4. A random sample of 60 children and a random sample of 50 adults were taken and each person was given the same task to complete.
The table below summarises the times taken, \(t\) seconds, to complete the task.
| Mean, \(\overline { \boldsymbol { t } }\) | Standard deviation, \(\boldsymbol { s }\) | \(\boldsymbol { n }\) |
| Children | 61.2 | 5.9 | 60 |
| Adults | 59.1 | 5.2 | 50 |
- Stating your hypotheses clearly, test, at the \(5 \%\) level of significance, whether or not there is evidence that the mean time taken to complete the task by children is greater than the mean time taken by adults.
(6) - Explain the relevance of the Central Limit Theorem to your calculation in part (a).
- State an assumption you have made to carry out the test in part (a).