The National Center for Education would like to estimate the proportion of students who defaulted on their student loans for the state of Arizona. The total sample size needed to construct a 95% confidence interval for the proportion of student loans in default with a margin of error equal to 4% is -------.
A)336
B)601
C)416
D)455

Question

Quizplus · Accepted Answer

The sample size needed for estimating a proportion with a specified margin of error (E) at a certain confidence level can be calculated using the formula: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (for 95% confidence, $Z = 1.96$), $p$ is the estimated proportion (if unknown, 0.5 is used for maximum sample size), and $E$ is the margin of error. Plugging the values into the formula: $n = \frac{1.96^2 \cdot 0.5 \cdot (1-0.5)}{0.04^2} = 600.25$, which rounds up to 601.

The National Center for Education Would Like to Estimate the Proportion