A random survey with a margin of error asks you to judge which population percentages are plausible. Subtract and add the margin in percentage points to find the range around the reported estimate. The sample can estimate the percentage for the population it came from, but it cannot establish an exact value. A percentage outside the range is unexpected, not impossible.
Hints
- Hint 1
The sample percentage describes the people surveyed; it estimates the percentage for all registered voters. Because it is an estimate, it need not equal the population percentage exactly. Which number does the article report as that estimate?
- Hint 2
A margin of error measured in percentage points is subtracted from and added to the reported percentage. What lower and upper percentages do you get by moving 3 points in each direction?
- Hint 3
A plausible interval is the range of population percentages reasonably consistent with the survey. Its endpoints are not hard limits. How should you describe a claimed percentage that lies outside the range?
Step-by-step
Build the plausible range
Step 1Identify what the survey estimates
No Desmos needed. The article gives the estimate, and each endpoint takes one operation. The 680 voters who said yes are part of a random sample of 1,250 registered voters. So the article's about 54% estimates support among all registered voters; it does not give their exact percentage.
- Step 2
Find the lower end
The margin of error is a distance of 3 percentage points from the reported 54%, not 3% of 54%. Subtract to find the lower end:
- Step 3
Find the upper end
Add the same 3 percentage points for the upper end:
So the plausible interval, the range reasonably supported by the survey, is 51% to 57% of all registered voters.
- Step 4
Judge the claim against the range
The claimed 59% is above the upper end, 57%. So it would be unexpected for 59% of all registered voters to support the policy. Outside the margin of error means unexpected, not impossible. Choice D.