A margin of error gives a plausible range around a sample estimate, not an exact population percent. With two polls, subtract and add each city’s margin in percentage points, then check whether the ranges overlap. The gap between the sample percentages doesn’t guarantee a gap between the actual population percentages.
Hints
- Hint 1
A margin of error is added to and subtracted from the sample percent, in percentage points, to form a plausible range for the citywide percent. What are City X’s two endpoints?
- Hint 2
An overlap means a percent falls in both plausible ranges. Find City Y’s endpoints, then check whether one percent could fit both cities instead of treating the sample gap as certain.
Step-by-step
Compare the two plausible ranges
Step 1Find City X’s range
The margin of error tells you how many percentage points to subtract from and add to the sample estimate. For City X, type and in Desmos. It shows and , so the plausible population range is to .
- Step 2
Find City Y’s range
City Y has its own margin, so don’t reuse City X’s. Add and in Desmos. It shows and , giving City Y a plausible population range of to .
- Step 3
Check what the ranges share
The two intervals, or plausible ranges, overlap from to . For example, fits both. So both cities could have of adults supporting the ordinance, even though their sample results differ. Overlap makes equal population percents possible, not certain. Choice D.