3. A motoring organisation wishes to determine whether or not the petrol consumption of two different car models \(A\) and \(B\) are the same. A trial is therefore carried out in which 6 cars of each model are given 10 litres of petrol and driven at a predetermined speed around a track until the petrol is used up. The distances travelled, in miles, are shown below
| Model A: | 86.3 | 84.2 | 85.8 | 83.1 | 84.7 | 85.3 |
| Model B: | 84.9 | 85.9 | 84.8 | 86.5 | 85.2 | 85.5 |
It is proposed to use a test with significance level \(5 \%\) based on the Mann-Whitney statistic \(U\).
- State suitable hypotheses.
- Find the critical region for the test.
- Determine the value of \(U\) for the above data and state your conclusion in context. You must justify your answer.