1 The birth weights, in kilograms, of a random sample of 9 captive-bred elephants are as follows.
$$\begin{array} { l l l l l l l l l }
94 & 138 & 130 & 118 & 146 & 165 & 82 & 115 & 69
\end{array}$$
A researcher uses software to produce a \(99 \%\) confidence interval for the mean birth weight of captive-bred elephants. The output from the software is shown in Fig. 1.
\begin{table}[h]
| Result |
| T Estimate of a Mean |
| Mean |
| s |
| SE |
| N |
| df |
| Lower limit |
| Upper limit |
| Interval |
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{table}
- State an assumption about the distribution of the population from which these weights come that is necessary in order to produce this interval.
- State the confidence interval which the software gives, in the form \(a < \mu < b\).
- Explain
- what the label df means,
- how the value of df is calculated for a confidence interval produced using the \(t\) distribution.
- State two ways in which the researcher could have obtained a narrower confidence interval.