A sommelier investigates whether the maturation period of single malt whiskey affects its perceived flavor complexity. They select 9 bottles of various ages and rank them based on a 'Complexity Index' (where 9 is the most complex). The results are shown below:
| Age AAA (years) | 45 | 12 | 28 | 15 | 33 | 10 | 21 | 40 | 18 |
|---|---|---|---|---|---|---|---|---|---|
| Complexity Rank CCC | 8 | 2 | 6 | 3 | 9 | 1 | 5 | 7 | 4 |
Calculate Spearman's rank correlation coefficient (rsr_srs) for these data.
Stating your hypotheses clearly and using a one-tailed test at the 5% level of significance, interpret your coefficient. (The critical value for n=9n=9n=9 at the 5% level is 0.6000).
State a reason why Spearman's rank correlation coefficient might be more appropriate than the product moment correlation coefficient (PMCC) for this specific dataset.
