Question at-a-l
At a large high school, 300 students were selected at random and were asked in a survey about a menu change in the school cafeteria. All 300 students completed the survey. It was estimated that 38% of the students were in support of a menu change, with a margin of error of 5.5%. Which of the following is the best interpretation of the survey results?
The percent of the students at the school who support a menu change is 38%.
The percent of the students at the school who support a menu change is greater than 38%.
Plausible values of the percent of the students at the school who support a menu change are between 32.5% and 43.5%.
Plausible values of the number of the students at the school who support a menu change are between 295 and 305.
At a large high school, 300 students were selected at random and were asked in a
Easy-difficulty · SAT Math · Inference from Samples & Margin of Error — Margin of error interpretation. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice C is correct. It’s given that an estimated 38% of sampled students at the school were in support of a menu change, with a margin of error of 5.5%. It follows that the percent of the students at the school who support a menu change is 38% plus or minus 5.5%. The lower bound of this estimation is 
, or 32.5%. The upper bound of this estimation is 
, or 43.5%. Therefore, plausible values of the percent of the students at the school who support a menu change are between 32.5% and 43.5%.
Choice A is incorrect. This is the percent of the sampled students at the school who support a menu change. Choices B and D are incorrect and may result from misinterpreting the margin of error.
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