9 Two fish farmers \(X\) and \(Y\) produce a particular type of fish. Farmer \(X\) chooses a random sample of 8 of his fish and records the masses, \(x \mathrm {~kg}\), as follows. $$\begin{array} { l l l l l l l l } 1.2 & 1.4 & 0.8 & 2.1 & 1.8 & 2.6 & 1.5 & 2.0 \end{array}$$ Farmer \(Y\) chooses a random sample of 10 of his fish and summarises the masses, \(y \mathrm {~kg}\), as follows. $$\Sigma y = 20.2 \quad \Sigma y ^ { 2 } = 44.6$$ You should assume that both distributions are normal with equal variances. Test at the \(10 \%\) significance level whether the mean mass of fish produced by farmer \(X\) differs from the mean mass of fish produced by farmer \(Y\).
[0pt] [10]