A chemist is investigating the effect of a specific catalyst on the speed of a chemical reaction. The chemist records the concentration of the catalyst, ccc grams per litre, and the reaction time, TTT seconds, for 8 experimental trials. The data is summarised as follows:
∑c=40∑T=520∑cT=2360∑T2=35300Scc=42 \sum c = 40 \quad \sum T = 520 \quad \sum cT = 2360 \quad \sum T^2 = 35300 \quad S_{cc} = 42 ∑c=40∑T=520∑cT=2360∑T2=35300Scc=42Calculate the exact value of ScTS_{cT}ScT and the exact value of STTS_{TT}STT.
Calculate the value of the product moment correlation coefficient between ccc and TTT.
Show that the equation of the regression line of TTT on ccc can be written as
T=93.6−5.71c T = 93.6 - 5.71c T=93.6−5.71cwhere the values of the intercept and gradient are given to 3 significant figures.
Give an interpretation, in context, of the gradient of the regression line.
Using the equation of the regression line given in part (c): (i) estimate the reaction time for a catalyst concentration of 6 g/L,
(ii) explain why an estimate for the reaction time for a catalyst concentration of 20 g/L is likely to be unreliable.
According to this model, calculate the increase in catalyst concentration, in g/L, required for the reaction time to decrease by 12 seconds.
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.