6 The time taken by volunteers to complete a certain task is normally distributed. In the past the time, in minutes, has had mean 91.4 and standard deviation 6.4. A new, similar task is introduced and the times, \(t\) minutes, taken by a random sample of 6 volunteers to complete the new task are summarised by \(\Sigma t = 568.5\). Andrea plans to carry out a test, at the \(5 \%\) significance level, of whether the mean time for the new task is different from the mean time for the old task.

1. Give a reason why Andrea should use a two-tail test.
2. State the probability that a Type I error is made, and explain the meaning of a Type I error in this context.
   You may assume that the times taken for the new task are normally distributed.
3. Stating another necessary assumption, carry out the test.