Which of the following is the minimum sample size that could be used to guarantee that the margin of error for a confidence interval for a proportion is no more than 0.025?
A) 100
B) 400
C) 1600
D) 2500

Question

Quizplus · Accepted Answer

The minimum sample size needed to guarantee a margin of error (E) no more than 0.025 for a confidence interval for a proportion can be calculated using the formula for the margin of error: $E = Z \sqrt{\frac{p(1-p)}{n}}$, where $Z$ is the Z-score corresponding to the desired confidence level, $p$ is the estimated proportion, and $n$ is the sample size. Without knowing the confidence level and assuming the worst-case scenario for $p$ (which maximizes the product $p(1-p)$) at $p = 0.5$, we simplify the formula to find $n$. For a maximum $E$ of 0.025 and using a Z-score for a common confidence level (e.g., 1.96 for 95% confidence), the calculation suggests a larger sample size is better for reducing the margin of error. Among the given options, 1600 is the minimum sample size that would typically be sufficient to ensure a margin of error no more than 0.025, even without specifying the confidence level, because the formula implies that a larger $n$ results in a smaller $E$, and 1600 is a common answer for such calculations with standard assumptions.

Which of the Following Is the Minimum Sample Size That