How to find 95% confidence interval?

Question

anonymous · Answer

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anonymous · Answer

You want to find an estimate for the population proportion $\hat{p}$ with 95% confidence. You're given a sample size of $n=70$ and a measured sample proportion of $p=\dfrac{13}{70}\approx0.19$.

For this estimate, you have an interval of the form
$$p\pm Z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$$
where $p$ and $n$ denote the given info, and $Z_{\alpha/2}$ is the critical value for a $(1-\alpha)\times100\%$ significance level. In this case, since $\alpha=0.05$, you have $Z_{0.05}=1.96$.

anonymous · Answer

Thank you @SithsAndGiggles ! Helped a lot

anonymous · Answer

yw

anonymous · Answer

One thing worth mentioning: You want to find an interval for the percentages, actually, not the proportions, but converting from one to the other is a matter of scaling by 100.