A data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales. Person 1 2 3 4 5 6 x rank 8 11 2 4 5 3 y rank 7 10 1 3 2 4 Person 7 8 9 10 11 x rank 7 9 10 1 6 y rank 8 11 9 6 5 Using a 1% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). Verify that the Spearman rank correlation coefficient . This implies that the P-value lies between 0.002 and 0.01. State the conclusion of the test and interpret your results with a 1% level of significance.
A data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales.
| Person |
1 |
2 |
3 |
4 |
5 |
6 |
| x rank |
8 |
11 |
2 |
4 |
5 |
3 |
| y rank |
7 |
10 |
1 |
3 |
2 |
4 |
| Person |
7 |
8 |
9 |
10 |
11 |
| x rank |
7 |
9 |
10 |
1 |
6 |
| y rank |
8 |
11 |
9 |
6 |
5 |
Using a 1% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). Verify that the Spearman rank correlation coefficient . This implies that the P-value lies between 0.002 and 0.01. State the conclusion of the test and interpret your results with a 1% level of significance.
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