A margin of error attached to a sample mean gives a plausible range for the mean of the whole population. Identify who was sampled and which group they came from. Then subtract and add the margin to find the endpoints. The trap is reading that range as a statement about individual commute times or about the sample mean, which is already known.
Hints
- Hint 1
The sample is the group surveyed; the population is the whole group they were selected from. Because employees were selected randomly from this company, whose average can their measured average help estimate?
- Hint 2
A margin of error goes below and above the estimate to form a plausible interval. Find both endpoints, then ask whether that interval describes the average for all employees or the commute times of individual employees.
Step-by-step
Find and interpret the population-mean interval
Step 1Identify the average being estimated
No Desmos needed. Each endpoint takes one operation; the key is interpreting the interval.
The 500 surveyed employees are the sample, the group measured. All employees at the company are the population, the group they were randomly selected from. So the sample mean of minutes estimates the average for all company employees.
- Step 2
Find both ends of the interval
The margin of error tells you how far below or above the estimate the population mean can reasonably be. Subtract minutes for the low end:
Add minutes for the high end:
- Step 3
State what the interval describes
The plausible interval describes the average for all employees, not each employee's commute or the already known sample average. So plausible values for the company's average one-way commute time are between and minutes. Choice C.