A random sample of 16 subjects was taken from a target population to study the prevalence of a disease \(p\). It turned out that six of them were diseased.

(a) Estimate the disease prevalence \(p\).

(b) Use the asymptotic procedure to test

\[\begin{equation*}H_{0}: p=0.3 \quad \text { vs. } \quad H_{a}: p>0.3 \tag{2.48}\end{equation*}\]

(c) Change \(H_{a}: p>0.3\) in (2.48) to \(H_{a}: p<0.3\) and repeat (b).

(d) Change \(H_{a}: p>0.3\) in (2.48) to \(H_{a}: p eq 0.3\) and repeat (b).