Two methods of extracting juice from an orange are to be compared. Eight oranges are halved. One half of each orange is chosen at random and allocated to Method $A$ and the other half is allocated to Method $B$. The amounts of juice extracted, in ml, are given in the table.

\includegraphics{figure_7}

One statistician suggests performing a two-sample $t$-test to investigate whether or not there is a difference between the mean amounts of juice extracted by the two methods.

\begin{enumerate}[label=(\alph*)]
\item Stating your hypotheses clearly and using a 5\% significance level, carry out this test.

(You may assume $\bar{x}_A = 26.125$, $s_A^2 = 7.84$, $\bar{x}_B = 25$, $s_B^2 = 4$ and $\sigma_A^2 = \sigma_B^2$.) [7]
\end{enumerate}

Another statistician suggests analysing these data using a paired $t$-test.

\begin{enumerate}[label=(\alph*)]
\item[(b)] Using a 5\% significance level, carry out this test. [9]

\item State which of these two tests you consider to be more appropriate. Give a reason for your choice. [1]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S4  Q7 [17]}}