Question

Ten new sales representatives for Clark Sprocket and Chain, Inc. were required to attend a training program before being assigned to a regional sales office. At the end of the program, the representatives took a series of tests and the scores were ranked. For example, Arden had the lowest test score and is ranked 1; Arbuckle had the highest test score and is ranked 10. At the end of the first sales year, the representatives’ ranks based on test scores were paired with their first year sales.

				Ranking in				Past		Ranking in
		Annual Sales		Training				Annual Sales		Training
Representative		($ thousands)		Program		Representative		($ thousands)		Program
Kitchen		319		8		Arden		300		1
Bond		150		2		Crane		280		6
Gross		175		5		Arthur		200		9
Arbuckle		460		10		Keene		190		4
Greene		348		7		Knopf		300		3

1. Compute and interpret the coefficient of rank correlation between first-year sales and class rank after the training program. (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places.)

	Representative Sales Rank Training d d-square 1 319 8.00    8    2 150 1.00 2 3 175 2.00 5 4 460 10.00 10 5 348 9.00 7 6 300 6.50 1 7 280 5.00 6 8 200 4.00 9 9 190 3.00 4 10 300 6.50 3 0.00

1. a-2. Determine Spearman’s rank correlation coefficient. (Round your answer to 3 decimal places.)

Spearman’s coefficient of rank correlation =

1. b-1. State the decision rule. Use the 0.05 significance level. (Round your answer to 3 decimal places.)

	Reject H0 if t >

  

1. b-2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

t=

1. b-3. At the 0.05 significance level, can we conclude that there is a positive association between first-year sales dollars and ranking in the training program?

H0 is(not rejected) .There is (no positive) association between first-year sales dollars and ranking in the training program.

Answer 1

a-1) From the given data

Representative	Sales	Rank	Training	d	d-square
1	319	8	8	0	0
2	150	1	2	-1	1
3	175	2	5	-3	9
4	460	10	10	0	0
5	348	9	7	2	4
6	300	6.5	1	5.5	30.25
7	280	5	6	-1	1
8	200	4	9	-5	25
9	190	3	4	-1	1
10	300	6.5	3	3.5	12.25
				Total:	83.5

a-2)

b-1) t - critical value = 2.306

Reject H0 if t > 2.306

b-2) Test Statistic:

b-3) since t value = 1.6066 < t critical value so we accept H0

Thus conclude that

H0 is(not rejected) .There is (no positive) association between first-year sales dollars and ranking in the training program.