For survey estimates with a margin of error, make a plausible interval for each population percentage by subtracting and adding the stated number of percentage points. Then compare the intervals' closest ends. If they don't overlap, the estimates support a comparison between the populations. The trap is turning that supported conclusion into a guarantee.
Hints
- Hint 1
A margin of error of percentage points means subtract from the reported percent for one end of its plausible interval and add for the other. What interval does that give State X?
- Hint 2
Two intervals overlap if they share at least one value. Compare the top of X's interval with the bottom of Y's interval: could a percentage plausible for X reach one plausible for Y?
Step-by-step
Compare the plausible intervals
Step 1Find State X's plausible interval
No Desmos needed. Each endpoint takes one addition or subtraction. A margin of error gives a plausible range around an estimate. Percentage points means add and subtract directly, not of . Subtract for State X's low end:
Add for its high end:
- Step 2
Find State Y's plausible interval
Apply the same -point margin to State Y's estimate. Subtract for its low end:
Add for its high end:
- Step 3
Compare the closest ends
The closest ends are X's high end, , and Y's low end, :
Separated plausible intervals support a comparison between the population percentages. The intervals aren't guarantees, so the reported estimates support a higher percentage of registered voters in State Y than in State X, but don't prove it with certainty. Choice D.