4 Members of the Sprints athletics club have been taking part in an intense training scheme, aimed at reducing their times taken to run 400 m . For a random sample of 9 athletes from the club, the times taken, in seconds, before and after the training scheme are given in the following table.

\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | c | }
\hline
Athlete & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ & $I$ \\
\hline
Time before & 48.8 & 48.2 & 50.3 & 49.6 & 49.4 & 48.9 & 47.6 & 50.3 & 48.4 \\
\hline
Time after & 47.9 & 47.8 & 49.6 & 49.1 & 49.6 & 48.9 & 47.7 & 49.1 & 48.1 \\
\hline
\end{tabular}
\end{center}

The organiser of the training scheme claims that on average an athlete's time will be reduced by at least 0.3 seconds.

Test at the 10\% significance level whether the organiser's claim is justified, stating any assumption that you make.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2020 Q4}}