- Table 1 below shows the number of car breakdowns in the Snoreap district in each of 60 months.
\begin{table}[h]
| 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 12 | 11 | 19 | 14 | 3 | 1 |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
Anja believes that the number of car breakdowns per month in Snoreap can be modelled by a Poisson distribution. Table 2 below shows the results of some of her calculations.
\begin{table}[h]
| Number of car breakdowns | 0 | 1 | 2 | 3 | 4 | \(\geqslant 5\) |
| Observed frequency (O) | 12 | 11 | 19 | 14 | 3 | 1 |
| Expected frequency ( \(\mathbf { E } _ { \mathbf { i } }\) ) | 9.92 | | | 9.64 | 4.34 | |
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{table}
- State suitable hypotheses for a test to investigate Anja's belief.
- Explain why Anja has changed the label of the final column to \(\geqslant 5\)
- Showing your working clearly, complete Table 2
- Find the value of \(\frac { \left( O _ { i } - E _ { i } \right) ^ { 2 } } { E _ { i } }\) when the number of car breakdowns is
- 1
- 3
- Explain why Anja used 3 degrees of freedom for her test.
The test statistic for Anja's test is 6.54 to 2 decimal places.
- Stating the critical value and using a \(5 \%\) level of significance, complete Anja's test.