City officials want to estimate the proportion of visitors who are repeat visitors to the Rideau Canal Skateway. From previous experience they believe the proportion is not larger than 20 percent. They want to estimate the proportion to within 0.04 percentage points with 95 % confidence. The sample size they should use is

Question

Quizplus · Accepted Answer

To estimate the sample size needed for a proportion with a specific margin of error and confidence level, the formula is $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score for the confidence level (1.96 for 95%), $p$ is the estimated proportion (0.20), and $E$ is the margin of error (0.04). Plugging in the values, $n = \frac{1.96^2 \cdot 0.20 \cdot (1-0.20)}{0.04^2}$, which calculates to approximately 385.

City Officials Want to Estimate the Proportion of Visitors Who