An environmental scientist monitors the turbidity of water, TTT (NTU), and the human population density, PPP (people per km2^22), in the surrounding river basins across six different geographical zones. The results for the six zones are shown in the table below.
| Zone | Alpha | Beta | Gamma | Delta | Epsilon | Zeta |
|---|---|---|---|---|---|---|
| Turbidity, TTT | 2.4 | 5.2 | 8.1 | 12.0 | 15.6 | 19.8 |
| Population Density, PPP | 110 | 450 | 240 | 680 | 1150 | 920 |
(You may use STT=214.21S_{TT} = 214.21STT=214.21, SPP=803083.33S_{PP} = 803083.33SPP=803083.33, STP=11529.83S_{TP} = 11529.83STP=11529.83)
Test, at the 5% level of significance, whether there is evidence of a non-zero correlation between water turbidity and population density using the product moment correlation coefficient (PMCC). State your hypotheses and the critical value used.
Calculate Spearman’s rank correlation coefficient between the rank of water turbidity and the rank of population density.
Test, at the 5% level of significance, whether there is evidence of a positive correlation between water turbidity and population density using Spearman's rank correlation. State your hypotheses and the critical value used.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.