5 Dev owns a small company which produces bottles of juice. He uses two machines, \(X\) and \(Y\), to fill empty bottles with juice. Dev is investigating the volumes of juice in the bottles. He chooses a random sample of 35 bottles filled by machine \(X\) and a random sample of 60 bottles filled by machine \(Y\). The volumes of juice, \(x\) and \(y\) respectively, measured in suitable units, are summarised by $$\sum x = 30.8 , \quad \sum x ^ { 2 } = 29.0 , \quad \sum y = 62.4 , \quad \sum y ^ { 2 } = 76.8 .$$ Dev claims that the mean volume of juice in bottles filled by machine \(Y\) is greater than the mean volume of juice in bottles filled by machine \(X\). A test at the \(\alpha \%\) significance level suggests that there is sufficient evidence to support Dev's claim. Find the set of possible values of \(\alpha\).
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