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.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.