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.
- 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)
- 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)