Question 16·Easy·Inference from Sample Statistics and Margin of Error
A high school has 800 students. A randomly selected sample of 40 students shows that 12 of them prefer taking classes online rather than in person.
Based on the sample, what is the best estimate of the number of students in the entire school who prefer taking classes online?
For this type of SAT question, always start by finding the sample proportion: divide the number with the trait by the total sample size (here, ). Then assume this proportion represents the whole population and multiply that proportion by the total population size (here, 800). Work with simple forms (like or ) to make the multiplication quick, and double-check that your final estimate is reasonable compared with the total (it should be a fraction of 800, not much bigger or much smaller than expected from the sample).
Hints
Use the sample to find a proportion
First, think about what fraction of the sample prefers online classes. How can you write "12 out of 40" as a fraction or decimal?
Connect the sample to the population
Once you know what fraction of the sample prefers online classes, assume the same fraction applies to all 800 students. What operation will you use to scale up from the sample to the whole school?
Do the scaling carefully
Take the proportion from the sample and multiply it by 800. Be careful with your multiplication and watch place values if you are using decimals.
Desmos Guide
Compute the estimated number using the sample proportion
In Desmos, type the expression (12/40)*800 and look at the numeric result it gives. That value is the estimated number of students in the school who prefer online classes.
Step-by-step Explanation
Find the sample proportion
From the sample, 12 out of 40 students prefer online classes.
Write this as a fraction:
Simplify or convert this fraction to understand what part of the students this represents.
Simplify or interpret the proportion
Simplify by dividing numerator and denominator by 4:
So, the sample suggests that about of students prefer online classes.
Apply the proportion to the whole school
Assume the same applies to all 800 students in the school.
Multiply the total number of students by this proportion:
So, the best estimate of the number of students in the entire school who prefer taking classes online is 240.