of the -hour sample mean, so subtract and add the margin around the sample mean:
- Step 2
Find the lower limit
Type in Desmos. It prints , the lower limit for the plausible population mean.
- Step 3
Find the upper limit
Keep the first line and type . Desmos prints , the upper limit. Adding the margin gives the same distance above the estimate as the lower limit is below it.
- Step 4
Match the range to the district mean
The plausible range for is hours. It describes the district’s mean homework time, not how long every student studied. Choice C.