8 The random variable \(R\) has the distribution \(\mathrm { B } ( 14 , p )\). A test is carried out at the \(\alpha \%\) significance level of the null hypothesis \(\mathrm { H } _ { 0 } : p = 0.25\), against \(\mathrm { H } _ { 1 } : p > 0.25\).
- Given that \(\alpha\) is as close to 5 as possible, find the probability of a Type II error when the true value of \(p\) is 0.4 .
- State what happens to the probability of a Type II error as
(a) \(p\) increases from 0.4,
(b) \(\alpha\) increases, giving a reason.