A marine biologist is researching the relationship between the depth, ddd (metres), of a specific reef and the biodiversity index, bbb, of the surrounding ecosystem. Data is collected from 8 distinct locations as shown in the table below.
| Depth ddd (m) | 5 | 12 | 20 | 35 | 45 | 60 | 75 | 90 |
|---|---|---|---|---|---|---|---|---|
| Index bbb | 7.9 | 8.2 | 5.8 | 6.3 | 4.4 | 3.1 | 2.5 | 1.2 |
Calculate the Spearman's rank correlation coefficient between ddd and bbb.
The biologist's initial hypothesis was that there would be no correlation between depth and biodiversity index.
Test, at the 5% level of significance, the biologist's claim. State your hypotheses clearly. (The critical value for sample size n=8n=8n=8 at the 5% two-tailed level is 0.7381).