What conditions help overweight people exercise regularly? Subjects were randoml
ID: 3228653 • Letter: W
Question
What conditions help overweight people exercise regularly? Subjects were randomly assigned to three treatments: a single long exercise period 5 days per week; several 10-minute exercise periods 5 days per week; and several 10-minute periods 5 days per week on a home treadmill that was provided to the subjects. The study report contains the following information about weight loss (in kilograms) after 6 months of treatment^14 (a) Show that the conditions for ANOVA are met. (b) Calculate the overall mean response x, the mean squares MSG and MSE, and the F statistic. (c) Which F distribution would you use to find the P-value of the ANOVA F test? Software says that P 0.634. What do you conclude from this study? Exercises 17 and 18 refer to the following setting. How does logging in a tropical rain forest affect the forest in later years? Researchers compared forest plots in Borneo that had never been logged (Group l) with similar plots nearby that had been logged l year earlier (Group 2) and 8 years earlier (Group 3). Although the study was not an experiment, the authors explain why we can consider the plots to be randomly selected. The data appear in the following table. The variable Trees is the count of trees in a plot; Species is the count of tree species in a plot^15Explanation / Answer
Answer:
a).
The subjects are randomly assigned.
Variance ratio of largest and smallest standard deviation is F=27.04/17.64=1.53 which is < 1.91 the critical value.
The equality of variance assumption is not violated.
Conditions are met.
b).
Group
Mean
SD
n
Total
SSGroups
SSError
1
10.2
4.2
37
377.4
2.936946692
635.04
2
9.3
4.5
36
334.8
13.7608741
708.75
3
10.2
5.2
42
428.4
3.33383138
1108.64
# Groups
3
# Subjects
115
XBAR
9.918261
Equal Variances Assumed
ANOVA
Source
df
SS
MS
F
P-value
Groups
2
20.03165
10.01583
0.457413
0.6340
Error
112
2452.43
21.8967
Total
114
2472.462
c).
F distribution with DF1=2 and DF2=112
calculated P=0.634 >0.05 level of significance.
Ho is not rejected.
There is no significant difference between the three groups.
Group
Mean
SD
n
Total
SSGroups
SSError
1
10.2
4.2
37
377.4
2.936946692
635.04
2
9.3
4.5
36
334.8
13.7608741
708.75
3
10.2
5.2
42
428.4
3.33383138
1108.64
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