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.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.