A survey table gives a sample proportion, the share of respondents who chose one answer. That share estimates the larger group's share. For the greatest plausible count, add the margin of error to the survey percent, then use Desmos to take that percent of the larger group. A margin stated in percentage points adds directly to the percent; it isn't a percent of the respondent count.
Hints
- Hint 1
The sample proportion for No compares people who answered No with everyone surveyed. Which two counts in the table make that fraction?
- Hint 2
A margin of error in percentage points moves the estimated percent up or down by that many points. For the greatest plausible number of No voters, which direction do you need?
- Hint 3
Once you have the upper plausible percent, apply it to the expected voters, not to the people surveyed. In Desmos, you can type that percent followed by
% ofand the voter count.
Step-by-step
Use the upper margin-of-error endpoint
Step 1Build the No fraction from the table
The No row has 576 respondents, and the Total row has 1,200. So the sample proportion, the share of surveyed people who said No, is . Don't use 25,000 as the denominator: those expected voters weren't the people surveyed.
- Step 2
Convert the fraction to a percent
Type in Desmos. It returns , meaning 48 out of every 100, or , of the survey respondents said No.
- Step 3
Choose the upper plausible percent
The margin of error is 3 percentage points, so add 3 points directly to the estimate for No: . Don't take of ; that would be a percent change, not 3 percentage points. For the greatest plausible count, use the upper percent.
- Step 4
Apply that percent to the expected voters
Type in Desmos. It returns . The percent applies to the 25,000 expected voters, so the greatest number who could reasonably be expected to vote No is . Choice D.