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

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.

H₀: Median_ACC = Median_{Big Ten} = Median_PAC-12 = Median_SEC
H_a: Median_ACC ≠ Median_{Big Ten} ≠ Median_PAC-12 ≠ Median_SECH₀: The populations for the mock draft positions of the four conferences are not all identical.
H_a: The populations for the mock draft positions of the four conferences are identical.    H₀: The populations for the mock draft positions of the four conferences are identical.
H_a: The populations for the mock draft positions of the four conferences are not all identical.H₀: Median_ACC = Median_{Big Ten} = Median_PAC-12 = Median_SEC
H_a: Median_ACC > Median_{Big Ten} < Median_PAC-12 > Median_SECH₀: Median_ACC ≠ Median_{Big Ten} ≠ Median_PAC-12 ≠ Median_SEC
H_a: Median_ACC = Median_{Big Ten} = Median_PAC-12 = Median_SEC

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

Answer 1

The statistical software output for this problem is:

Kruskal-Wallis results: Data stored in separate columns. DF Chi-Square P-value 3 0.82172414 0.8443 Summary statistics Column. nMedian Ave. Rank ACC 14 14.625 Big Ten 14 17.2 PAC-12 8 17.5 15.875 SEC 8 13.125 5

Hence,

Hypotheses:

H₀: The populations for the mock draft positions of the four conferences are identical.
H_a: The populations for the mock draft positions of the four conferences are not all identical.

Test statistic = 0.82

p - Value = 0.844

Conclusion: Option B is correct.