14.42 Petron has formulated a new chemical to be added in their petrol. To determine the effectiveness of the new formulated chemical, they recorded the amount of chemical had been added in the petrol (in liter) and the distances traveled (in km) by 10 automobiles in the follow table:

Chemical 1.8 1.2 2 1 1 1.2 0.8 0.6 1 0.85 Distance 50 75 120 40 48 50 40 41 45 50

a. Calculate the Spearman rank correlation coefficient.

b. Carry out a test of the null hypothesis for Petron to determine the association between the amount of chemical added and distances traveled.