During the graduation ceremonies, a student who writes for the school newspaper decides to sample some of the graduating seniors for a quick survey. After the students receive their diploma and step off the stage, he will ask them the question: "Have you already been accepted to college at this point?" What sample size would be needed to provide a margin of error of about 10%?
A) n = 1
B) n = 10
C) n = 100
D) n = 1000

Question

Quizplus · Accepted Answer

To achieve a margin of error of about 10% in a proportion for a simple random sample, the sample size can be approximated using the formula for the margin of error in a proportion, which is $ME = z \sqrt{\frac{p(1-p)}{n}}$. Without knowing the exact proportion (p) or the z-score (which depends on the confidence level), a rough estimate can be made by assuming p=0.5 (which maximizes the product p(1-p)) and ignoring the z-score for simplicity. Solving for n to get a margin of error of 0.10 (or 10%) with these assumptions leads to needing a sample size around 100. This is a simplification but gives a ballpark figure that is commonly used for such estimations.

During the Graduation Ceremonies, a Student Who Writes for the School