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 2 4 5 3 7 9 y rank 3 6 5 8 9 11 ​ Person 7 8 9 10 11 x rank 10 1 6 8 11 y rank 10 1 4 7 2 ​ Using a 10% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). Estimate the P-value.

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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

2

4

5

3

7

9

y rank

3

6

5

8

9

11

Person

7

8

9

10

11

x rank

10

1

6

8

11

y rank

10

1

4

7

2

Using a 10% level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing). Estimate the P-value.

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