Question

Suppose a team of doctors wanted to study the effect of different types of exercise on reducing body fat percentage in adult men. The 57 participants in the study consist of men between the ages of 40 and 49 with body fat percentages ranging from 32%â34%. The participants were each randomly assigned to one of four exercise regimens.Ten were instructed to complete 45 min of aerobic exercise four times a week.Eleven were instructed to complete 45 min of anaerobic exercise four times a week.Nine were instructed to complete 45 min of aerobic exercise twice a week and 45 minutes of anaerobic exercise twice a week.Nine were instructed not to exercise at all.All participants were asked to adhere to their assigned exercise regimens for eight weeks. Additionally, to control for the effect of diet on weight loss, the doctors provided the participants with all meals for the duration of the study. After eight weeks, the doctors recorded the change in body fat percentage for each of the participants.The doctors plan to use the change in body fat percentage data in a one-way ANOVA F?test. They calculate the mean square between as MSbetween=11.632991 and the mean square within as MSwithin=1.261143. Assume that the requirements for a one-way ANOVA F?test have been met for this study.Choose all of the correct facts about the F statistic for the doctors' ANOVA test.A. The F statistic increases as the differences among the sample means for the exercise groups increase.B. The F statistic is 0.1084.C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.D. The F statistic indicates which exercise treatment groups, if any, are significantly different from each other.E. The F statistic has 4 degrees of freedom in the numerator and 38 degrees of freedom in the denominator.F. The F statistic is 9.2242.

Answer 1

A. The F statistic increases as the differences among the sample means for the exercise groups increase.

C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.

F. The F statistic is 9.2242.

Explanation:

Given that

Observations Samples Total

40-49 10 11 9 9 39

The degrees of freedom is given by

For numerator= k-1 = 4-1=3

For denominator= n-k= 39-4= 35

F statistic is given by

F= MS between/ MS within

=11.632991 / 1.261143 = 9.2242

Where

Mean Square Between = MS between = 11.632991

Mean Square Within = MS within = 1.261143

Hence the correct choices are A, C and F

A. The F statistic increases as the differences among the sample means for the exercise groups increase.

C. The F statistic has 3 degrees of freedom in the numerator and 35 degrees of freedom in the denominator.

F. The F statistic is 9.2242.

Suppose we have

Mean Square Between = MS between = 18.632991

Mean Square Within = MS within = 1.261143

Then F statistic would be = 14.77468 > 9.2242

which tells that The F statistic increases as the differences among the sample means for the exercise groups increase.