1 Jasmine is researching the heights of pine trees in forests in two regions \(A\) and \(B\). She chooses a random sample of 50 pine trees in region \(A\) and records their heights, \(x \mathrm {~m}\). She also chooses a random sample of 60 pine trees in region \(B\) and records their heights, \(y \mathrm {~m}\). 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 \(B\).

1 Jasmine is researching the heights of pine trees in forests in two regions $A$ and $B$. She chooses a random sample of 50 pine trees in region $A$ and records their heights, $x \mathrm {~m}$. She also chooses a random sample of 60 pine trees in region $B$ and records their heights, $y \mathrm {~m}$. 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 $B$.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2022 Q1}}