6 Jade is a swimming instructor at a sports college. She claims that, as a result of an intensive training course, the mean time taken by students to swim 50 metres has reduced by more than 1 second. She chooses a random sample of 10 students. The times taken, in seconds, before and after the training course are recorded in the table.

\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Student & A & B & C & D & $E$ & $F$ & G & $H$ & I & J \\
\hline
Time before course & 54.2 & 47.4 & 52.1 & 59.0 & 55.3 & 51.0 & 48.9 & 52.2 & 58.4 & 51.4 \\
\hline
Time after course & 50.1 & 46.3 & 52.5 & 58.8 & 51.4 & 48.4 & 49.5 & 48.7 & 58.3 & 51.4 \\
\hline
\end{tabular}
\end{center}

(a) Test, at the 10\% significance level, whether Jade's claim is justified.\\

(b) State an assumption that is necessary for this test to be valid.\\

\hfill \mbox{\textit{CAIE Further Paper 4 2024 Q6}}