Find the \((1-\alpha) 100 \%\) confidence interval \(\hat{I_{\alpha}^{p}}\).

(a) \(k=17\) positive and \(l=25\) negative. \(\alpha=0.05\).

(b) You have heard that Coca and Pepsi have an equal share in the Cola market at your university, and decide to investigate if this is true. Your investigations find 46 Pepsi drinkers and 54 Coca drinkers. Give a 90\% confidence interval for \(\pi\), the proportion of Coca drinkers in your entire university.