5 Raman is researching the heights of male giraffes in a particular region. Raman assumes that the heights of male giraffes in this region are normally distributed. He takes a random sample of 8 male giraffes from the region and measures the height, in metres, of each giraffe. These heights are as follows.
$$\begin{array} { c c c c c c c c }
5.2 & 5.8 & 4.9 & 6.1 & 5.5 & 5.9 & 5.4 & 5.6
\end{array}$$
- Find a \(90 \%\) confidence interval for the population mean height of male giraffes in this region. [5]
Raman claims that the population mean height of male giraffes in the region is less than 5.9 metres. - Test at the \(2.5 \%\) significance level whether this sample provides sufficient evidence to support Raman's claim.