A survey’s margin of error gives a plausible range around its estimated percentage. For the greatest reasonable count, add the margin in percentage points, then use Desmos to take that upper percentage of the entire school. Don’t take the percentage of the surveyed group: the sample estimates a rate for the whole school.
Hints
- Hint 1
A percentage point is a direct difference between percentages: from to is percentage points. To find the greatest reasonable count, would you add or subtract the margin?
- Hint 2
The population is the whole group the survey estimates. Use all the students at the school as the base for your percent calculation, not just the students who were surveyed.
- Hint 3
An estimated count may end in a fraction even though students are counted in whole numbers. After Desmos gives you the upper-end estimate, round it to the nearest whole student.
Step-by-step
Use the upper end of the survey estimate
Step 1Find the greatest plausible percentage
The margin of error is percentage points above or below the survey’s . For the greatest count, add points directly, rather than taking of :
Pick the upper percentage before turning it into a count.
- Step 2
Estimate the count for the whole school
The population is all students. Type in Desmos; it prints . That’s the upper-end estimate for the school. Using the surveyed students instead would estimate a count for the sample, not the school.
- Step 3
Give a whole-student count
Students are counted in whole numbers, so round to the nearest whole student, . The greatest number reasonably expected to have a part-time job is Jefferson High School students. Choice D.