1 A manager is investigating the times taken by employees to complete a particular task as a result of the introduction of new technology. He claims that the mean time taken to complete the task is reduced by more than 0.4 minutes. He chooses a random sample of 10 employees. The times taken, in minutes, before and after the introduction of the new technology are recorded in the table.
| Employee | \(A\) | \(B\) | \(C\) | D | \(E\) | \(F\) | G | \(H\) | I | J |
| Time before new technology | 10.2 | 9.8 | 12.4 | 11.6 | 10.8 | 11.2 | 14.6 | 10.6 | 12.3 | 11.0 |
| Time after new technology | 9.6 | 8.5 | 12.4 | 10.9 | 10.2 | 10.6 | 12.8 | 10.8 | 12.5 | 10.6 |
- Test at the 10\% significance level whether the manager's claim is justified.
- State an assumption that is necessary for this test to be valid.