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# In a research to determine the relationship between performance of students in an entrance examination…

In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten randomly selected students wre obtained as follows;

 Students A B C D E F G H I Performance in Entrance Examination 11 12 8 13 6 15 10 14 17 School Performance 5 10 9 7 4 8 6 14 11

1, Calculate the spearman’s rank correlation coefficient

2. What would be the researcher’s from the result in a?

##### Explanation

(a)

 R(_1) 4 5 2 6 1 8 3 7 10 9 R(_2) 2 7 6 4 1 5 3 10 8 9 d(_1) 2 -2 -4 2 0 3 0 -3 2 0 d(_2) 4 4 16 4 0 9 0 9 4 0

Then (sum d_1^2) = 50

The spearman’s coefficient = 1 – (frac{6 times 50}{10(100 – 1)}) = 1 – 0.30303 = 0.697

(b) We conclude that there exist positive correlation between performance in entrance examination and school performance