The NIH wants to compare the mean weight loss for five different diets. They mea
ID: 3150390 • Letter: T
Question
The NIH wants to compare the mean weight loss for five different diets. They measure the weight loss (in pounds) of 5 men assigned to each of the diets for one month. The resulting data set is below.
DATA
a) Which of the following is NOT an assumption that should be checked before performing an ANOVA?
A) The variability in weight loss should be roughly the same for each diet.
B) The average weight loss should be roughly the same for each diet.
C) Weight loss should be roughly normally distributed for each diet.
b) What is the F statistic for the ANOVA? Give your answer to at least three decimal places.
c) Using a 0.01 level of significance, what is the critical point that one would compare to the F statistic in order to make a conclusion? Give your answer to three decimal places.
d) What is the P-value from the ANOVA? Give your answer to four decimal places.
e) What is the proper conclusion for NIH in this case?
A) Diet 5 has the largest mean weight loss because the F statistic is larger than the critical point.
B) Reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is larger than the critical point.
C) Fail to reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is larger than the critical point.
D) Fail to reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is smaller than the critical point.
E) Diet 4 has the largest mean weight loss because the F statistic is larger than the critical point.
Explanation / Answer
The NIH wants to compare the mean weight loss for five different diets. They measure the weight loss (in pounds) of 5 men assigned to each of the diets for one month. The resulting data set is below.
DATA
Diet 1,Diet 2,Diet 3,Diet 4,Diet 5
0.7,-0.1,0.2,-1.8,-2.2
1.9,0.2,-0.8,-2.7,-0.9
0.8,0.2,-0.8,-3,-2.5
0.5,-0.3,-0.1,-2.2,-1.7
-0.2,-0.8,0.7,-0.3,-1.3
a) Which of the following is NOT an assumption that should be checked before performing an ANOVA?
A) The variability in weight loss should be roughly the same for each diet.
B) The average weight loss should be roughly the same for each diet.
C) Weight loss should be roughly normally distributed for each diet.
b) What is the F statistic for the ANOVA? Give your answer to at least three decimal places.
F=12.424
c) Using a 0.01 level of significance, what is the critical point that one would compare to the F statistic in order to make a conclusion? Give your answer to three decimal places.
F (4,20) critical value =4.431
d) What is the P-value from the ANOVA? Give your answer to four decimal places.
P=0.0000
e) What is the proper conclusion for NIH in this case?
The null hypothesis is rejected.
A) Diet 5 has the largest mean weight loss because the F statistic is larger than the critical point.
B) Reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is larger than the critical point.
C) Fail to reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is larger than the critical point.
D) Fail to reject the claim that all diets are equivalent in terms of mean weight loss because the F statistic is smaller than the critical point.
E) Diet 4 has the largest mean weight loss because the F statistic is larger than the critical point.
One factor ANOVA
Mean
n
Std. Dev
0.74
5
0.757
D1
-0.16
5
0.416
D2
-0.16
5
0.650
D3
-2.00
5
1.056
D4
-1.72
5
0.650
D5
-0.66
25
1.254
Total
ANOVA table
Source
SS
df
MS
F
p-value
Treatment
26.896
4
6.7240
12.424
0.0000308
Error
10.824
20
0.5412
Total
37.720
24
One factor ANOVA
Mean
n
Std. Dev
0.74
5
0.757
D1
-0.16
5
0.416
D2
-0.16
5
0.650
D3
-2.00
5
1.056
D4
-1.72
5
0.650
D5
-0.66
25
1.254
Total
ANOVA table
Source
SS
df
MS
F
p-value
Treatment
26.896
4
6.7240
12.424
0.0000308
Error
10.824
20
0.5412
Total
37.720
24