- The number of hurricanes per year in a particular region was recorded over 80 years. The results are summarised in Table 1 below.
\begin{table}[h]
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Frequency | 0 | 2 | 5 | 17 | 20 | 12 | 12 | 12 |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
- Write down two assumptions that will support modelling the number of hurricanes per year by a Poisson distribution.
- Show that the mean number of hurricanes per year from Table 1 is 4.4875
- Use the answer in part (b) to calculate the expected frequencies \(r\) and \(s\) given in Table 2 below to 2 decimal places.
\begin{table}[h]
| \(h\) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 or more |
| 0.90 | 4.04 | \(r\) | 13.55 | \(s\) | 13.65 | 10.21 | 13.39 |
\captionsetup{labelformat=empty}
\caption{Table 2}
- Test, at the \(5 \%\) level of significance, whether or not the data can be modelled by a Poisson distribution. State your hypotheses clearly.