Ellie is investigating the heights of two types of beech tree, \(A\) and \(B\), in a certain region. She has chosen a random sample of 60 beech trees of type \(A\) in the region, recorded their heights, \(x \mathrm{~m}\), and calculated unbiased estimates for the population mean and population variance as 35.6 m and \(4.95 \mathrm{~m}^{2}\) respectively.

Ellie also chooses a random sample of 50 beech trees of type \(B\) in the region and records their heights, \(y \mathrm{~m}\). Her results are summarised as follows.
\(\sum y=1654 \quad \sum y^{2}=54850\)

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