he 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 s ach will be selected in what are called mock drafts. Players who are considered to have superior potential as professional football players are sele ervice of what position in the first round players from the Atlantic Coast Conference, the Big Ten Conference, the PAC-12 Conference, and the Sou ACC Big Ten PAC-12 SEC College Attended Projected Draft Projected Draft College Attended Projected Draft College Attended Projected Draft College Attended Position Position Position Position Florida State Iowa USC Florida 1 Clemson 5. Michigan St 10 Oregon Alabama 3. Miami 9. Nebraska 14 Oregon 15 Kentucky Georgia Tech 11 Minnesota 28 Washington 18 Texas A&M 12 Louisville 16 Wisconsin 29 UCLA 19 Missouri 13 Wake Forest 20 UCLA 21 Alabama 17 Florida State 22 Stanford 23 LSU 25 Virginia Tech 26 Arizona St 24 LSU 27 Use the Kruskal-Wallis test to determine if there is any difference among NFL teams for players from these four conferences. Use a = 0.05. State the null and alternative hypotheses. O Ho: The populations for the mock draft positions of the four conferences are identical. H: The populations for the mock draft positions of the four conferences are not all identical. O Ho: Median H MedianACC= Mediangig Ten ACC Median Big Ten * MedianpAC-12 * MedianSEC = Median PAC-12 %23 = Mediansec %3D O H: Median Median gig Ten Median PAC-12 MediansEC %3D %3D ACC H: Median ACC Mediangig Ten < Median PAC-12 > MedianSEC O Ho: Median H: MedianACC * Median Big Ten Median pAC-12 = Median SEC Median PAC-12 ACC MediangBig Ten %3D + MedianSEC O Ho: The populations for the mock draft positions of the four conferences are not all identical. H The populations for the mock draft positions of the four conferences are identical.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
The second slide is the first part of the question and the first slide is the second part of the question.
![Find the value of the test statistic. (Round your answer to two decimal places.)
\[ \text{Value: } \_\_\_ \]
What is the \( p \)-value? (Round your answer to three decimal places.)
\[ p\text{-value: } \_\_\_ \]
What is your conclusion?
- O Reject \( H_0 \). There is sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.
- O Do not reject \( H_0 \). There is sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.
- O Do not reject \( H_0 \). There is not sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.
- O Reject \( H_0 \). There is not sufficient evidence to conclude that there is a significant difference among NFL teams for players from these four conferences.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70237df8-dfb4-41d0-af11-e6f29414ce12%2F1fde355e-e5c3-4e36-9ed3-c1c650eb0056%2F58th3p6_processed.jpeg&w=3840&q=75)
Given Information :
The National Football League (NFL) at the a g e s Anach year to the da t ing news Services project the players who will be drafted along with the order in which each will be selected in what are called mock des Players who we condered to have w e a polesaltooth e rs are wected earlier in the deal. Suppose the following table shows prosections 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 Southern Conference will be seated PAC 12 Projected College College bra Antended Position Floride Alabama .
