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.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.