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Consider the accompanying data collected for a two-way ANOVA.
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a) |
Using α = 0.05, is there significant interaction between Factors A and B? |
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b) |
Using α = 0.05, are the Factor A means different? |
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c) |
Using α = 0.05, are the Factor B means different? |
a) Usingα= 0.05, is there significant interaction between Factors A and B?
Identify the hypotheses for the interaction between Factors A and B. Choose the correct answer below.
A.H0: Factor A and B do not interact, Upper H 1H1: Factor A and B do interact
B.H0: Factor A and B do interact, Upper H 1H1: Factor A and B do not interact
C.H0:
D.H0:
Find the p-value for the interaction between Factors A and B.
p-value =
(Round to three decimal places as needed.)
Draw the appropriate conclusion for the interaction between Factors A and B. Choose the correct answer below.
A.Reject the null hypothesis. There is sufficient evidence to conclude that Factors A and B interact.
B.Do not rejectthe null hypothesis. There is insufficientevidence to conclude that Factors A and interact.
C.Do not reject the null hypothesis. There is insufficient evidence to conclude that the means differ.
D.Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.
b) Usingα= 0.05, are the Factor A means different?
Identify the hypotheses to test for Factor A. Choose the correct answer below.
A.
B. Not all Factor A means are equal
C.
D.
Find the p-value for Factor A.
p-value=
(Round to three decimal places as needed.)
Draw the appropriate conclusion for Factor A. Choose the correct answer below.
A.Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor A means are equal.
B.Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.
C.Do not reject the null hypothesis. There is insufficient evidence to conclude that not all Factor A means are equal.
D.It is inappropriate to draw a conclusion from this test because the Factors A and B interact.
c) Usingα= 0.05, are the Factor B means different?
Identify the hypotheses to test for Factor B. Choose the correct answer below.
A.
B.
C. ,
D.
Find the p-value for Factor B.
p-value=
(Round to three decimal places as needed.)
Draw the appropriate conclusion for Factor B. Choose the correct answer below.
A.Do not reject the null hypothesis. There is insufficient evidence to conclude that not all Factor B means are equal.
B. Reject the null hypothesis. There is insufficient evidence to conclude that the means differ.
C.Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor B means are equal.
D.It is inappropriate to draw a conclusion from this test because the Factors A and B interact.
applying two way ANOVA on above data:
| Source of Variation | SS | df | MS | F | P-value |
| factor B | 0 | 1 | 0 | 0.000 | 1.000 |
| factor A | 367 | 2 | 183.5 | 4.850 | 0.029 |
| Interaction | 1 | 2 | 0.5 | 0.013 | 0.987 |
| error | 454 | 12 | 37.83333 | ||
| Total | 822 | 17 |
a) option A.H0: Factor A and B do not interact, Upper H 1H1: Factor A and B do interact
p-value =0.987
option B.Do not rejectthe null hypothesis. There is insufficientevidence to conclude that Factors A and interact.
b)
Ho: all factor A means are equal
Ha:Not all Factor A means are equal
p value =0.029
A.Reject the null hypothesis. There is sufficient evidence to conclude that not all Factor A means are equal.
c)
Ho: all factor B means are equal
Ha:Not all Factor B means are equal
p value =1.000
A.Do not reject the null hypothesis. There is insufficient evidence to conclude that not all Factor B means are equal.
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