9 A geyser is a hot spring which erupts from time to time. For two geysers, the duration of each eruption, \(x\) minutes, and the waiting time until the next eruption, \(y\) minutes, are recorded.
- For a random sample of 50 eruptions of the first geyser, the correlation coefficient between \(x\) and \(y\) is 0.758 .
The critical value for a 2 -tailed hypothesis test for correlation at the \(5 \%\) level is 0.279 . Explain whether or not there is evidence of correlation in the population of eruptions.
The scatter diagram in Fig. 9 shows the data from a random sample of 50 eruptions of the second geyser.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{e9f3a5f3-210b-453d-9ff5-8518340f5689-07_794_1298_383_251}
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\caption{Fig. 9}
\end{figure} - Stella claims the scatter diagram shows evidence of correlation between duration of eruption and waiting time. Make two comments about Stella's claim.