Question

In: Statistics and Probability

The National Football League (NFL) holds its annual draft of the nation's best college football players...

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 12 Oregon 15 Kentucky 8
Georgia Tech 13 Minnesota 27 Washington 17 Texas A&M 11
Louisville 19 Wisconsin 29 UCLA 18 Missouri 14
Wake Forest 20 UCLA 22 Alabama 16
Florida State 21 Stanford 23 LSU 25
Virginia Tech 28 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: MedianACC = MedianBig Ten = MedianPAC-12 = MedianSEC
Ha: MedianACC > MedianBig Ten < MedianPAC-12 > MedianSEC

H0: MedianACC = MedianBig Ten = MedianPAC-12 = MedianSEC
Ha: MedianACC ≠ MedianBig Ten ≠ MedianPAC-12 ≠ MedianSEC    

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

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

H0: MedianACC ≠ MedianBig Ten ≠ MedianPAC-12 ≠ MedianSEC
Ha: MedianACC = MedianBig Ten = MedianPAC-12 = MedianSEC

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 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.   

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.

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

Solutions

Expert Solution

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

test stast:H= =(12/(N*(N+1)))*∑(∑Ri)2/ni )-3*(N+1)= 0.89
degree of freedom =number of groups-1= 3
p value = 0.829 (from excel:chidist(0.886,3)

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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