The times taken, in hours, by cyclists from two different clubs, \(A\) and \(B\), to complete a 50 km time trial are being compared. The times taken by a cyclist from club \(A\) and by a cyclist from club \(B\) are denoted by \(t _ { A }\) and \(t _ { B }\) respectively. A random sample of 50 cyclists from \(A\) and a random sample of 60 cyclists from \(B\) give the following summarised data. $$\Sigma t _ { A } = 102.0 \quad \Sigma t _ { A } ^ { 2 } = 215.18 \quad \Sigma t _ { B } = 129.0 \quad \Sigma t _ { B } ^ { 2 } = 282.3$$ Using a 5\% significance level, test whether, on average, cyclists from club \(A\) take less time to complete the time trial than cyclists from club \(B\). A test at the \(\alpha \%\) significance level shows that there is evidence that the population mean time for cyclists from club \(B\) exceeds the population mean time for cyclists from club \(A\) by more than 0.05 hours. Find the set of possible values of \(\alpha\).