7 The lengths in mm of a random sample of 6 one-year-old fish of a particular species are as follows.
\(\begin{array} { l l l l l l } 271 & 293 & 306 & 287 & 264 & 290 \end{array}\)
- State an assumption required in order to find a confidence interval for the mean length of one-year-old fish of this species.
Fig. 7 shows a Normal probability plot for these data.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8d36bc92-07ac-40c3-9e75-26f2bc9d2fcc-07_599_753_646_246}
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{figure} - Explain why the Normal probability plot suggests that the assumption in part (a) may be valid.
- In this question you must show detailed reasoning.
Assuming that this assumption is true, find a 95\% confidence interval for the mean length of one-year-old fish of this species.