A survey that gives a randomly selected sample and asks for a count in the whole group calls for a sample proportion: the number with the preference divided by the number surveyed. Use that fraction to estimate the share of the larger group, then multiply by its total size. Don't use the whole-group size as the denominator when finding the sample fraction.
Hints
- Hint 1
A sample proportion is the part of the sample with a preference divided by everyone in the sample. Which number counts students who prefer online classes, and which number counts all students surveyed?
- Hint 2
Because the students were randomly selected, their share is a reasonable estimate for the whole school. Once you find that share, apply it to the school’s total, not to the sample size again.
Step-by-step
Use the sample proportion
Step 1Write the sample’s part-to-whole fraction
A sample proportion is the part of the sample with a preference divided by everyone sampled. The students who prefer online classes are part of the surveyed, so write:
Use as the whole here, because the came from the sample, not from all students.
- Step 2
Find the share to estimate
Type in Desmos. It shows , or . Because the sample was randomly selected, use that share to estimate the fraction of the whole school that prefers online classes.
- Step 3
Estimate the count for the whole school
Apply the estimated share to all students: type on the next Desmos line. It shows . So the best estimate is students who prefer online classes. Find the share in the sample, then apply it to the whole population. Choice C.