10 The times taken to run 400 metres by students at two large colleges \(P\) and \(Q\) are being compared. There is no evidence that the population variances are equal. The time taken by a student at college \(P\) and the time taken by a student at college \(Q\) are denoted by \(x\) seconds and \(y\) seconds respectively. A random sample of 50 students from college \(P\) and a random sample of 60 students from college \(Q\) give the following summarised data. $$\Sigma x = 2620 \quad \Sigma x ^ { 2 } = 138200 \quad \Sigma y = 3060 \quad \Sigma y ^ { 2 } = 157000$$

1. Using a 10\% significance level, test whether, on average, students from college \(P\) take longer to run 400 metres than students from college \(Q\).
2. Find a \(90 \%\) confidence interval for the difference in the mean times taken to run 400 metres by students from colleges \(P\) and \(Q\).