An experiment is conducted to compare the heat retention of two brands of flasks, brand $$\(A\)$$ and brand $$\(B\)$$. Both brands of flask have a capacity of $$\(750 \mathrm{ml}\)$$. In the experiment $$\(750 \mathrm{ml}\)$$ of boiling water is poured into the flask, which is then sealed. Four hours later the temperature, in $$\({ }^{\circ} \mathrm{C}\)$$, of the water in the flask is recorded. A random sample of 100 flasks from brand $$\(A\)$$ gives the following summary statistics, where $$\(x\)$$ is the temperature of the water in the flask after four hours. $$\[ \sum x=7690 \quad \sum(x-\bar{x})^{2}=669.24 \]$$ Test, at the $$\(1 \%\)$$ significance level, whether there is a difference in the mean water temperature after four hours between brand $$\(A\)$$ and brand $$\(B\)$$. You should state your hypotheses, test statistic and critical value clearly. (7)

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