A poll’s margin of error gives a plausible interval around a sample percentage, not an exact population percentage. A simple random sample can support an estimate for the population it was drawn from. Subtract and add the stated number of percentage points, then check that the conclusion names that same population. The right interval for a different group is still the wrong conclusion.
Hints
- Hint 1
A simple random sample uses chance to pick people from a particular group. Its result can estimate the percentage for that whole group, but not for people who could never have been picked. Who could have been selected for this poll?
- Hint 2
A margin of error of 3 percentage points means moving 3 points below and 3 points above the sample percentage. It does not mean finding 3% of that percentage. What are the two endpoints?
- Hint 3
A sample percentage is an estimate for a population, not a promise that the population percentage is exactly the same. What kind of conclusion can a margin of error support, and what kind can it rule out?
Step-by-step
Find the interval and match the population
Step 1Identify whom the poll can describe
No Desmos needed. Each endpoint takes one arithmetic operation; the key is whom the poll can describe. A simple random sample picks people by chance from a group. Here, that group is registered voters in the state, so the poll can estimate their support, not the support of all adults in the nation.
- Step 2
Find the lower endpoint
The margin of error tells you how many percentage points to move from the sample result. Subtract points from for the lower end:
- Step 3
Find the upper endpoint
Add the same percentage points to find the upper end:
- Step 4
State what the interval estimates
A plausible interval gives a reasonable range, not an exact result. The interval estimates the percentage of all registered voters in the state, the group the sample came from. So between and of those voters support the bond measure. Choice D.