A reported percent with a margin of error gives a range for the whole population, not one fixed count. Percentage points are added to and subtracted from the reported percent directly. Build the percent interval first, then turn its endpoints into population counts. Type each endpoint as % of the population in Desmos, and check which choice falls outside the count interval.
Hints
- Hint 1
A margin of error tells you how far the population percentage may be from the reported estimate. Since the error is in percentage points, subtract and add it directly; don't take a percent of the reported percent.
- Hint 2
The surveyed voters are a sample, the smaller group measured. The question asks about all registered voters in the county. Which number should you use when you turn your percent endpoints into voter counts?
- Hint 3
A confidence interval has a lower and an upper endpoint. Type each percent endpoint as
% of 52000in Desmos, then look for the choice outside those two counts.
Step-by-step
Convert the percent interval to a count interval
Step 1Find the lower percent endpoint
The 4.8 percentage points are subtracted directly from ; they aren't of . Subtract the margin to find the lower endpoint, the lowest percent in the reported interval:
- Step 2
Find the upper percent endpoint
Add the same margin to find the upper endpoint, the highest percent in the interval:
- Step 3
Turn the lower percent into a voter count
Use all 52,000 registered voters, not the people in the sample. Type in Desmos. It prints , the lowest count in the reported interval.
- Step 4
Turn the upper percent into a voter count
Use the upper percent with the same county population. Add in Desmos; it prints . That's the highest count in the reported interval.
- Step 5
Check which count is outside
Counts from through are within the reported interval. , , and fit, but is above the upper endpoint. So registered voters is the count not within the interval. Choice D.