A marine biologist is investigating the relationship between the depth of a coral reef and the biodiversity index recorded at that depth. The biologist records the biodiversity index, BBB, at 9 different depths, d d\,d metres, as shown in the table below.
| Depth (ddd) | 5 | 12 | 18 | 25 | 30 | 42 | 55 | 60 | 75 |
|---|---|---|---|---|---|---|---|---|---|
| Biodiversity Index (BBB) | 82 | 90 | 75 | 60 | 68 | 45 | 30 | 40 | 20 |
Calculate Spearman's rank correlation coefficient for these data.
The biologist suspects that as depth increases, the biodiversity index decreases.
Stating your hypotheses clearly, test at the 1% level of significance whether the data provide evidence to support the biologist's suspicion.
State the assumption required for a product moment correlation coefficient (PMCC) to be a valid test for association between these two variables.
The mean biodiversity index for this sample is 56.7 and the median index is 60.0. Explain how these statistics provide evidence for or against the validity of the assumption stated in part (c).
