4. A farmer set up a trial to assess the effect of two different diets on the increase in the weight of his lambs. He randomly selected 20 lambs. Ten of the lambs were given \(\operatorname { diet } A\) and the other 10 lambs were given diet \(B\). The gain in weight, in kg , of each lamb over the period of the trial was recorded.

1. State why a paired \(t\)-test is not suitable for use with these data.
2. Suggest an alternative method for selecting the sample which would make the use of a paired \(t\)-test valid.
3. Suggest two other factors that the farmer might consider when selecting the sample. The following paired data were collected.

   Diet \(A\)	5	6	7	4.6	6.1	5.7	6.2	7.4	5	3
   Diet \(B\)	7	7.2	8	6.4	5.1	7.9	8.2	6.2	6.1	5.8

4. Using a paired \(t\)-test, at the \(5 \%\) significance level, test whether or not there is evidence of a difference in the weight gained by the lambs using \(\operatorname { diet } A\) compared with those using \(\operatorname { diet } B\).
5. State, giving a reason, which diet you would recommend the farmer to use for his lambs.
   (Total 13 marks)