Kayla is investigating the lengths of the leaves of a certain type of tree found in two forests \(X\) and \(Y\). She chooses a random sample of 40 leaves of this type from forest \(X\) and records their lengths, \(x \mathrm{~cm}\). She also records the lengths, \(y \mathrm{~cm}\), for a random sample of 60 leaves of this type from forest \(Y\). Her results are summarised as follows.
\(\sum x=242.0 \quad \sum x^{2}=1587.0 \quad \sum y=373.2 \quad \sum y^{2}=2532.6\)

Find a \(90 \%\) confidence interval for the difference between the population mean lengths of leaves in forests \(X\) and \(Y\).