1 A certain industrial process requires a supply of water. It has been found that, for best results, the mean water pressure in suitable units should be 7.8. The water pressure is monitored by taking measurements at regular intervals. On a particular day, a random sample of the measurements is as follows.
$$\begin{array} { l l l l l l l l l }
7.50 & 7.64 & 7.68 & 7.51 & 7.70 & 7.85 & 7.34 & 7.72 & 7.74
\end{array}$$
These data are to be used to carry out a hypothesis test concerning the mean water pressure.
- Why is a test based on the Normal distribution not appropriate in this case?
- What distributional assumption is needed for a test based on the \(t\) distribution?
- Carry out a \(t\) test, with a \(2 \%\) level of significance, to see whether it is reasonable to assume that the mean pressure is 7.8 .
- Explain what is meant by a \(95 \%\) confidence interval.
- Find a \(95 \%\) confidence interval for the actual mean water pressure.