You plan to determine an approximate 95% confidence interval for a population proportion; you plan to use a conservative margin of error of 5%. How large a sample size do you need?
A) 100
B) 400
C) 2500
D) None of the above

Question

Quizplus · Accepted Answer

To determine a sample size for a 95% confidence interval with a margin of error of 5% (or 0.05) using a conservative estimate, we use the formula for the sample size of a proportion, which is $n = \left(\frac{Z^2 \cdot p \cdot (1-p)}{E^2}\right)$. For a conservative estimate, we use $p = 0.5$ because this maximizes the product $p(1-p)$, giving the largest sample size. With $Z = 1.96$ for a 95% confidence level and $E = 0.05$, the calculation is $n = \left(\frac{1.96^2 \cdot 0.5 \cdot 0.5}{0.05^2}\right) = 384.16$. Rounding up, we need at least 385 participants, which makes option B (400) the closest and correct choice.

You Plan to Determine an Approximate 95% Confidence Interval for a Population