Obesity and being overweight is caused by excessive adipose tissues, or body fat
ID: 3364927 • Letter: O
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 Aerobic training Resistancetraining Aerobic plus resistance training 37 25.6 32 43 8.2 53 32 28.8 38 (a) Do the standard deviations satisfy the rule of thumb for safe use of one-way ANOVA F-test? Yes, the largest sample standard deviation is less than twice as large as the smallest sample standard deviation No, the largest sample standard deviation is more than twice as large as the smallest sample standard deviation (b) The report does not provide the distributions of subcutaneous fat reduction. ANOVA F-test is nonetheless safe for these data. Why? The sample sizes are large The sample sizes are small The standard deviation has Normality The populations have the same standard deviation (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) S.S 9622.63 df Source Between Groups Within Groups C.Total M.S 2 209228.63 (e) Perform a ANOVA F-test of hypotheses: Ho: All three population means of subcutaneous fat reductions are equal versus Ha: Not all three population means of subcutaneous fat reductions are equalExplanation / Answer
a) yes the largest sample std deviation is less then twice................
b)
the sample size are large
c)
from above data:
overall mean respnse xbar=19.83
d)
e) p value for above test statistic F =0.0768
as p value is greater then 0.05 level; we reject null hypothesis.
i ni Xi Si^2 ni*(Xi- grand mean)^2 (ni-1)*Si^2 aerobic 37 25.6 1024.000 1230.160 36864.000 resistance 43 8.2 2809.000 5819.977 117978.000 aerobic and resistance 32 28.8 1444.000 2572.494 44764.000 Weighted mean 19.834 9622.631 199606.000 SSG SSE Source of variation SS df MS F P value F crit treatment 9622.631 2 4811.316 2.627 0.0768 3.0796 error 199606.000 109 1831.248 total 209228.631 111Related Questions
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