6 A company has two machines, \(A\) and \(B\), which independently fill small bottles with a liquid. The volumes of liquid per bottle, in suitable units, filled by machines \(A\) and \(B\) are denoted by \(x\) and \(y\) respectively. A scientist at the company takes a random sample of 40 bottles filled by machine \(A\) and a random sample of 50 bottles filled by machine \(B\). The results are summarised as follows. $$\sum x = 1120 \quad \sum x ^ { 2 } = 31400 \quad \sum y = 1370 \quad \sum y ^ { 2 } = 37600$$ The population means of the volumes of liquid in the bottles filled by machines \(A\) and \(B\) are denoted by \(\mu _ { A }\) and \(\mu _ { B }\).

1. Test at the \(2 \%\) significance level whether there is any difference between \(\mu _ { A }\) and \(\mu _ { B }\).
2. Find the set of values of \(\alpha\) for which there would be evidence at the \(\alpha \%\) significance level that \(\mu _ { \mathrm { A } } - \mu _ { \mathrm { B } }\) is greater than 0.25.
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