3 A biology student is doing an experiment in which plants are inoculated with a particular microorganism in an attempt to help them grow. She is investigating whether there is any association between the percentage of roots which have been colonised by the microorganism and the dry weight of the plant shoots. After the plants have grown for a few weeks, the student takes a random sample of 10 plants and measures the percentage of roots which have been colonised by the microorganism and the dry weight of the plant shoots. The spreadsheet output shows the data, together with a scatter diagram to illustrate the data.
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1. The student decides that a test based on Pearson’s product moment correlation coefficient may not be valid. Explain why she comes to this conclusion.
2. Calculate the value of Spearman’s rank correlation coefficient.
3. Carry out a test based on this coefficient, at the \(5 \%\) significance level, to investigate whether there is any association between percentage colonisation and shoot dry weight.