9 A cyclist who lives on an island suspects that car drivers with locally registered number plates allow more space when passing her than those with non-locally registered number plates. She decides to carry out a hypothesis test and so over a period of time selects a random sample of 250 cars which pass her. For each car she estimates whether the car driver allows at least the recommended 1.5 metres when passing her. The table shows the data which she collected.
| Where registered |
| \cline { 3 - 4 }
\multicolumn{2}{|c|}{} | Local | Non-local |
| \multirow{2}{*}{} | Under 1.5 m | 12 | 11 |
| \cline { 2 - 4 } | At least 1.5 m | 157 | 70 |
- In this question you must show detailed reasoning.
Carry out the test at the \(5 \%\) significance level to examine whether there is any association between where the car is registered and passing distance.
- A friend of the cyclist suggests that there may be a problem with the data, since the cyclist may have introduced some bias in estimating whether cars were allowing the recommended distance.
Explain how any bias might have arisen.