5. The manager of a hockey team studies last season's results and puts forward the theory that the number of goals scored per match by her team can be modelled by a Poisson distribution with mean 2.0. The number of goals scored during the season are summarised below.
| Goals scored | 0 | 1 | 2 | 3 | 4 or more |
| Frequency | 6 | 11 | 15 | 10 | 8 |
- State suitable hypotheses to carry out a goodness of fit test.
- Carry out a \(\chi ^ { 2 }\) goodness of fit test on this data set, using a \(5 \%\) level of significance and draw a conclusion in context.