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.
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.