5 A car manufacturer keeps a record of how many of the new cars that it has sold experience mechanical problems during the first year. The manufacturer also records whether the cars have a petrol engine or a diesel engine. Data for a random sample of 250 cars are shown in the table.
| Problems during first 3 months | Problems during first year but after first 3 months | No problems during first year | Total |
| Petrol engine | 10 | 35 | 170 | 215 |
| Diesel engine | 4 | 8 | 23 | 35 |
| Total | 14 | 43 | 193 | 250 |
- Use a \(\chi ^ { 2 }\)-test to investigate, at the \(10 \%\) significance level, whether there is an association between the mechanical problems experienced by a new car from this manufacturer and the type of engine.
- Arisa is planning to buy a new car from this manufacturer. She would prefer to buy a car with a diesel engine, but a friend has told her that cars with diesel engines experience more mechanical problems.
Based on your answer to part (a), state, with a reason, the advice that you would give to Arisa.
[0pt]
[2 marks]