A civil engineer investigates the relationship between the concentration of a chemical additive, ccc (grams per litre), and the setting time of a high-performance concrete, ttt (minutes). A random sample of 50 batches was analysed, and the following summary statistics were obtained:
∑c=450,∑c2=4275,∑t=7200,∑ct=63650,Stt=8200 \sum c = 450, \quad \sum c^2 = 4275, \quad \sum t = 7200, \quad \sum ct = 63650, \quad S_{tt} = 8200 ∑c=450,∑c2=4275,∑t=7200,∑ct=63650,Stt=8200Determine the values of SccS_{cc}Scc and SctS_{ct}Sct.
Calculate the product moment correlation coefficient between c c\,c and ttt, giving your answer to 3 significant figures.
Interpret your result from part (b) in the context of the engineer's investigation.
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.