Two surveys can report different percentages without conflicting. A margin of error gives a plausible range around each sample estimate. Type each estimate minus and plus its margin into Desmos, then check whether the ranges overlap. Overlapping ranges mean the results are compatible, not that either estimate is exact. A smaller margin means a more precise estimate.
Hints
- Hint 1
A margin of error of percentage points means subtract and add to the reported percentage. It does not mean take of that percentage. What are Survey A's two endpoints?
- Hint 2
A plausible interval runs from the estimate minus its margin to the estimate plus its margin. Find Survey B's endpoints the same way, then ask whether its interval shares any percentages with Survey A's.
- Hint 3
A smaller margin of error gives a more precise estimate. Compare the two margins separately from the estimates themselves: a higher reported percentage does not make a survey more precise.
Step-by-step
Compare the plausible ranges
Step 1Find Survey A's range
A margin of error in percentage points is subtracted from and added to the reported percentage. Type and in Desmos. It shows and , so Survey A's plausible range for city residents who favor the proposal is to .
- Step 2
Find Survey B's range
Use Survey B's own margin to find its plausible interval. Add and in Desmos. It shows and , so Survey B's range is to .
- Step 3
Compare precision
A smaller margin of error gives a narrower range, so it makes the estimate more precise. Survey B's -point margin is smaller than Survey A's -point margin. So B is more precise; its higher reported percentage isn't the reason.
- Step 4
Check whether the results conflict
The two plausible intervals share through . That overlap means both surveys could fit the same percentage for all city residents; the gap between their estimates doesn't prove a conflict. Survey B is more precise, and the results are compatible. Choice A.