A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 90% reliability, how many students would need to be sampled?
A) 728
B) 176
C) 443
D) 22

Question

Quizplus · Accepted Answer

To estimate the proportion with a margin of error of 3% and 90% confidence, the sample size can be calculated using the formula for sample size in proportion estimation: n = (Z^2 * p * (1-p)) / E^2. Here, Z is the Z-score for 90% confidence (approximately 1.645), p is the sample proportion (118/200 = 0.59), and E is the margin of error (0.03). Plugging in these values gives a sample size of approximately 728.

A University Dean Is Interested in Determining the Proportion of Students