A random sample can support an estimate for the larger population, but it cannot give the exact population percentage. A margin of error gives a plausible range: subtract it from the estimate for the low end, then add it for the high end. For a percent estimate, use percentage points, not a percentage of the estimate, and look for a conclusion that allows uncertainty.
Hints
- Hint 1
A random sample chooses students by chance rather than selecting them for their texting habits. So the survey can support an estimate for all high school students, even though most weren't surveyed.
- Hint 2
A margin of error of puts the population percentage plausibly 4 percentage points below or above the estimate. What do you get by subtracting and adding to ?
Step-by-step
Build the plausible percent range
Step 1Connect the sample to the population
A random sample picks students by chance, so the students can support an estimate for the population, meaning all high school students. You don't need to survey everyone to draw a reasonable conclusion.
- Step 2
Translate the margin of error
The margin of error tells you how far the population percentage could reasonably be from the estimate. Here it means 4 percentage points on either side, so write the endpoints as and . Don't take of ; that would treat the margin as a percent change.
- Step 3
Find the lower endpoint
Type in Desmos. It shows , so the lower endpoint is .
- Step 4
Find the upper endpoint and choose the conclusion
Keep the first line and type . Desmos shows , so the plausible range for the percentage of all high school students who send at least text messages per day is to . The estimate doesn't promise an exact percentage. Choice B.