A sample proportion is the fraction of a surveyed group with a particular habit. When students are randomly selected from a school, use that fraction to estimate the fraction of all students with the habit. In Desmos, find how much larger the school is than the sample, then scale the sample count by that factor. Don't mistake the sample count for the school count.
Hints
- Hint 1
The sample proportion compares students with the habit to all students in the sample. Put the number who reported the habit over the number surveyed. Which two numbers make that fraction?
- Hint 2
A scale factor tells you how many times larger one group is than another. Divide the school total by the sample size, then multiply the sample's habit count by that same factor.
Step-by-step
Scale the sample to the school
Step 1Find the share in the sample
A sample proportion is the fraction of sampled students with the habit. Here, that fraction is . Because the students were randomly selected from this school, use that share to estimate the schoolwide share. Scale both the habit count and the group total by the same factor.
- Step 2
Find the scale factor
The sample has students, and the school has . Type in Desmos; it shows . So the scale factor, the number that takes the sample total to the school total, is .
- Step 3
Scale the habit count
Apply the same factor to the sampled students who reported the habit. Type below the first line; Desmos shows . So the best estimate is students at the school who drink at least glasses of water each day. Choice D.