Question

Obesity and being overweight is caused by excessive adipose tissues, or body fat. Visceral fat, surrounding internal organs, is clearly associated with heart disease and diabetes. Subcutaneous fat, found just below the skin (often in the buttocks and thighs), is not. A study examined the impact of exercise type on visceral and subcutaneous fat. Overweight, sedentary, but otherwise disease-free adults were randomly assigned to 3 exercise regimens for eight months: aerobic training, resistance training, aerobic plus resistance training. All exercise sessions were supervised to ensure correct completion. The subjects' body fat amount was assessed with computed tomography imaging (in cm²) at the beginning and end of the experiment. The study report contains the following information about the visceral fat reduction (in cm²) achieved by the subjects in each group (note that the reduction is indicated as a positive value):

Treatment	n	x	s
Aerobic training	37	25.2	30
Resistance training	43	8.2	55
Aerobic plus resistance training	35	28.9	36

(c) Calculate the overall mean response x =  (round to 2 decimal places)

(d) Complete the one-way ANOVA table (round your answer to two decimal places when it applies)

Source	df	S.S.	M.S.	F
Between Groups	2	9760.04
Within Groups				N/A
C.Total		213274.04	N/A	N/A

(e) Perform a ANOVA F-test of hypotheses: H₀: All three population means of subcutaneous fat reductions are equal versus H_a: Not all three population means of subcutaneous fat reductions are equal
Find the test statistic F ratio from the ANOVA table and estimate the P-value.
P-value:

a. P < 0.001

b. 0.001 < P < 0.010  

c. 0.010 < P < 0.025

d. 0.025 < P < 0.050

e. 0.050 < P < 0.100

f. P > 0.100

Answer 1

c) Overall mean score = (25.2*37 + 8.2*43 + 28.9*35)/(37+43+35) = 19.97

d) Number of treatment, k = 3

Total sample Size, N = 115

df(between) = k-1 = 2

df(within) = N-k = 112

df(total) = N-1 = 114

SS(within) = SST + SS(between)= 203514

MS(between) = SS(between)/df(between) = 4880.02

MS(within) = SS(within)/df(within) = 1817.09

F = MS(between)/MS(within) = 2.69

p-value = F.DIST.RT(2.6856, 2, 112) = 0.0726

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	9760.04	2	4880.02	2.69	0.0726
Within Groups	203514.00	112	1817.09
Total	213274.04	114

e) Answer : e. 0.050 < P < 0.100