Question 13·Easy·Inference from Sample Statistics and Margin of Error
A high school has 240 teachers. A random sample of 40 of these teachers was surveyed about whether they support adding an annual field trip to the curriculum. Of those surveyed, 75% responded that they support the field trip.
Based on this survey, which of the following is the best estimate of the total number of teachers at the high school who support adding the annual field trip?
For SAT questions that use a random sample to estimate a total, first interpret the sample result as a proportion or percentage. Assume this proportion holds for the entire population (unless the question says otherwise), then multiply that proportion by the total population size. Use simple forms like decimals (e.g., 0.75) or easy fractions (e.g., 3/4) to do the multiplication quickly, and finally choose the answer choice that matches your computed estimate.
Hints
Think about what 75% means
If 75% of the 40 teachers in the sample support the field trip, how many teachers is that out of 40? What fraction of the sample does that represent?
Use a proportion or a percentage
Once you know that 75% (or an equivalent fraction) of the sample supports the trip, assume roughly the same percentage for all 240 teachers. How can you apply that same percentage to 240?
Set up the calculation
Express 75% as either a decimal or a simple fraction, then multiply that by 240. Write this multiplication down before you calculate the result.
Desmos Guide
Use Desmos to calculate the estimate
In Desmos, type either 0.75*240 or (3/4)*240 and press Enter. The output shown by Desmos is the estimated number of teachers who support the field trip; match that number to the closest answer choice.
Step-by-step Explanation
Use the sample percentage as the estimate
The survey found that 75% of the sampled teachers support the field trip. On the SAT, when a question asks for an estimate for the whole group based on a random sample, you usually apply the sample percentage to the entire population.
So we will assume that about 75% of all 240 teachers support the field trip.
Write 75% as a decimal or fraction
To apply 75% to 240 teachers, rewrite 75% in a more useful form:
- As a decimal:
- As a fraction:
Now we want to calculate either or .
Multiply the total number of teachers by the percentage
Now compute the estimated number of teachers who support the trip:
So the best estimate of the number of teachers who support adding the annual field trip is 180, which corresponds to choice C.