3 The height, in metres, of adult male African elephants may be assumed to be normally distributed with mean \(\mu\) and standard deviation 0.20 .
The heights of a sample of 12 such elephants were measured with the following results, in metres.
$$\begin{array} { l l l l l l l l l l l l }
3.37 & 3.45 & 2.93 & 3.42 & 3.49 & 3.67 & 2.96 & 3.57 & 3.36 & 2.89 & 3.22 & 2.91
\end{array}$$
- Stating a necessary assumption, construct a \(98 \%\) confidence interval for \(\mu\). (6 marks)
- The mean height of adult male Asian elephants is known to be 2.90 metres.
Using your confidence interval, state, with a reason, what can be concluded about the mean heights of adult males in these two types of elephant.