A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary.
-Sample size $= 3025$, sample proportion $= 0.89$
A) $0.8786

Question

A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary.
-Sample size $= 3025$, sample proportion $= 0.89$
A) $0.8786 < p < 0.9014$
B) $0.8898 < p < 0.8902$
C) $0.8718 < p < 0.8898$
D) $0.882 < p < 0.898$

Quizplus · Accepted Answer

The 95% confidence interval for a population proportion can be calculated using the formula: $\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $n$ is the sample size, and $Z_{\alpha/2}$ is the Z-score for a 95% confidence level (approximately 1.96). Plugging in the given values: $0.89 \pm 1.96 \sqrt{\frac{0.89(1-0.89)}{3025}}$, we get the interval $0.8786 < p < 0.9014$.

A Population Proportion Is to Be Estimated from the Sample =3025= 3025=3025

A Population Proportion Is to Be Estimated from the Sample $= 3025$