Question 46·Easy·Inference from Sample Statistics and Margin of Error

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A survey of 200 students at a high school asked whether they plan to attend a four-year college. Of those surveyed, 135 students said they plan to attend a four-year college. The school enrolls 1,050 students in total. Based on the survey results, about how many students at the school would be expected to plan to attend a four-year college?

A survey question that asks for an expected count uses a sample proportion: the share of surveyed people with the trait. Find that share by dividing the number who said yes by the number surveyed, then use Desmos to multiply it by the full population. Don't multiply by the sample size again; that only takes a share of the students already surveyed.

Hints

Hint 1
A sample proportion compares the students who said yes with everyone surveyed. Which given number is the yes count, and which is the total surveyed?
Hint 2
The survey's share is an estimate for the school. To turn a share into an expected number of students, multiply it by the school's total enrollment, not by the number surveyed.

Step-by-step

Scale the survey share to the school
Step 1
Find the share who said yes
The sample proportion is the fraction of surveyed students who said yes, so it's $\frac{135}{200}$ . Type $135/200$ in Desmos. It prints $0.675$ , meaning 67.5% of the surveyed students said yes.
Step 2
Estimate the count for the whole school
Use the survey share to estimate the share of all $1{,}050$ students: multiply by the whole school, not by the $200$ surveyed students again. Keep the first Desmos line and type $0.675\times1050$ . Desmos prints $708.75$ , so the expected count is about $710$ students. Choice C.

Question 46·Easy·Inference from Sample Statistics and Margin of Error

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