2 Syd, a snooker player, believes that the outcome of any frame of snooker in which he plays may be influenced by the time of day that the frame takes place.
The results of 100 randomly selected frames of snooker, played by Syd, are recorded below.
| \cline { 2 - 4 }
\multicolumn{1}{c|}{} | Afternoon | Evening | Total |
| Win | 30 | 24 | 54 |
| Lose | 18 | 28 | 46 |
| Total | 48 | 52 | 100 |
Use a \(\chi ^ { 2 }\) test, at the \(5 \%\) level of significance, to test Syd's belief.
(10 marks)