6 Records show that before the year 1990 the maximum daily temperature \(T ^ { \circ } \mathrm { C }\) at a seaside resort in August can be modelled by a distribution with mean 24.3. The maximum temperatures of a random sample of 50 August days since 1990 can be summarised by $$n = 50 , \quad \Sigma t = 1314.0 , \quad \Sigma t ^ { 2 } = 36602.17 .$$

1. Test, at the \(1 \%\) significance level, whether there is evidence of a change in the mean maximum daily temperature in August since 1990.
2. Give a reason why it is possible to use the Central Limit Theorem in your test.