A margin of error in percentage points gives a plausible range for a population percent: subtract it from and add it to the survey estimate. To estimate a range of counts, find each endpoint as a percent of the whole weekly customer group. Desmos can calculate those counts with % of. Don't apply the margin to the sample size.
Hints
- Hint 1
A margin of error in percentage points is a distance from the survey's percent, not a percent of that percent. Subtract the given margin from the estimate to find the lower endpoint.
- Hint 2
The percent interval estimates the whole customer group, not only the people surveyed. Find each endpoint as a percent of the weekly customer total. The lower percent gives the lower count.
Step-by-step
Find the percent interval, then convert it to counts
Step 1Find the lower percent
The survey found in favor, with a margin of error of percentage points. Percentage points are subtracted from or added to the estimated percent directly. Subtract points for the lower endpoint:
- Step 2
Find the upper percent
Add the same percentage points to get the upper endpoint:
- Step 3
Convert the lower percent to customers
The question asks about the roughly customers served per week, not the surveyed. Type in Desmos. It shows , the lower estimated number of weekly customers in favor.
- Step 4
Convert the upper percent and give the interval
Add in Desmos. It shows , the upper estimated count. So the best interval estimate is to customers per week who favor the new system. Choice C.