To determine diet quality, male weanling rats were fed diets with various protein levels. Each of 15 rats was randomly assigned to one of three diets, and their weight gain in grams was recorded in the following table: Low 9.72 Diet protein level Medium 8.54 High 9.19 9.67 9.32 11.11 8.15 8.76 14.45 6.75 9.30 10.39 9.55 10.45 12.16 Sample Mean Sample Variance 1.696 8.768 9.274 11.460 0.547 3.963 Suppose we fit the data with the following model: Xij = µ + a; + €ij, i = 1,2, 3; j = 1,...,5, where a1 + a2 + az = 0 and ɛij ~ N (0, o²) independently. Define Xi. i = 1, 2, 3, X. = E=1 Xij, and SS(E) = C=1 E=1(Xij – X¡,)². {E Xij for %3D Some R output that may help. > p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99) > qf (p1, 2, 12) [1] 0.010 0.025 0.052 0.106 2.807 3.885 5.096 6.927 > qf (p1, 2, 14) [1] 0.010 0.025 0.051 0.106 2.726 3.739 4.857 6.515 > qf (p1, 3, 12) [1] 0.037 0.070 0.114 0.192 2.606 3.490 4.474 5.953 > qf (p1, 3, 14) [1] 0.037 0.070 0.115 0.192 2.522 3.344 4.242 5.564 (a) Complete the following ANOVA table for the model. Source df SS MS F Worker Error Total 45.293
To determine diet quality, male weanling rats were fed diets with various protein levels. Each of 15 rats was randomly assigned to one of three diets, and their weight gain in grams was recorded in the following table: Low 9.72 Diet protein level Medium 8.54 High 9.19 9.67 9.32 11.11 8.15 8.76 14.45 6.75 9.30 10.39 9.55 10.45 12.16 Sample Mean Sample Variance 1.696 8.768 9.274 11.460 0.547 3.963 Suppose we fit the data with the following model: Xij = µ + a; + €ij, i = 1,2, 3; j = 1,...,5, where a1 + a2 + az = 0 and ɛij ~ N (0, o²) independently. Define Xi. i = 1, 2, 3, X. = E=1 Xij, and SS(E) = C=1 E=1(Xij – X¡,)². {E Xij for %3D Some R output that may help. > p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99) > qf (p1, 2, 12) [1] 0.010 0.025 0.052 0.106 2.807 3.885 5.096 6.927 > qf (p1, 2, 14) [1] 0.010 0.025 0.051 0.106 2.726 3.739 4.857 6.515 > qf (p1, 3, 12) [1] 0.037 0.070 0.114 0.192 2.606 3.490 4.474 5.953 > qf (p1, 3, 14) [1] 0.037 0.070 0.115 0.192 2.522 3.344 4.242 5.564 (a) Complete the following ANOVA table for the model. Source df SS MS F Worker Error Total 45.293
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 4AGP
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![To determine diet quality, male weanling rats were fed diets with various protein levels. Each
of 15 rats was randomly assigned to one of three diets, and their weight gain in grams was
recorded in the following table:
Diet protein level
Low
Medium
High
9.72
8.54
9.19
9.67
9.32
11.11
8.15
8.76
14.45
6.75
9.30
10.39
9.55
10.45
12.16
Sample Mean
Sample Variance 1.696
8.768
9.274
11.460
0.547
3.963
Suppose we fit the data with the following model:
Xij = µ+ a; + Eij; i= 1,2, 3; j = 1, ..., 5,
E=1 Xij for
N(0, o?) independently. Define X¡.
i= 1,2,3, Χ. ΣΣ Xj, and SS(E) ΣΣ Σ(Xj- X.).
where aj + a2 + a3 = 0 and eij ~
%3D
Some R output that may help.
> p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99)
> qf (p1, 2, 12)
[1] 0.010 0.025 0.052 0.106 2.807 3.885 5.096 6.927
> qf (p1, 2, 14)
[1] 0.010 0.025 0.051 0.106 2.726 3.739 4.857 6.515
> qf (p1, 3, 12)
[1] 0.037 0.070 0.114 0. 192 2.606 3.490 4.474 5.953
> qf (p1, 3, 14)
[1] 0.037 0.070 0.115 0.192 2.522 3.344 4.242 5.564
(a) Complete the following ANOVA table for the model.
Source
df
SS
MS
F
Worker
Error
Total
45.293](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F433c14e3-652f-4add-95c2-5fe04b0fff82%2F9114ecbf-b4ad-4a47-9447-9f8ee5948aff%2F5ckfjlw_processed.png&w=3840&q=75)
Transcribed Image Text:To determine diet quality, male weanling rats were fed diets with various protein levels. Each
of 15 rats was randomly assigned to one of three diets, and their weight gain in grams was
recorded in the following table:
Diet protein level
Low
Medium
High
9.72
8.54
9.19
9.67
9.32
11.11
8.15
8.76
14.45
6.75
9.30
10.39
9.55
10.45
12.16
Sample Mean
Sample Variance 1.696
8.768
9.274
11.460
0.547
3.963
Suppose we fit the data with the following model:
Xij = µ+ a; + Eij; i= 1,2, 3; j = 1, ..., 5,
E=1 Xij for
N(0, o?) independently. Define X¡.
i= 1,2,3, Χ. ΣΣ Xj, and SS(E) ΣΣ Σ(Xj- X.).
where aj + a2 + a3 = 0 and eij ~
%3D
Some R output that may help.
> p1 <- c(0.01, 0.025, 0.05, 0.1, 0.9, 0.95, 0.975, 0.99)
> qf (p1, 2, 12)
[1] 0.010 0.025 0.052 0.106 2.807 3.885 5.096 6.927
> qf (p1, 2, 14)
[1] 0.010 0.025 0.051 0.106 2.726 3.739 4.857 6.515
> qf (p1, 3, 12)
[1] 0.037 0.070 0.114 0. 192 2.606 3.490 4.474 5.953
> qf (p1, 3, 14)
[1] 0.037 0.070 0.115 0.192 2.522 3.344 4.242 5.564
(a) Complete the following ANOVA table for the model.
Source
df
SS
MS
F
Worker
Error
Total
45.293
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