A margin of error paired with a sample mean signals an interval for the mean of the whole population. Subtract and add the margin to the sample estimate to find the two endpoints. You can type each endpoint into Desmos. The sample mean is an estimate, not a promise that the population mean equals it.
Hints
- Hint 1
A sample mean is the average of the surveyed group, not a known average for the whole company. Because the employees were selected at random, whose mean can this sample help estimate?
- Hint 2
A margin of error gives a distance on either side of an estimate. What two expressions put that distance below and above the sample mean?
Step-by-step
Build the plausible interval
Step 1Connect the sample to the company
A simple random sample gives each employee the same chance to be picked, so the surveyed employees' -minute mean estimates the mean for all company employees. It doesn't establish that the company-wide mean is exactly .
- Step 2
Write the interval using the margin
A margin of error gives a plausible distance below and above the sample estimate, so write the interval for the company-wide mean as .
- Step 3
Find the lower endpoint
Type in Desmos. It shows , the lower endpoint in minutes for the company-wide mean.
- Step 4
Find the upper endpoint
Add in Desmos. It shows , the upper endpoint in minutes for the company-wide mean.
- Step 5
State what the interval describes
The plausible interval is to minutes for the mean of all employees' one-way commute times, not for every employee's commute. Values outside it aren't supported by this margin of error, though they aren't proven impossible. So it is plausible that the company-wide mean is between and minutes. Choice C.