The carbon mass percentage, CCC, and the Vickers hardness index, HHH, of n=12n = 12n=12 steel alloy specimens were recorded during a quality control test.
Summary statistics for the data are as follows:
∑C=5.4∑C2=2.5074SHH=45.6SCH=1.62 \sum C = 5.4 \quad \sum C^2 = 2.5074 \quad S_{HH} = 45.6 \quad S_{CH} = 1.62 ∑C=5.4∑C2=2.5074SHH=45.6SCH=1.62(i) Calculate the mean carbon mass percentage, Cˉ\bar{C}Cˉ.
(ii) Show that the standard deviation of the carbon mass percentages is 0.08030.08030.0803 to 3 significant figures.
Calculate the product moment correlation coefficient (PMCC) between CCC and HHH.
For an industrial report, the carbon data were transformed using the linear coding P=100C−10P = 100C - 10P=100C−10.
Use your results from part (a) to calculate the mean and the standard deviation of the transformed values, PPP.
Given that QQQ is the transformed hardness index using the same linear coding Q=100H−10Q = 100H - 10Q=100H−10, state the value of the product moment correlation coefficient between PPP and QQQ. Give a reason for your answer.
