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

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.

State the null and alternative hypotheses.

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 =

What is your conclusion?

Reject H₀. There is sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.

Reject H₀. There is not sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.   

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.

Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.

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

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

Sample 1	Sample 2	Sample 3	Sample 4
4	8	3	1
5	10	7	2
6	11	15	9
13	26	16	12
19	27	17	14
20		21	18
23		22	25
28		24	29

Assign rank to the values taking all the samples as one sample.

Rank for sample 1	Rank for sample 2	Rank for sample 3	Rank for sample 4
4	8	3	1
5	10	7	2
6	11	15	9
13	26	16	12
19	27	17	14
20		21	18
23		22	25
28		24	29

N = 29

n1 = 8

n2 = 5

n3 = 8

n4 = 8

With the information provided we can now easily compute the sum of ranks for each of the samples:

Sum of Rank for Sample 1 = 118

Sum of Rank for Sample 2 = 82

Sum of Rank for Sample 3 = 125

Sum of Rank for Sample 4 = 110

Null and Alternative hypothesis:

Ho: The samples come from populations with equal medians

Ha: The samples come from populations with medians that are not all equal

Test statistic:

H = (12/(N*(N+1))) * (R1²/n1 + R2²/n2 +….+ Rk²/nk) - 3(N+1) = (12/(29*(29+1) * (118²/8 + 82²/5 + 125²/8 + 110²/8) - 3(29+1) = 0.358

df = n-13

p-value = CHISQ.DIST.RT(0.3576, 3) = 0.949

Conclusion:

p-value > α, Do not reject the null hypothesis

Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.

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Q2:

Sample 1	Sample 2	Sample 3	Sample 4
3	9	4	1
5	10	6	2
8	11	15	7
13	26	17	12
18	27	19	14
20		21	16
23		22	25
29		24	28

Rank for sample 1	Rank for sample 2	Rank for sample 3	Rank for sample 4
3	9	4	1
5	10	6	2
8	11	15	7
13	26	17	12
18	27	19	14
20		21	16
23		22	25
29		24	28

N = 29

n1 = 8

n2 = 5

n3 = 8

n4 = 8

With the information provided we can now easily compute the sum of ranks for each of the samples:

Sum of Rank for Sample 1 = 119

Sum of Rank for Sample 2 = 83

Sum of Rank for Sample 3 = 128

Sum of Rank for Sample 4 = 105

Null and Alternative hypothesis:

Ho: The samples come from populations with equal medians

Ha: The samples come from populations with medians that are not all equal

Test statistic:

H = (12/(N*(N+1))) * (R1²/n1 + R2²/n2 +….+ Rk²/nk) - 3(N+1) = (12/(29*(29+1) * (119²/8 + 83²/5 + 128²/8 + 105²/8) - 3(29+1) = 0.677

df = n-13

p-value = CHISQ.DIST.RT(0.6766, 3) = 0.879

Conclusion:

p-value > α, Do not reject the null hypothesis