A chemical engineer is investigating the relationship between the temperature of a solvent, TTT (in ∘C^\circ\text{C}∘C), and the mass of a specific solute that dissolves in it, ddd (in grams). A random sample of 15 trials was conducted, and the following summary statistics were recorded:
∑T=975∑T2=64125∑d=420Sdd=560∑Td=27930 \sum T = 975 \quad \sum T^2 = 64125 \quad \sum d = 420 \quad S_{dd} = 560 \quad \sum Td = 27930 ∑T=975∑T2=64125∑d=420Sdd=560∑Td=27930Find the values of STTS_{TT}STT and STdS_{Td}STd.
Calculate, to 3 significant figures, the product moment correlation coefficient between TTT and ddd.
The engineer also measured the viscosity of the solvent, vvv, during these 15 trials. The product moment correlation coefficient between TTT and vvv was found to be −0.552-0.552−0.552.
Describe, giving a reason, the nature of the correlation you would expect to find between vvv and ddd.
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.