Question

Statistics Help: assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level
n=600, x=240, 90% confidence

Answer 1

A \((1-\alpha)\times100\%\) confidence interval for a proportion has the form
\[\left(\hat p-Z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}},~\hat p+Z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\right)\]
where \(\hat p\) is the estimated proportion, \(Z_{\alpha/2}\) is the critical value used for the significance level \(\alpha\), and \(n\) is the sample size.

The error margin is the second term,
\[MOE=Z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\]