A population proportion is to be estimated from the sample described. Approximate the margin of error for the 95% confidence interval. Round your answer to four decimal places, if necessary.
-Sample size $= 1600$, sample proportion $= 0.93$
A) $0.0128$
B) $0.0003$
C) $0.009$
D) $0.0064$

Question

Quizplus · Accepted Answer

The margin of error for a 95% confidence interval for a population proportion is calculated using the formula $ME = Z \times \sqrt{\frac{p(1-p)}{n}}$, where $Z$ is the Z-score for the desired confidence level (approximately 1.96 for 95%), $p$ is the sample proportion, and $n$ is the sample size. Substituting the given values, $ME = 1.96 \times \sqrt{\frac{0.93(1-0.93)}{1600}} = 1.96 \times \sqrt{\frac{0.0651}{1600}} = 1.96 \times 0.0064 = 0.012544$, which rounds to $0.0128$.

A Population Proportion Is to Be Estimated from the Sample =1600= 1600=1600

A Population Proportion Is to Be Estimated from the Sample $= 1600$