A margin of error in percentage points gives a plausible range around a sample percentage. Subtract and add the margin, then use Desmos’s percent-of entry to turn both endpoints into counts of the whole population. Compare the choices with that count range. The sample size and confidence level are not percentages to apply to the town’s voters.
Hints
- Hint 1
A sample percentage describes the people surveyed and estimates the percentage for the larger group they came from. The survey size tells you how many people were asked; which number represents the whole group you need to count?
- Hint 2
A margin of error measured in percentage points moves the reported percentage down and up by the stated number of points. Don’t take that percent of the estimate. What are the low and high percentages?
- Hint 3
Convert both endpoints of the percentage range into voter counts. In Desmos, enter each endpoint as a percent of the town’s total number of registered voters. Which choice falls between the two counts?
Step-by-step
Build a plausible count range
Step 1Connect the sample to the town
The random sample of registered voters gives a Yes rate. Because those voters were sampled from the town’s registered voters, that rate estimates the Yes rate among all registered voters. Use for a townwide count, not the people surveyed.
- Step 2
Find the plausible percentage range
The margin of error is percentage points, so move points below and above . Don’t take of . Build the percent interval before converting it to a population count. Subtract for the low end:
Add for the high end:
- Step 3
Convert the range into voter counts
Type and in Desmos. It displays and . Those are the low and high plausible counts of town voters who would vote Yes.
- Step 4
Choose a count inside the range
Only is between and , so it’s a reasonable estimate for the number of town voters who would vote Yes. The confidence level describes the poll’s uncertainty; it isn’t another percent to multiply by. Choice B.