A survey’s margin of error tells you how far the sample estimate could reasonably be from the percentage for the whole group. First check that the random sample came from the group named in the conclusion. Then use Desmos to subtract and add the margin in percentage points. The trap is treating a sample percentage as an exact population percentage.
Hints
- Hint 1
A random sample uses chance to choose people from a larger group. Since the survey chose registered voters, its result can estimate the support rate for all registered voters, even though it didn’t ask everyone.
- Hint 2
A margin of error gives the distance from an estimate to either end of a plausible range. For a percent estimate, subtract the margin as percentage points to find the lower end.
- Hint 3
Find the upper end by adding the same margin to the sample percentage. The resulting range describes what’s plausible for all registered voters; it doesn’t give their exact support rate.
Step-by-step
Build a margin-of-error interval
Step 1Connect the sample to all registered voters
The people form a random sample: a smaller group chosen by chance from registered voters. So their support rate can estimate the rate for all registered voters, but it doesn’t establish that rate exactly.
- Step 2
Find the lower end
The margin of error tells you how far the population percentage could reasonably be from the sample estimate. Subtract and add the margin as percentage points, rather than taking of . For the lower end, type in Desmos. It shows , meaning .
- Step 3
Find the upper end and read the interval
Type on the next Desmos line. It shows , meaning . So the reasonable range for the percentage of all registered voters who support the law is to . That’s an estimate, not a guarantee. Choice B.