Question

The National Football League (NFL) holds its annual draft of the nation's best college football players in April each year. Prior to the draft, various sporting news services project the players who will be drafted along with the order in which each will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are selected earlier in the draft. Suppose the following table shows projections by one mock draft service of what position in the first round players from the Atlantic Coast Conference, the Big Ten Conference, the PAC-12 Conference, and the Southeastern Conference will be selected.

ACC		Big Ten		PAC-12		SEC
College Attended	Projected Draft Position	College Attended	Projected Draft Position	College Attended	Projected Draft Position	College Attended	Projected Draft Position
Florida State	3	Iowa	6	USC	1	Florida	2
Clemson	5	Michigan St	10	Oregon	8	Alabama	4
Miami	9	Nebraska	12	Oregon	15	Kentucky	7
Georgia Tech	13	Minnesota	26	Washington	17	Texas A&M	11
Louisville	16	Wisconsin	27	UCLA	19	Missouri	14
Wake Forest	20			UCLA	21	Alabama	18
Florida State	23			Stanford	22	LSU	25
Virginia Tech	29			Arizona St	24	LSU	28

Use the Kruskal-Wallis test to determine if there is any difference among NFL teams for players from these four conferences. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.) ____________.

What is the p-value? (Round your answer to three decimal places.)

p-value =__________.

Answer 1

The data is given as ranks only and no need to arrange the whole data in order. We can directly proceed with the analysis.

Null Hypothesis: Population medians are equal.

Alternate Hypothesis: Population medians are not equal.

Test Statistic: follows a

where

• n = sum of sample sizes for all samples,
• c = number of samples,
• = sum of ranks in the sample,
• = size of the sample.

We calculate the total ranks and the size in each group:

ACC		Big Ten		PAC-12		SEC
College	Projected	College	Projected	College	Projected	College	Projected
Attended	Draft	Attended	Draft	Attended	Draft	Attended	Draft
	Position		Position		Position		Position
Florida State	3	Iowa	6	USC	1	Florida	2
Clemson	5	Michigan St	10	Oregon	8	Alabama	4
Miami	9	Nebraska	12	Oregon	15	Kentucky	7
Georgia Tech	13	Minnesota	26	Washington	17	Texas A&M	11
Louisville	16	Wisconsin	27	UCLA	19	Missouri	14
Wake Forest	20			UCLA	21	Alabama	18
Florida State	23			Stanford	22	LSU	25
Virginia Tech	29			Arizona St	24	LSU	28
	118		81		127		109
	8		5		8		8

We have n=total number=29

c=number of groups=4 ,

and

Find the value of the test statistic. (Round your answer to two decimal places.) 6.856.

The critical value of H is 7.815.

What is the p-value? (Round your answer to three decimal places.)

p-value =0.077