2 A company wishes to buy a new lathe for making chair legs. Two models of lathe, 'Allegro' and 'Vivace', were trialled. The company asked 12 randomly selected employees to make a particular type of chair leg on each machine. The times, in seconds, for each employee are shown in the table.
| Employee | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| Time on Allegro | 162 | 111 | 194 | 159 | 202 | 210 | 183 | 168 | 165 | 150 | 185 | 160 |
| Time on Vivace | 182 | 130 | 193 | 181 | 192 | 205 | 186 | 184 | 192 | 180 | 178 | 189 |
The company wishes to test whether there is any difference in average times for the two machines.
- State the circumstances under which a non-parametric test should be used.
- Use two different non-parametric tests and show that they lead to different conclusions at the 5\% significance level.
- State, with a reason, which conclusion is to be preferred.