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3)Answer :

Do Kruskal-Wallis Analysis

Hypotheses

Ho: The three populations represented by the data are identical.

H1: There is a difference between the three groups. (claim)

Let Group 1= control, Group 2= LSD, Group 3= UML

Test Statistic

Group Ranks Rank Sums

1

2

3

7.5 7.5 11 17.5 17.5 20.5 20.5 23.5 25 26 27

2 4.5 4.5 7.5 11 14 16 20.5

1 3 7.5 11 14 14 20.5 23.5

203.5

80.0

94.5

N=27, R1=203.5, R2=80, R3=94

H=

H=

H =6.17508

Decision

Since the sample sizes all exceed 5, we must use the chi-square table (A.11). Thecritical value of chi-square for -1=2 for = 0.05 is 5.991.

Thus, with H = 6.17508 which is greater than 5.991 we reject H0.

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Conclusion

There is enough evidence to support the claim that there is a difference among the

three groups.

We continuous the step by doing multiple comparison.

Using multiple comparison test to test each pair of medians in exercise 6.1 to

see whether a specific difference exists at =0.2.

Since H0: The three population represented by the data are identical is

rejected. Means that there is a difference among the medians, we are

interested to know where the difference is.

Multiple Comparison

1) Hypothesis:

a) H0: M1 = M2

H1: M1 M2

b) H0: M1 = M3

H1: M1 M3

c) H0: M2 = M3

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H1: M2 M3

2) Test statistic:

=0.2

k=3

So there will be k (k-1) = 3(3-1) =3 comparison to make

The next step is to find in table A.2 the value ofz that has area to it

right.

From table A.2, value of z for 0.033 of the area to the right is 1.84

/k (k-1) =0.2/3(2)=0.033, .

The mean of the rank for the three samples:

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1) 1= = 18.5

2) 2= = 10

3) 3= = 11.81

ksamples are all of the different size

Compare group 1 and 2

Hence 8.5 > 6.79

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Compare group 1 and 3

Hence 6.69 < 6.79

Compare group 2 and 3

Hence 1.81 < 7.30

3)Decision :

a) Since 8.5 > 6.79 reject the H0. The comparison is significant.

b) Since 6.69 < 6.79, do not reject the H0. The comparison is not

significant.

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c) Since 1.81 < 7.30, do not reject the H0. The comparison is not

significant.

4) Conclusion:

a) There are enough evident to support the claim that there are different

between median group 1 and 2. We can conclude that the medians of

populations 1 and 2 are not equal.

b) There are not enough evident to support the claim that there are different

between median group 1 and 3. We cannot conclude that the medians of

populations 1 and 3 may be equal.

c) There are not enough evident to support the claim that there are different

between median group 2 and 3. We can conclude that medians of

populations 2 and 3 may be equal.