4. A hospital administrator is assessing staffing needs for its Accident and Emergency Department at different times of day. The administrator already has data on the number of admissions at different times of day but needs to know if the proportion of the cases that are serious remains constant.
Staff are asked to assess whether each person arriving at Accident and Emergency has a "minor" or "serious" problem and the results for three different time periods are shown below.
| \cline { 2 - 3 }
\multicolumn{1}{c|}{} | Minor | Serious |
| 8 a.m. - 6 p.m. | 45 | 11 |
| 6 p.m. - 2 a.m. | 49 | 22 |
| 2 a.m. - 8 a.m. | 14 | 7 |
Stating your hypotheses clearly, test at the \(5 \%\) level of significance whether or not there is evidence of the proportion of serious injuries being different at different times of day.
(11 marks)