Question

ANOVA summary table. A partially completed ANOVA tale for a competely randomized design is shown here.

Source |
df |
SS |
MS |
F |

Treatments Error |
4 |
24.7 |
||

Total |
34 |
62.4 |

(a) Complete the ANOVA table.

(b) How many treatments are involved in the experiment?

(c) Do the data provide sufficient evidence to indicate a difference among the treatment means? Test using α = .10.

Answer #1

(A) df(error) = df(total)-df(treatments) = 34-4 = 30

ss(error) = ss(total)-ss(treatments) = 62.4 - 24.7 = 37.7

MS(error) = ss(error)/df(error) = 37.7/30 = 1.26

MS(treatment) = ss(treatment)/df(treatment) = 24.7/4 = 6.18

F = MS(treatment)/MS(error)= 6.18/1.26 = 4.90

(B) Number of treatments = df(treatments) + 1

= 4 + 1

= 5

(C) Using F distribution to find the p value corresponding F statistics, we get

p value = 0.0037

p value is less than 0.10 level of significance, rejecting the null hypothesis.

**We can conclude that there is sufficient evidence to
indicate a difference among the treatment means**

The partially completed ANOVA table for a randomized block
design is presented here. If critical F for treatment is 2.78 and
for blocks is 2.62, Is there any significant effect of treatments
and blocks?
Source
df
SS
MS
calculated F
tabulated F
Treatments
4
14.2
2.78
Blocks
18.4
2.62
Error
24
Total
34
41.7

Consider the partially completed one-way ANOVA summary
table.
Source
SS
df
MS
F
Treatment
150
Error
17
Total
840
21
Using α = 0.05, the critical F-score for this ANOVA procedure
is ________.

The following ANOVA table was obtained from a balanced
completely randomized design:
Source
df
SS
MS
F
Treatment
126
Error
20
16
Total
23
Fill in the blanks in this table.
Determine the number of treatments.
Determine the number of replications per treatment.
Perform a statistical test to see if there is a difference
between the true mean responses to the treatment.

In computing an ANOVA involving four groups of 12 each, the
following partially completed ANOVA table was given. Complete this
table.
Source
SS
df
MS
F
Between
9
Within
Total
20

Consider the partially completed ANOVA summary table below.
Complete parts a through d below. Source df SS MS F Regression 1
700 Residual Total 9 1000
a. Complete the remaining entries in the table. Source df SS MS
F Regression 1 700 nothing nothing Residual nothing nothing nothing
Total 9 1000 (Type integers or decimals rounded to two decimal
places as needed.)
b. How many ordered pairs are in this sample?
c. Calculate the sample coefficient of determination.
d. Using...

6. (36 pts) The following is an incomplete
ANOVA summary table:
Source
df
SS
MS
F
Among Groups
3
63
Within Groups
16
97
Total
(a) Complete the ANOVA summary table.
(b) Determine the number of groups.
(b) At the α = 0.05 level of significance, determine whether
there is evidence of difference in the population means.

The data in the table to the right resulted from an experiment
that utilized a completely randomized design. Complete parts a and
b below.
Treatment 1
Treatment 2
Treatment 3
3.7
5.2
1.81
1.2
2.8
0.30
4.3
4.2
2.1
5.9
3.8
1.8
a.
Use statistical software or the appropriate calculation formulas
to complete the ANOVA table below.
Source
df
SS
MS
F statistic
Treatments
Error
Total
(Round to three decimal places as needed.)
b.
Test the null hypothesis...

Complete the following ANOVA summary table. There are seven
groups of plants receiving different fertilizer treatments, each
with 24 samples. Use a significance level of α=0.10
Source
SS
df
MS
F
P
Between
124.875
Within
TOTAL
1511.085

Respond to each of the following questions using this partially
completed one-way ANOVA table. Source SS DF MS F Between 470 Within
40 Total 1264 44 (a). How many different populations are being
compared? (b). Fill in the ANOVA table with the missing (c). State
the appropriate null and the alternative (d). Based on the analysis
of variance F-test, what conclusion should be reached regarding the
null hypothesis? Test Using an α =0.05.

Consider the partial ANOVA table shown below. Let a = .01
Source of Variation
DF
SS
MS
F
Between Treatments
3
180
Within Treatments (Error)
Total
19
380
If all the samples have five observations each:
there are 10 possible pairs of sample means.
the only appropriate comparison test is the Tukey-Kramer.
all of the absolute differences will likely exceed their
corresponding critical values.
there is no need for a comparison test – the null hypothesis is
not rejected.
2...

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