Question

In: Statistics and Probability

Professor Bert Forman believes the students who complete his examinations in the shortest time receive the...

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.

Solutions

Expert Solution

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.

Hope this will be helpful. Thanks and God Bless You:) Thumbs up, if this will helps:)


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