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=0.9128r = 0.9128r=0.9128.
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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.