A marine biologist is investigating the attenuation of light in a high-altitude freshwater lake. She hypothesizes that the light intensity decreases as the depth from the surface increases. She records the depth below the surface, xxx meters, and the light intensity, LLL lux, at seven different points. The data collected is shown in the table below:
Depth x (m)2.56.010.516.022.530.040.0Intensity L (lux)580420450280190230110\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text{Depth } x \text{ (m)} & 2.5 & 6.0 & 10.5 & 16.0 & 22.5 & 30.0 & 40.0 \\ \hline \text{Intensity } L \text{ (lux)} & 580 & 420 & 450 & 280 & 190 & 230 & 110 \\ \hline \end{array}Depth x (m)Intensity L (lux)2.55806.042010.545016.028022.519030.023040.0110Calculate Spearman's rank correlation coefficient for these data.
Stating your hypotheses clearly, test at the 5% level of significance whether or not the data provides support for the biologist's hypothesis that light intensity decreases as depth increases.
