Question

Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.

Treatment **A B C**

**1** 11 10 9

Blocks **2** 12 6 6

**3** 18 16 14

**4** 21 18 19

**5** 8 8 9

Use = .05 to test for any significant differences. 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 p-value

Answer #1

To test the treatment factor,

P-value = 0.048 < 0.05, so we fail to reject H_{0}
and we can conclude that there is significant treatment factor
present in response variable or we can say that alteast one
treatment mean is significantly different.

To test the block factor,

P-value = 0 < 0.05, so we reject H_{0} and we can
conclude that there is significant block factor present in response
variable or we can say that alteast one block mean is significantly
different.

In a completely randomized design, 12 experimental units were
used for the first treatment, 15 for the second treatment, and 20
for the third treatment. Complete the following analysis of
variance (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
Treatments
1400
Error
Total
1800
At a .05 level of significance, is there a significant
difference between the treatments?
The p-value is - Select...

In a completely randomized design, 12 experimental units were
used for the first treatment, 15 for the second treatment, and 20
for the third treatment. Complete the following analysis of
variance (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
Treatments
1,200
Error
Total
1,800
At a .05 level of significance, is there a significant
difference between the treatments?
The -value is - Select...

In a completely randomized design, 12 experimental units were
used for the first treatment, 15 for the second treatment, and 20
for the third treatment. Complete the following analysis of
variance (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
Treatments
1100
Error
700
44
xx
xxxx
Total
1800
xx
xxx

In a completely randomized design, eight experimental units were
used for each of the five levels of the factor. Complete the
following ANOVA table.
Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F
p-value
Treatments
360
Error
Total
470

Part B
In a completely randomized design, 7 experimental units were
used for each of
the three levels of the factor. (2
points each; 6 points total)
Source of
Variation
Sum of
Squares
Degrees of
Freedom
Mean
Square
F
Treatment
Error
432076.5
Total
675643.3
Complete the ANOVA table.
Find the critical value at the 0.05 level of significance from
the F table for testing whether the population means for the three
levels of the factors are different.
Use the critical...

An experiment has been conducted for four treatments with eight
blocks. Complete the following analysis of variance table (to 2
decimals but p-value to 4 decimals, if necessary). If
answer is zero enter "0".
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Treatments
700
Blocks
400
Error
Total
1,500
Use alpha= .05 to test for any significant differences.

In a completely randomized experimental design, 6 experimental
units were used for each of the 4 levels of the factor (i.e., 4
treatments):
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
Between Treatments
2434220
3
811406.7
Error (Within Treatments)
3883910
20
194195.5
Total
6318130
23
1. What is the null and alternative
hypothesis for this ANOVA test? (2 Points)
2. Calculate the F test statistic. (2
Points)
3. What is the rejection rule for the F test at
the 0.05...

An experiment has been conducted for four treatments with eight
blocks. Complete the following analysis of variance table (to 2
decimals, if necessary and p-value to 4 decimals). If your
answer is zero enter "0".
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Treatments
900
Blocks
400
Error
Total
1,700

An experiment has been conducted for four treatments with eight
blocks. Complete the following analysis of variance table (to 2
decimals, if necessary and p-value to 4 decimals). If your
answer is zero enter "0".
Source of Variation
Sum of Squares
Degrees of Freedom
Mean Square
F
p-value
Treatments
800
Blocks
300
Error
Total
1,700

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

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