A research laboratory is investigating the relationship between the toxicity of 10 experimental chemical compounds and their production costs. The toxicity of each compound is ranked from 1 (most toxic) to 10 (least toxic). The table below displays the toxicity rank and the production cost per gram (CCC) for each compound, along with some initial cost rankings (assigning rank 1 to the highest cost).
| Compound | Toxicity Rank (TTT) | Production Cost (CCC) | Cost Rank |
|---|---|---|---|
| A | 7 | 42.20 | 8 |
| B | 3 | 105.30 | 2 |
| C | 1 | 112.00 | |
| D | 5 | 67.80 | |
| E | 10 | 25.10 | |
| F | 2 | 98.40 | |
| G | 4 | 85.50 | |
| H | 8 | 55.00 | |
| I | 6 | 74.60 | |
| J | 9 | 33.90 |
By completing the rankings for the production costs, calculate Spearman's rank correlation coefficient for these data.
Stating your hypotheses clearly, test at the 5% level of significance whether or not there is a positive correlation between toxicity and production cost. (The critical value for n=10n=10n=10 at a 5% significance level is 0.5636).