To test the effect of three different cofactors on the growth of newborn mice, a
ID: 3277547 • Letter: T
Question
To test the effect of three different cofactors on the growth of newborn mice, a scientist administers solutions containing magnesium to one group of five newborn mice, iron to another group of five mice, and potassium to a third group of five. She also administers a saline solution to a control group of five mice. She measures the weight of each mouse before and 1 week after administering the solutions, and records the difference in the two weights. When she performs an ANOVA to test for differences amongst groups she obtains the following results:
Groups
Count
Sum
Average
Variance
control
5
21.60
4.32
7.58
magnesium
5
22.82
4.56
2.30
iron
5
33.20
6.64
5.33
potassium
5
47.89
9.58
3.40
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Between Groups
88.96
b
d
f
0.0048
3.24
Within Groups
a
c
e
Total
163.38
19
1. The value of a is:
2. The value of b is:
3. The value of c is:
4. The value of d is:
5. The value of e is:
6. The value of f is:
7.what null hypotheses is the ANOVA testing?
8. Is there a statistically significant difference amongst the groups?
9. The researcher constructs two linear contrasts: (1) to test the hypothesis that the average differences in weights for the cofactor-treated groups is the same as the average difference in weight for the control group, and (2) to statistically compare the average differences in weights between the control and the magnesium-treated mice. Are these contrasts orthogonal or not?
Groups
Count
Sum
Average
Variance
control
5
21.60
4.32
7.58
magnesium
5
22.82
4.56
2.30
iron
5
33.20
6.64
5.33
potassium
5
47.89
9.58
3.40
Explanation / Answer
As per the chegg policy, we are advised to do four subparts at a time. I will still complete 6 subparts so that ANOVA table will be completed.
1. a = SS(Total) - SS(Between) = 163.38 - 88.96 = 74.42
2. b = Number of Groups - 1 = 4 - 1 = 3
3. c = Total - b = 19 - 3 = 16
4. d = SS(Between) / df(Between) = 88.96/3 = 29.653 [Rounded off to 3 decimal places]
5. e = SS(Within)/ df(Within) = 74.42/16 = 4.651 [Rounded off to 3 decimal places]
6. f = d/e = 29.653/4.651 = 6.375 [Rounded off to 3 decimal places]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.