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 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.

\begin{enumerate}[label=(\alph*)]
\item State why a paired $t$-test is not suitable for use with these data. [1]

\item Suggest an alternative method for selecting the sample which would make the use of a paired $t$-test suitable. [1]

\item Suggest two other factors that the farmer might consider when selecting the sample. [2]
\end{enumerate}

The following paired data were collected.

\includegraphics{figure_4}

\begin{enumerate}[label=(\alph*)]
\item[(d)] 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 diet $A$ compared with those using diet $B$. [8]

\item State, giving a reason, which diet you would recommend the farmer to use for his lambs. [1]
\end{enumerate}

(Total 13 marks)

\hfill \mbox{\textit{Edexcel S4  Q4 [13]}}