2 A group of estate agents in a particular area claimed that, after the introduction of a new search procedure at the Land Registry, the mean completion time for the purchase of a house in the area had not changed from 8 weeks.
\begin{enumerate}[label=(\alph*)]
\item A random sample of 9 house purchases in the area revealed that their completion times, in weeks, were as follows.

$$\begin{array} { l l l l l l l l l } 
6 & 7 & 10 & 12 & 9 & 11 & 7 & 8 & 14
\end{array}$$

Assuming that completion times in the area are normally distributed with standard deviation 2.5 weeks, test, at the $5 \%$ level of significance, the group's claim. (7 marks)
\item It was subsequently discovered that, after the introduction of the new search procedure at the Land Registry, the mean completion time for the purchase of a house in the area remained at 8 weeks.

Indicate whether a Type I error, a Type II error or neither has occurred in carrying out your hypothesis test in part (a). Give a reason for your answer.\\
(2 marks)
\end{enumerate}

\hfill \mbox{\textit{AQA S2 2009 Q2 [9]}}