11 In an experiment involving a bivariate distribution ( \(X , Y\) ) a random sample of 7 pairs of values was obtained and Pearson's product-moment correlation coefficient \(r\) was calculated for these values.
- The value of \(r\) was found to be 0.894 . Use the table below to test, at the \(5 \%\) significance level, whether there is positive linear correlation in the population, stating your hypotheses and conclusion clearly.
| 1-tail test 2-tail test | 5\% | 2.5\% | 1\% | 0.5\% |
| 10\% | 5\% | 2\% | 1\% |
| \(n\) | | | | |
| 1 | - | - | - | - |
| 2 | - | - | - | - |
| 3 | 0.9877 | 0.9969 | 0.9995 | 0.9999 |
| 4 | 0.9000 | 0.9500 | 0.9800 | 0.9900 |
| 5 | 0.8054 | 0.8783 | 0.9343 | 0.9587 |
| 6 | 0.7293 | 0.8114 | 0.8822 | 0.9587 |
| 7 | 0.6694 | 0.7545 | 0.8329 | 0.9745 |
| 8 | 0.6215 | 0.7067 | 0.7887 | 0.8343 |
| 9 | 0.5882 | 0.6664 | 0.7498 | 0.7977 |
| 10 | 0.5494 | 0.6319 | 0.7155 | 0.7646 |
\includegraphics[alt={},max width=\textwidth]{85de9a39-f8be-40ee-b0c8-e2e632be93d8-8_380_371_301_191}
\captionsetup{labelformat=empty}
\caption{Diagram A}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{85de9a39-f8be-40ee-b0c8-e2e632be93d8-8_373_373_301_628}
\captionsetup{labelformat=empty}
\caption{Diagram B}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{85de9a39-f8be-40ee-b0c8-e2e632be93d8-8_378_373_301_1064}
\captionsetup{labelformat=empty}
\caption{Diagram C}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{85de9a39-f8be-40ee-b0c8-e2e632be93d8-8_378_373_301_1503}
\captionsetup{labelformat=empty}
\caption{Diagram D}
\end{figure}
It is given that \(r = 0.894\) for one of these diagrams. - For each of the other diagrams, state how you can tell that \(r \neq 0.894\).