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 of11 salespeopletrained in the last year follow, wherexis rank in training class andyis rank in sales after1 year.Lower ranks mean higher standing in class and higher net sales.

Person1234567891011xrank3245161110978yrank2154627111098

Using a 0.05 level of significance, test the claim that the relation betweenxandyis monotone (either increasing or decreasing).

(a)

What is the level of significance?

State the null and alternate hypotheses.

H_o:_s= 0;H₁:_s> 0

H_o:_s= 0;H₁:_s< 0

H_o:_s0;H₁:_s= 0

H_o:_s= 0;H₁:_s0

(b)

Compute the sample test statistic. (Use 3 decimal places.)

(c)

Find theP-value interval of the sample test statistic.

0.002 <P-value < 0.01

0.01 <P-value < 0.05

0.05 <P-value < 0.10

(d)

Conclude the test.

At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e)

Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that a monotonic relationship exists between the rank in training class and sales.

Fail to reject the null hypothesis, there is insufficient evidence that a monotonic relationship exists between the rank in training class and sales.

Reject the null hypothesis, there is sufficient evidence that a monotonic relationship exists between the rank in training class and sales.

Reject the null hypothesis, there is insufficient evidence that a monotonic relationship exists between the rank in training class and sales.