A margin of error turns each sample mean into a plausible range for the whole university’s mean. To compare two groups quickly, use Desmos to check whether the highest plausible mean for the group with the lower estimate is still below the other group’s lowest plausible mean. Separate ranges help you judge the comparison, but don’t treat sample estimates as exact population values.
Hints
- Hint 1
A margin of error gives a reasonable distance above and below a sample mean for the whole university’s mean. Which school’s highest plausible mean should you compare with the other school’s lowest?
- Hint 2
If the plausible ranges for the two means don’t touch, even their closest values keep the same order. What are the closest endpoints for these two sample means?
Step-by-step
Compare the closest plausible means
Step 1Choose the endpoints to compare
A margin of error tells you how far a population mean could reasonably be from its sample mean. Since A’s estimate is lower, make the toughest comparison: A’s highest plausible mean against B’s lowest plausible mean. Compare with .
- Step 2
Find A’s upper endpoint
Type in Desmos. It shows , so A’s highest plausible population mean is hours.
- Step 3
Find B’s lower endpoint
Keep the first line and type . Desmos shows , so B’s lowest plausible population mean is hours.
- Step 4
State what the comparison supports
Even at these closest endpoints, , so the plausible ranges for the two means don’t overlap. The random samples provide evidence that University B’s mean daily study time is greater than University A’s. They don’t prove the exact population means. Choice B.