The following table displays the amount of nitrogen supplement added to the soil, xxx (kg/hectare), and the resulting yield of a specific variety of beetroot, www (tonnes/hectare), for a random sample of 6 test plots.
| Plot | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| Nitrogen (xxx) | 10 | 50 | 30 | 70 | 20 | 40 |
| Yield (www) | 1.2 | 2.8 | 2.0 | 3.2 | 1.5 | 1.9 |
(You may use Sxx=2333.33S_{xx} = 2333.33Sxx=2333.33, Sww=2.92S_{ww} = 2.92Sww=2.92, Sxw=80S_{xw} = 80Sxw=80)
Test, at the 5% level of significance, whether there is evidence of a correlation between the amount of nitrogen and the beetroot yield using the product moment correlation coefficient (PMCC). State your hypotheses and the critical value used.
Calculate Spearman’s rank correlation coefficient between the rank of nitrogen added and the rank of yield achieved.
Test, at the 5% level of significance, whether there is evidence of a positive correlation between the nitrogen supplement and the yield using Spearman's rank correlation. State your hypotheses and the critical value used.