2. A test statistic has a distribution \(\mathrm { B } ( 25 , p )\).
Given that
$$\mathrm { H } _ { 0 } : p = 0.5 \quad \mathrm { H } _ { 1 } : p \neq 0.5$$
- find the critical region for the test statistic such that the probability in each tail is as close as possible to \(2.5 \%\).
- State the probability of incorrectly rejecting \(\mathrm { H } _ { 0 }\) using this critical region.