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 three exercise regimens for eight months, aerobic training, resistance training, and 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 squared centimeters, cm^2 at the beginning and end of the experiment. The study report contains the following information about the visceral fat reduction in cm^2 achieved by the subjects in each group. Note that the reduction is indicated as a positive value.

Treatment	n	x-bar	s
Aerobic training	36	15.9	34
Resistance training	39	0.8	19
Aerobic plus resistance training	35	10.9	33

Question 1: Do the standard deviations satisfy the rule of thumb for safe use of ANOVA?

a) Yes

b) No

Question 2: The report does not provide the distributions of visceral fat reduction. ANOVA is nonetheless safe for these data. Select the correct response.

a) None of the options are correct.

b) The samples are all obviously Normally distributed, and the F test is robust against Normal distributions.

c) The sample sizes are large, and the F test is robust against non‑Normality with large samples.

d) The sample standard deviations are very large, and the F test is robust against wildly varying standard deviations.

Question 3: Calculate the overall mean response x¯, the sum of squares for groups (SSG), the mean square for groups (MSG), the sum of squares for error (SSE), and the mean square for error, MSE. (Enter all of your answers rounded to two decimal places.)

x-bar =

SSG =

MSG =

SSE =

MSE =

Question 4: Obtain the ANOVA F statistic and the test P‑value. Is there evidence that the mean visceral fat reduction in overweight adults depends on which three exercise programs they follow? (Enter your answer rounded to two decimal places.)

F =

Question 5: With degrees of freedom 2 and 107, or 100 in Table F, we find that Answer 1<?‑value<Answer 2 (Enter your answers rounded to two decimal places.)

Answer 1 =

Answer 2 =

Answer 1

Q1) A rule of thumb is that if we compare the ratio of largest to the smallest variance should be less than 3 or 4. It this is satisfied F test is valid.

now largest variance = 34² = 1156

smallest variance = 19² = 361

ratio largest/smallest = 1156/361 = 3.20 which is less than 4 so yes we can apply F test. Rule of thumb is satisfied.

answer is YES.

Q2) option c) is correct .

usually normality is required but if samples are large greater than 30 then F test(anova) is robust against non-normality.

Q3)

calculations-