2 A large number of students are taking a Physics course. They are assessed by a practical examination and a written examination. The marks out of 100 obtained by a random sample of 15 students in each of the examinations are as follows.

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Student & A & $B$ & C & D & $E$ & $F$ & $G$ & H & I & J & $K$ & $L$ & $M$ & $N$ & $O$ \\
\hline
Practical examination & 66 & 63 & 24 & 52 & 59 & 76 & 88 & 51 & 48 & 36 & 91 & 72 & 68 & 67 & 60 \\
\hline
Written examination & 63 & 57 & 39 & 50 & 47 & 71 & 87 & 65 & 56 & 39 & 78 & 70 & 61 & 62 & 70 \\
\hline
\end{tabular}
\end{center}

Use a sign test, at the $10 \%$ significance level, to test whether, on average, the practical examination marks are higher than the written examination marks.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2024 Q2}}