2 A company supplying cattle feed to dairy farmers claims that its new brand of feed will increase average milk yields by 10 litres per cow per week. A farmer thinks the increase will be less than this and decides to carry out a statistical investigation using a paired \(t\) test. A random sample of 10 dairy cows are given the new feed and then their milk yields are compared with their yields when on the old feed. The yields, in litres per week, for the 10 cows are as follows.

1. Why is it sensible to use a paired test?
2. State the condition necessary for a paired \(t\) test.
3. Assuming the condition stated in part (ii) is met, carry out the test, using a significance level of \(5 \%\), to see whether it appears that the company's claim is justified.
4. Find a 95\% confidence interval for the mean increase in the milk yield using the new feed.