5 Members of a residents' association are concerned about the speeds of cars travelling through their village. They decide to record the speed, in mph , of each of a random sample of 10 cars travelling through their village, with the following results:
$$\begin{array} { l l l l l l l l l l }
33 & 27 & 34 & 30 & 48 & 35 & 34 & 33 & 43 & 39
\end{array}$$
- Construct a \(99 \%\) confidence interval for \(\mu\), the mean speed of cars travelling through the village, stating any assumption that you make.
- Comment on the claim that a 30 mph speed limit is being adhered to by most motorists.
(3 marks)