A margin of error turns a survey estimate into a plausible range for the whole population, not an exact prediction. Because the margin is in percentage points, subtract it from and add it to the estimated percent directly; don't take it as a percent of that percent. Then look for a claim about the whole population, rather than a count of people surveyed.
Hints
- Hint 1
A sample is the group surveyed; the population is every adult resident the council wants to describe. Does knowing how many people were surveyed tell you how many adults live in the whole city?
- Hint 2
A margin of error gives a distance from the estimate in both directions. Because the margin is in percentage points, what do you get by subtracting points directly from ?
- Hint 3
Add the same percentage points to find the upper end. The conclusion should describe a plausible percentage of all adult residents, not an exact percentage or a count of surveyed people.
Step-by-step
Find and interpret the percent range
Step 1Separate the sample from the population
No Desmos needed. The given estimate and margin require only one subtraction and one addition. A sample is the adults surveyed; the population is all adult residents. The estimate comes from the sample, so it is not an exact promise about the population.
- Step 2
Find the lower end
The margin of error is percentage points below and above the estimate, not of . Subtract points for the lower end:
- Step 3
Find the upper end
Add the same percentage points for the upper end:
- Step 4
Interpret the range
The margin of error gives a plausible range for the population percentage, not an exact prediction or a count of surveyed people. So between and of all adult residents will likely vote in favor. Choice C.