2. A school uses online report cards to promote both hard work and good behaviour of its pupils. Each card details a pupil's recent achievement and contains exactly one of three inspirational messages \(A , B\) or \(C\), chosen by the pupil's teacher.
The headteacher believes that there is an association between the pupil's gender and the inspirational message chosen. He takes a random sample of 225 pupils and examines the card for each pupil. His results are shown in Table 1.
\begin{table}[h]
| \cline { 2 - 5 }
\multicolumn{2}{c|}{} | Inspirational message | \multirow{2}{*}{Total} |
| \cline { 3 - 5 }
\multicolumn{2}{c|}{} | \(\boldsymbol { A }\) | \(\boldsymbol { B }\) | \(\boldsymbol { C }\) | |
| \multirow{2}{*}{} | Male | 25 | 37 | 45 | 107 |
| \cline { 2 - 6 } | Female | 32 | 50 | 36 | 118 |
| Total | 57 | 87 | 81 | 225 |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
Stating your hypotheses clearly, test, at the \(10 \%\) level of significance, whether or not there is evidence to support the headteacher's belief. Show your working clearly. You should state your expected frequencies correct to 2 decimal places.