An industrial chemist is investigating the relationship between the reaction temperature, T T\,T in Kelvin (K\text{K}K), and the resulting chemical yield, Y Y\,Y in grams (g\text{g}g), of a specific synthetic process. A series of 12 experimental trials is conducted, and the data are recorded.
The summary statistics for the trials are as follows:
n=12,∑T=3900,∑Y=1800,∑Y2=273600,STT=2400,STY=2100 n = 12, \quad \sum T = 3900, \quad \sum Y = 1800, \quad \sum Y^2 = 273600, \quad S_{TT} = 2400, \quad S_{TY} = 2100 n=12,∑T=3900,∑Y=1800,∑Y2=273600,STT=2400,STY=2100Calculate the product moment correlation coefficient between T T\,T and YYY.
Give an interpretation of your product moment correlation coefficient in the context of the study.
Find the equation of the least squares regression line of Y Y\,Y on T T\,T in the form Y=a+bTY = a + bTY=a+bT.
Give an interpretation of the value of b b\,b in your regression line.
(i) Use the regression line from part (c) to estimate the chemical yield for a reaction performed at a temperature of 380 K.
(ii) Comment on the reliability of your answer in part (i) given that the range of temperatures in the sample was 305 K to 345 K.
Using the regression line from part (c), the researcher estimates that for a temperature increase of x Kx\text{ K}x K, there will be an increase of 14 g in the chemical yield.
Find the value of xxx.
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.