9231 P41 - Jun 2022 - Q1 - 8 marks
6702
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 |
(a) Test at the \(10\%\) significance level whether the manager's claim is justified.
(b) State an assumption that is necessary for this test to be valid.
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