Question

.A researcher is interested in comparing sunblocks and their protection level for various skin types. He designed a two-factor factorial design with Factor A as type of sunblock with 4 levels and Factor B as skin type with 5 levels. He used 4 replications for each treatment. The protection level was measured on a scale from 1 to 5 based on the overall amount of sunburn for a 8 square centimeter patch of skin on the subjects' backs. Based on the researcher's design, how many total degrees of freedom are there for this experiment?

How many degrees of freedom are associated with the error for this experiment?

The SST was found to be 386.4 and the MSE was found to be 4.78. Compute the value of the F test statistic for the treatments.

Find the appropriate critical value for the hypothesis test for Factor B using an alpha of 0.05.

The results of a two-factor factorial experiment are shown in the table below:

Levels of Factor B : 1, 2

Levels of Factor A: A, B

A1: 8, 7

A2: 11, 13

B1: 10, 12

B2: 6, 5

Compute the SSA for this experiment

Answer #1

Based on the researcher's design, how many total degrees of freedom are there for this experiment?

(4-1) + (5-1) + 3*4 + 60 - 1= 79

How many degrees of freedom are associated with the error for this experiment?

60

The SST was found to be 386.4 and the MSE was found to be 4.78. Compute the value of the F test statistic for the treatments.

Not possible from this data.

Find the appropriate critical value for the hypothesis test for Factor B using an alpha of 0.05.

The critical value is 2.525.

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 = 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 = 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=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 = 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...

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