5. The number of goals scored by a football team is recorded for 100 games. The results are summarised in Table 1 below.
\begin{table}[h]
| Number of goals | Frequency |
| 0 | 40 |
| 1 | 33 |
| 2 | 14 |
| 3 | 8 |
| 4 | 5 |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
- Calculate the mean number of goals scored per game.
The manager claimed that the number of goals scored per match follows a Poisson distribution. He used the answer in part (a) to calculate the expected frequencies given in Table 2.
\begin{table}[h]
| Number of goals | Expected Frequency |
| 0 | 34.994 |
| 1 | \(r\) |
| 2 | \(s\) |
| 3 | 6.752 |
| \(\geqslant 4\) | 2.221 |
\captionsetup{labelformat=empty}
\caption{Table 2}
- Find the value of \(r\) and the value of \(s\) giving your answers to 3 decimal places.
- Stating your hypotheses clearly, use a \(5 \%\) level of significance to test the manager's claim.