A survey’s margin of error turns a sample percentage into a range of plausible percentages for the population. Check that the sample was randomly drawn from the group the question asks about. Then subtract the margin for the lower endpoint and add it for the upper endpoint. Don’t treat the sample percentage as an exact result for everyone.
Hints
- Hint 1
A sample is the group surveyed; the population is the larger group the survey aims to describe. A random sample can support an estimate for the group it came from. Who could have been selected for this survey?
- Hint 2
A margin of error gives a distance on both sides of an estimate. Treat it as percentage points: subtract it from the sample percentage for the low end, then add it for the high end.
Step-by-step
Build a plausible population interval
Step 1Identify whom the estimate describes
The sample is the voters interviewed; the population is all registered voters in the state. Because the sample was randomly drawn from that group, its support rate can estimate the statewide rate. It doesn't establish that rate exactly.
- Step 2
Put the margin on both sides of the estimate
A margin of error tells you how far above or below the sample estimate the population percentage may plausibly be. Here, means percentage points, not of . Subtract and add the margin to make the two endpoints. So the interval runs from to .
- Step 3
Find the lower endpoint
Type in Desmos. It shows , so the lower plausible percentage is .
- Step 4
Find the upper endpoint and interpret the interval
Type on the next Desmos line. It shows , the upper endpoint. So it is plausible that between and of all registered voters in the state support the bond measure. The interval describes what is plausible, not what is guaranteed. Choice C.