A marine biologist is investigating whether species biodiversity decreases as the depth of a coral reef increases. She maintains a database of 150 identified reef locations in a protected zone and selects a random sample of 8 sites.
Outline how the biologist should select this random sample of 8 sites.
The biologist recorded the maximum depth (hhh meters) of each reef site and ranked the sites according to their Biodiversity Index (BBB), where 1 represents the highest biodiversity and 8 represents the lowest biodiversity. The results are shown in the table below:
| Site | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Depth hhh (m) | 54 | 12 | 33 | 45 | 8 | 22 | 60 | 28 |
| Biodiversity Rank BBB | 8 | 2 | 5 | 7 | 1 | 4 | 6 | 3 |
Calculate Spearman's rank correlation coefficient for these data, ranking depth such that 1 is the deepest reef.
Test the biologist's claim at a 5% level of significance. State your hypotheses clearly. (The critical value for n=8n=8n=8 at the 5% level of significance is 0.6429).
