A population proportion is to be estimated. Estimate the minimum sample size needed to achieve the specified margin of error with a 95% degree of confidence.
-$E = 0.012$
A)6944
B)3472
C)13,888
D)83

Question

Quizplus · Accepted Answer

To achieve a specified margin of error $E = 0.012$ with a 95% degree of confidence, where the standard normal value $Z = 1.96$ (for 95% confidence) and assuming the worst-case scenario for population proportion $p = 0.5$ (which maximizes the product $p(1-p)$ and thus the sample size), the formula for the minimum sample size $n$ is $n = \left(\frac{Z}{E}\right)^2 p(1-p)$. Substituting the values, $n = \left(\frac{1.96}{0.012}\right)^2 \times 0.5 \times 0.5 = 6944$.

A Population Proportion Is to Be Estimated E=0.012E = 0.012E=0.012 A)6944 B)3472 C)13,888 D)83

A Population Proportion Is to Be Estimated $E = 0.012$ A)6944
B)3472
C)13,888
D)83