Problem

A farmer is investigating whether using a new fertiliser will increase the yield of tomato plants. The farmer selects 40 tomato plants at random and gives them the new fertiliser. The crop mass, $x$ kg, of each of these 40 plants is recorded. The farmer selects a further 60 tomato plants at random and gives them a standard fertiliser. The crop mass, $y$ kg, of each of these 60 plants is recorded. The results are summarised as follows.

$\sum x = 168 \qquad \sum x^2 = 720 \qquad \sum y = 228 \qquad \sum y^2 = 900$

Find a 90% confidence interval for the difference in mean crop mass associated with each type of fertiliser.