8 Bottles of sherry nominally contain 1000 millilitres. After the introduction of a new method of filling the bottles, there is a suspicion that the mean volume of sherry in a bottle has changed.

In order to investigate this suspicion, a random sample of 12 bottles of sherry is taken and the volume of sherry in each bottle is measured.

The volumes, in millilitres, of sherry in these bottles are found to be

\begin{center}
\begin{tabular}{ r r r r r r }
996 & 1006 & 1009 & 999 & 1007 & 1003 \\
998 & 1010 & 997 & 996 & 1008 & 1007 \\
\end{tabular}
\end{center}

Assuming that the volume of sherry in a bottle is normally distributed, investigate, at the $5 \%$ level of significance, whether the mean volume of sherry in a bottle differs from 1000 millilitres.

\hfill \mbox{\textit{AQA S2  Q8}}