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.
