Question

In: Statistics and Probability

Use the accompanying partially completed​ two-way ANOVA summary table to complete parts a through e below....

Use the accompanying partially completed​ two-way ANOVA summary table to complete parts a through e below.

Click the icon to view the table. ​

a) Complete the​ two-way ANOVA table below.

Source Sum of Squares Degrees of Freedom Mean Sum of Squares    F

Factor A    140 2    ? ?

Factor B    ?    2 ? ?

Interaction 20    ?    ? ?

Error 36 ?

Total 700 44

​(Type integers or​ decimals.) ​

b) How many replications are present for each​ cell?

r= ​

c) Using α=0.10​, 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. H 0 H0​: mu Subscript Upper A Baseline equals mu Subscript Upper B μA=μB​, Upper H 1 H1​: mu Subscript Upper A Baseline not equals mu Subscript Upper B μA≠μB

B. H 0 H0​: Factor A and B do not​ interact, Upper H 1 H1​: Factor A and B do interact

C. H 0 H0​: Factor A and B do​ interact, Upper H 1 H1​: Factor A and B do not interact

D. H 0 H0​: μA≠μB​, H1​: μA=μB

Find the​ p-value for the interaction between Factors A and B.

​p-value equals = ​(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. Do not reject Do not reject the null hypothesis. There is insufficient evidence to conclude that the means differ

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 Factors A and B interact.

D. Do not reject the null hypothesis. There is insufficient evidence to conclude that Factors A and B interact. ​

d) Using α ​= 0.10​, are the Factor A means​ different?

Identify the hypotheses to test for Factor A. Choose the correct answer below.

A. H0​: μA1=μA2=μA3​, H1​:μA1>μA2>μA3

B. H0​:μA1=μA2=μA3​, Upper H 1 H1​: Not all Factor A means are equal

C. H0​: μA=μB​, H1​:μA≠μB

D. H0​: μA1≠μA2≠μA3​, H1​: μA1=μA2=μA3

Find the​ p-value for Factor A. ​

p-value equals = ​(Round to three decimal places as​ needed.) Draw the appropriate conclusion for Factor A. Choose the correct answer below.

A. Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.

B. Do not reject the null hypothesis. There is insufficient evidence to conclude that not all Factor A means are equal.

C. Reject the null hypothesis. There is sufficient 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. ​

e) Using a α ​= 0.10​, are the Factor B means​ different? Identify the hypotheses to test for Factor B. Choose the correct answer below.

A. H0​: μA=μB​, H1​:μA≠μB

B. H0​:μB1≠μB2≠μB3​, H1​:μB1=μB2=μB3

C. H0: ​μB1=μB2​, H1​: Not all Factor B means are equal

D. H0​: μB1=μB2=μB3​, H1​: Not all Factor B means are equal

Find the​ p-value for Factor B.

​p-value equals = ​(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 sufficient evidence to conclude that not all Factor B means are equal.

C. Do not reject the null hypothesis. There is sufficient evidence to conclude that the means differ.

D. It is inappropriate to draw a conclusion from this test because the Factors A and B interact. .

Solutions

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