4 Manet has developed a new training course to help athletes improve their time taken to run 800 m . Manet claims that his course will decrease an athlete's time by more than 2 s on average. For a random sample of 10 athletes the times taken, in seconds, before and after the course are given in the following table.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | c | }
\hline
Athlete & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ & $J$ \\
\hline
Before & 150 & 146 & 131 & 135 & 126 & 142 & 130 & 129 & 137 & 134 \\
\hline
After & 145 & 138 & 129 & 135 & 122 & 135 & 132 & 128 & 127 & 137 \\
\hline
\end{tabular}
\end{center}

Use a $t$-test, at the $5 \%$ significance level, to test whether Manet's claim is justified, stating any assumption that you make.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2021 Q4}}