In a research to determine the relationship between performance of students in an entrance examination...
FURTHER MATHEMATICS
WAEC 2019
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
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