Question

In a trial of 136 patients, 34 claimed to experience head aches from a test medicine.
a) what is the 95% confidence interval in ascending order?
b)Interpret the confidence interval.

Answer 1

You have an estimated proportion of \(\hat{p}=\dfrac{34}{136}=0.25\). The \((1-\alpha)\times100\%\) confidence interval for a proportion is given by
\[\left(\hat{p}-Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},~\hat{p}+Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)\]
where \(Z_{\alpha/2}=Z_{0.025}=1.96\). The sample size is \(n=136\).