Professor Bert Forman believes the students who complete his examinations in the shortest time receive the highest grades and those who take the longest to complete them receive the lowest grades. To verify his suspicion, he assigns a rank to the order of finish and then grades the examinations. The results are as follows:


Student Order of Completion Score (50 possible) Student Order of Completion Score (50 possible)
Gromney 1 30 Smythe 7 31
Bates 2 45 Arquette 8 28
MacDonald 3 34 Govito 9 23
Sosa 4 12 Gankowski 10 11
Harris 5 16 Bonfigilo 11 14
Cribb 6 12 Matsui 12 13

Convert the test scores to a rank and find the coefficient of rank correlation between the order of completion and the rank of the test score. At the 0.05 significance level, can Professor Forman conclude there is a positive association between the order of finish and the test scores?

a. Calculate the coefficient of rank correlation. (Round your answer to 3 decimal places.)
b. State the decision rule. (Round your answer to 3 decimal places.)
c. Calcualte the test statistic. (Round your answer to 3 decimal places.)