A margin of error in percentage points puts a plausible population percent the stated number of points below and above a sample percent. Find those two endpoints first, then use Desmos’s % of to turn each into a count of the whole population. Using the sample estimate as an endpoint shifts the range instead of placing it in the middle.
Hints
- Hint 1
A sample proportion describes the surveyed households. Because they were chosen at random, it can estimate the recycling proportion among all Greenville households. Which reported percent is the center of that estimate?
- Hint 2
A margin of error measured in percentage points is added to and subtracted from the reported percent directly. It isn’t a percent of that percent. What are the low and high percent endpoints?
- Hint 3
To turn a percent into a count, take that percent of the whole population, not of the sample. Which two percent endpoints should you apply to the number of Greenville households?
Step-by-step
Find the percent interval, then convert to counts
Step 1Find the plausible percent range
Because the households were sampled at random, their recycling rate estimates the rate for all Greenville households. A confidence interval is a plausible range for that population rate. The percentage points means subtract and add points directly, not take of :
- Step 2
Convert the lower percent to a count
The lower endpoint is . For the lower household count, take that percent of the population, not of the sampled households. Type in Desmos; it prints .
- Step 3
Convert the upper percent and give the range
Keep the first line and add . Desmos prints , the upper household count. So the estimated range is to Greenville households that recycle at least once a week. Choice B.