1 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 \(Y\).