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