Question

Tom designed a complete factorial experiment with 2 factors. One factor had 4 levels, the other had 5 levels. For each combination of levels of factors, there were 6 replicates.

**A) In the ANOVA table associated with this design, what
were the degrees of freedom of the interaction?**

a. 7

b. 12

c. 20

d. 24

e. 30

**B) Suppose we want to test the significance of the main
effect of the factor with 4 levels. What is the distribution we use
to calculate p-value**.

a. F (3,100)

b. F (4,120)

c. F (4,100)

d. F (5,100)

e. F (5,120)

Answer #1

**(A) **the correct answer is option
**b. 12**

**(B) **the correct answer is option
**a. F(3,100)**

For a complete factorial experiment with 6 factors each having 2
levels, find the following –
Total degrees of freedom
Specify the highest order interaction effect
Number of 3 factor interaction
Number of 6 factor interaction
Specify the main factor effects
Number of 4 factor interaction
Number of 7 factor interaction
Total number of factorial effects

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 284, SSA = 29,
SSB = 24, SSAB = 176. Set up the ANOVA table. (Round your values
for mean squares and F to two decimal places, and your
p-values to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Factor A
Factor B
Interaction
Error...

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 282, SSA =
28,SSB = 23, SSAB = 173. Set up the ANOVA table. (Round your values
for mean squares and F to two decimal places, and your
p-values to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Factor A
?
?
?
?
?...

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST= 248, SSA= 22,
SSB= 21, SSAB= 155.
Set up the ANOVA table and test for significance using alpha=
.05 . Show entries to 2 decimals, if necessary. If the answer is
zero enter “0”.
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Factor A
Factor B
Interaction
Error
Total

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST=286, SSA=24,
SSB=22, SSAB=185..
Set up the ANOVA table and test for significance using a=.05.
Show entries to 2 decimals, if necessary. If the answer is zero
enter “0”.
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Factor A
Factor B
Interaction
Error
Total
The -value for Factor A is...

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 291, SSA = 20,
SSB = 24, SSAB = 195.
Set up the ANOVA table and test for significance
using = .05. Show entries to 2 decimals, if necessary.
Round p-value to four decimal places. If your answer is
zero enter "0".
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F...

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 269, SSA = 26,
SSB = 21, SSAB = 171. Set up the ANOVA table. (Round your values
for mean squares and F to two decimal places, and your
p-values to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Factor A
Factor B
Interaction
Error...

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 282, SSA = 28,
SSB = 24, SSAB = 176. Set up the ANOVA table. (Round your values
for mean squares and F to two decimal places, and your
p-values to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Factor A
Factor B
Interaction
Error...

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: SST = 286, SSA = 28,
SSB = 22, SSAB = 177. Set up the ANOVA table. (Round your values
for mean squares and F to two decimal places, and your
p-values to three decimal places.)
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Factor A
Factor B
Interaction
Error...

The calculations for a factorial experiment involving four
levels of factor A, three levels of factor B, and three
replications resulted in the following data: ,STT = 261, SSA=21,
SSB=22, SSAB=165
Set up the ANOVA table and test for significance using a=.05 .
Show entries to 2 decimals, if necessary. If the answer is zero
enter “0”.
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Factor A
Factor B
Interaction
Error
Total
The -value for...

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