Question

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 shown below:

Student	Order of Completion	Score (50 possible)		Student	Order of Completion			Score (50 possible)
Gromney	1	84		Smythe		7		59
Bates	2	81		Arquette		8		79
MacDonald	3	82		Govito		9		61
Sosa	4	67		Gankowski		10		62
Harris	5	66		Bonfigilo		11		74
Cribb	6	48		Matsui		12		65

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? (Round your answers to 3 decimal places.)

	Coefficient of rank correlation =___

	H0: There is (a positive correlation, no correlation) between the order of completion and the rank of the scores. H1: There is (a positive correlation, no correlation) between the order of completion and the ranks of the scores.

	Reject H0 if t >___ t =___

	H0 is (not rejected, rejected) . There is (a positive association, no association) between the order of finish and the rank of the scores.

Answer 1

Using Excel :

Student	Order of Completion	Score (50 possible)	Rank	d	d^2
Gromney	1	84	12	-11	121
Bates	2	81	10	-8	64
MacDonald	3	82	11	-8	64
Sosa	4	67	7	-3	9
Harris	5	66	6	-1	1
Cribb	6	48	1	5	25
Smythe	7	59	2	5	25
Arquette	8	79	9	-1	1
Govito	9	61	3	6	36
Gankowski	10	62	4	6	36
Bonfigilo	11	74	8	3	9
Matsui	12	65	5	7	49
					440

Spearman's Rank Correlation Coefficient:

=1-1.5384

=-0.5385

The value -0.5384 indicates there exists negative relation between two variables.

H0: The rank correlation in the population is 0

H1: There is positive association between rankings

here alpha=0.05 and degrees of freedom=12-2=10 so t critical value is 1.182

Test statistic

Since the computed t test statistic < 1.182, we do not reject the null hypothesis. So it is reasonable to conclude that there is no positive association between rankings.

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