1 A manager is investigating the times taken by employees to complete a particular task as a result of the introduction of new technology. He claims that the mean time taken to complete the task is reduced by more than 0.4 minutes. He chooses a random sample of 10 employees. The times taken, in minutes, before and after the introduction of the new technology are recorded in the table.

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\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
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Employee & $A$ & $B$ & $C$ & D & $E$ & $F$ & G & $H$ & I & J \\
\hline
Time before new technology & 10.2 & 9.8 & 12.4 & 11.6 & 10.8 & 11.2 & 14.6 & 10.6 & 12.3 & 11.0 \\
\hline
Time after new technology & 9.6 & 8.5 & 12.4 & 10.9 & 10.2 & 10.6 & 12.8 & 10.8 & 12.5 & 10.6 \\
\hline
\end{tabular}
\end{center}

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

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

\hfill \mbox{\textit{CAIE Further Paper 4 2022 Q1}}