1 Farmer \(A\) grows apples of a certain variety. Each tree produces 14.8 kg of apples, on average, per year. Farmer \(B\) grows apples of the same variety and claims that his apple trees produce a higher mass of apples per year than Farmer \(A\) 's trees. The masses of apples from Farmer \(B\) 's trees may be assumed to be normally distributed. A random sample of 10 trees from Farmer \(B\) is chosen. The masses, \(x \mathrm {~kg}\), of apples produced in a year are summarised as follows. $$\sum x = 152.0 \quad \sum x ^ { 2 } = 2313.0$$ Test, at the \(5 \%\) significance level, whether Farmer \(B\) 's claim is justified.