Ellie is investigating the heights of two types of beech tree, $$\(A\)$$ and $$\(B\)$$, in a certain region. She has chosen a random sample of 60 beech trees of type $$\(A\)$$ in the region, recorded their heights, $$\(x \mathrm{~m}\)$$, and calculated unbiased estimates for the population mean and population variance as 35.6 m and $$\(4.95 \mathrm{~m}^{2}\)$$ respectively. Ellie also chooses a random sample of 50 beech trees of type $$\(B\)$$ in the region and records their heights, $$\(y \mathrm{~m}\)$$. Her results are summarised as follows. $$\[ \Sigma y=1654 \quad \Sigma y^{2}=54850 \]$$ Find a $$\(95 \%\)$$ confidence interval for the difference between the population mean heights of type $$\(A\)$$ and type $$\(B\)$$ beech trees in the region. ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ . ................................................................................................................................................................ .

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