An agricultural scientist is investigating the relationship between soil acidity, ppp (measured in pH), and the concentration of a specific nutrient, ccc (measured in mg/kg), in 8 different experimental plots. The data collected is shown in the table below:
Plot12345678Soil Acidity (p)5.84.17.04.58.25.27.56.4Nutrient Concentration (c)2015271238244231\begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \text{Plot} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text{Soil Acidity } (p) & 5.8 & 4.1 & 7.0 & 4.5 & 8.2 & 5.2 & 7.5 & 6.4 \\ \hline \text{Nutrient Concentration } (c) & 20 & 15 & 27 & 12 & 38 & 24 & 42 & 31 \\ \hline \end{array}PlotSoil Acidity (p)Nutrient Concentration (c)15.82024.11537.02744.51258.23865.22477.54286.431
Calculate the value of Spearman's rank correlation coefficient between p p\,p and ccc.
Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence of a positive correlation between soil acidity and nutrient concentration.
The product moment correlation coefficient (PMCC) for this data is calculated as r=0.9612r = 0.9612r=0.9612.
Use the given PMCC value to test, at the 5% level of significance, whether there is evidence of a positive correlation between soil acidity and nutrient concentration.
Based on your conclusions from parts (b) and (c), describe the nature of the relationship between soil acidity and nutrient concentration.
