6 Records for a doctors' surgery over a long period suggest that the time taken for a consultation, \(T\) minutes, has a mean of 11.0. Following the introduction of new regulations, a doctor believes that the average time has changed. She finds that, with new regulations, the consultation times for a random sample of 120 patients can be summarised as $$n = 120 , \Sigma t = 1411.20 , \Sigma t ^ { 2 } = 18737.712 .$$

1. Test, at the \(10 \%\) significance level, whether the doctor's belief is correct.
2. Explain whether, in answering part (i), it was necessary to assume that the consultation times were normally distributed.