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, $x$ meters, and the light intensity, $L$ lux, at seven different points. The data collected is shown in the table below:

(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}

Calculate 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.

(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}

Calculate 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.

2.2.2 Scatter diagrams and correlation

Question 76

Markscheme

2.2.2 Scatter diagrams and correlation

Question 76

Markscheme

2.2.2 Scatter diagrams and correlation

Question 76

2.2.2 Scatter diagrams and correlation Questions

2.2.2 Scatter diagrams and correlation

Question 76

2.2.2 Scatter diagrams and correlation Questions