An acoustic engineer suspects that as the Signal-to-Noise Ratio (SSS, measured in dB) of a digital transducer increases, the Subjective Clarity Rating (RRR, measured on a scale of 1 to 10) also increases. The engineer tests five prototype transducers, α,β,γ,δ \alpha, \beta, \gamma, \delta\,α,β,γ,δ and ϵ\epsilonϵ, and records the following metrics:
TransducerαβγδϵSignal-to-Noise Ratio S (dB)18.225.415.122.812.5Subjective Clarity Rating R4.37.95.66.83.9 \begin{array}{|l|c|c|c|c|c|} \hline \text{Transducer} & \alpha & \beta & \gamma & \delta & \epsilon \\ \hline \text{Signal-to-Noise Ratio } S \text{ (dB)} & 18.2 & 25.4 & 15.1 & 22.8 & 12.5 \\ \hline \text{Subjective Clarity Rating } R & 4.3 & 7.9 & 5.6 & 6.8 & 3.9 \\ \hline \end{array} TransducerSignal-to-Noise Ratio S (dB)Subjective Clarity Rating Rα18.24.3β25.47.9γ15.15.6δ22.86.8ϵ12.53.9Calculate Spearman's rank correlation coefficient for this sample.
Stating your hypotheses clearly, test at the 5% level of significance whether these data provide evidence to support the engineer's suspicion.
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