2. An emission-control device is tested to see if it reduces \(\mathrm { CO } _ { 2 }\) emissions from cars. The emissions from 6 randomly selected cars are measured with and without the device. The results are as follows.
| Car | A | \(B\) | C | D | E | \(F\) |
| Emissions without device | 151.4 | 164.3 | 168.5 | 148.2 | 139.4 | 151.2 |
| Emissions with device | 148.9 | 162.7 | 166.9 | 150.1 | 140.0 | 146.7 |
- State an assumption that needs to be made in order to carry out a \(t\)-test in this case.
- State why a paired \(t\)-test is suitable for use with these data.
- Using a \(5 \%\) level of significance, test whether or not there is evidence that the device reduces \(\mathrm { CO } _ { 2 }\) emissions from cars.
- Explain, in context, what a type II error would be in this case.