A scientist is investigating the heights of pine trees in two regions, \(A\) and \(B\). She takes a random sample of 50 pine trees in region \(A\) and records their heights, \(x\) m. She takes a random sample of 60 pine trees in region \(B\) and records their heights, \(y\) m. Her results are summarised as follows.

\(\sum x=1625 \quad \sum x^{2}=53200 \quad \sum y=1854 \quad \sum y^{2}=57900\)

Find a 95% confidence interval for the difference between the population mean heights of pine trees in regions \(A\) and \(B\).