A polling organization conducts a poll by making a random survey and is willing to accept a margin of error of 4% at a confidence level of 95%. What should the sample size be?
A)625
B)750
C)380
D)500

Question

Quizplus · Accepted Answer

The sample size for a given margin of error (E) at a certain confidence level (Z) can be calculated using the formula $n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)$, where $p$ is the population proportion (assumed to be 0.5 for maximum sample size), and $Z$ is the Z-score corresponding to the confidence level (approximately 1.96 for 95% confidence). Plugging in the values, $n = \left(\frac{1.96^2 \cdot 0.5 \cdot (1-0.5)}{0.04^2}\right) = 600.25$, which rounds up to the nearest whole number, but since none of the options exactly match this calculation and 625 is the closest option that would ensure the margin of error and confidence level are met, option A is selected.

A Polling Organization Conducts a Poll by Making a Random