A university conducted two surveys, Survey A and Survey B, to estimate the proportion of its students who use the campus library regularly. Survey A had a sample size of 500 students, and Survey B had a sample size of 1,200 students. Both surveys used the same methodology and were conducted on the same student population.
Which of the following statements about the margins of error for Survey A and Survey B must be true?
The margin of error for Survey A is smaller than the margin of error for Survey B.
The margin of error for Survey B is smaller than the margin of error for Survey A.
The margins of error for Survey A and Survey B are approximately equal, assuming the proportions are similar.
The margins of error cannot be compared without knowing the exact percentages of students who use the library in each survey.
