A sound engineer conducts an experiment to investigate the relationship between the peak volume levels of a concert PA system and the perceived audio clarity for the audience. At five different locations, A,B,C,D A, B, C, D\,A,B,C,D and EEE, the peak volume vvv (in decibels) and a clarity score sss (on a scale from 0 to 100) are recorded. The results are summarized in the table below:
| Location | AAA | BBB | CCC | DDD | EEE |
|---|---|---|---|---|---|
| Volume vvv (dB) | 98 | 105 | 92 | 112 | 100 |
| Clarity sss (score) | 62 | 48 | 85 | 35 | 70 |
Determine the value of Spearman’s rank correlation coefficient for these data.
The engineer suspects that higher volume levels lead to a decrease in perceived clarity. Test this suspicion at the 5% level of significance, stating your hypotheses clearly.