First, all the data needs to be put together in one column as shown below:
| Sample | Value |
| 1 | 4 |
| 1 | 5 |
| 1 | 9 |
| 1 | 11 |
| 1 | 16 |
| 1 | 20 |
| 1 | 22 |
| 1 | 26 |
| 2 | 6 |
| 2 | 10 |
| 2 | 14 |
| 2 | 28 |
| 2 | 29 |
| 3 | 2 |
| 3 | 7 |
| 3 | 15 |
| 3 | 18 |
| 3 | 19 |
| 3 | 21 |
| 3 | 23 |
| 3 | 24 |
| 4 | 1 |
| 4 | 3 |
| 4 | 8 |
| 4 | 12 |
| 4 | 13 |
| 4 | 17 |
| 4 | 25 |
| 4 | 27 |
Now, the data needs to be organized in ascending order by value (keeping track of what sample the values belongs to). The results are shown below:
| Sample | Value (In Asc. Order) |
| 4 | 1 |
| 3 | 2 |
| 4 | 3 |
| 1 | 4 |
| 1 | 5 |
| 2 | 6 |
| 3 | 7 |
| 4 | 8 |
| 1 | 9 |
| 2 | 10 |
| 1 | 11 |
| 4 | 12 |
| 4 | 13 |
| 2 | 14 |
| 3 | 15 |
| 1 | 16 |
| 4 | 17 |
| 3 | 18 |
| 3 | 19 |
| 1 | 20 |
| 3 | 21 |
| 1 | 22 |
| 3 | 23 |
| 3 | 24 |
| 4 | 25 |
| 1 | 26 |
| 4 | 27 |
| 2 | 28 |
| 2 | 29 |
Now, we need to assign ranks to the values that are already organized in ascending order. Make sure that take the average of ranks in case of rank ties (Ex. If two values shared the first place in the list, instead of assigning rank 1 and rank 2 to them, assign rank 1.5 to both) The following ranks are obtained:
| Sample | Value (In Asc. Order) | Rank | Rank (Adjusted for ties) |
| 4 | 1 | 1 | 1 |
| 3 | 2 | 2 | 2 |
| 4 | 3 | 3 | 3 |
| 1 | 4 | 4 | 4 |
| 1 | 5 | 5 | 5 |
| 2 | 6 | 6 | 6 |
| 3 | 7 | 7 | 7 |
| 4 | 8 | 8 | 8 |
| 1 | 9 | 9 | 9 |
| 2 | 10 | 10 | 10 |
| 1 | 11 | 11 | 11 |
| 4 | 12 | 12 | 12 |
| 4 | 13 | 13 | 13 |
| 2 | 14 | 14 | 14 |
| 3 | 15 | 15 | 15 |
| 1 | 16 | 16 | 16 |
| 4 | 17 | 17 | 17 |
| 3 | 18 | 18 | 18 |
| 3 | 19 | 19 | 19 |
| 1 | 20 | 20 | 20 |
| 3 | 21 | 21 | 21 |
| 1 | 22 | 22 | 22 |
| 3 | 23 | 23 | 23 |
| 3 | 24 | 24 | 24 |
| 4 | 25 | 25 | 25 |
| 1 | 26 | 26 | 26 |
| 4 | 27 | 27 | 27 |
| 2 | 28 | 28 | 28 |
| 2 | 29 | 29 | 29 |
In order to compute the sum of rank for each sample, it is easier to organize the above table by samples. The following is obtained:
| Sample | Value | Rank (Adjusted for ties) |
| 1 | 4 | 4 |
| 1 | 5 | 5 |
| 1 | 9 | 9 |
| 1 | 11 | 11 |
| 1 | 16 | 16 |
| 1 | 20 | 20 |
| 1 | 22 | 22 |
| 1 | 26 | 26 |
| 2 | 6 | 6 |
| 2 | 10 | 10 |
| 2 | 14 | 14 |
| 2 | 28 | 28 |
| 2 | 29 | 29 |
| 3 | 2 | 2 |
| 3 | 7 | 7 |
| 3 | 15 | 15 |
| 3 | 18 | 18 |
| 3 | 19 | 19 |
| 3 | 21 | 21 |
| 3 | 23 | 23 |
| 3 | 24 | 24 |
| 4 | 1 | 1 |
| 4 | 3 | 3 |
| 4 | 8 | 8 |
| 4 | 12 | 12 |
| 4 | 13 | 13 |
| 4 | 17 | 17 |
| 4 | 25 | 25 |
| 4 | 27 | 27 |
With the information provided we can now easily compute the sum of ranks for each of the samples:
R1 = 4 + 5 + 9 + 11 + 16 + 20 + 22 + 26 = 113
R2 = 6 + 10 + 14 + 28 + 29 = 87
R3 = 2 + 7 + 15 + 18 + 19 + 21 + 23 + 24 = 129
R4 = 1 + 3 + 8 + 12 + 13 + 17 + 25 + 27 = 106
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