Question

You are the top statistician for the health department and have been assigned to testing three different weight loss programs. 15 people in the age group 30-35 in good health with a body mass index of 30, were selected for the two-month program. Each were required to eat an equal strict diet of 1800 calories and assigned different number of hours of prescribed exercise per week. The amount of weight loss in pounds after two months is recorded in the table below.

4 hours of exercise	9 hours of exercise	11 hours of exercise
5	7	10
6	12	13
8	15	18
3	9	10
3	7	14

1. Write up your conclusions and recommendations to the health department.

Answer 1

The null and alternative hypotheses are: Ho: U1 = U2=U3 Hj: At least one pair of means significantly differs The value of test statistic is: F= 8.9091 P-value = 0.0042 Conclusion: The p-value of F test is less than the 0.05. Hence we reject null hypothesis and conclude that there is significant difference in amount of weight loss between three weight loss programs. The mean weight loss for 11 hours of exercise program is less. Hence we recommend the 11 hours exercise program to the health department.

Anova: Single Factor Count Sum Variance SUMMARY Groups 4 hours of exercise 9 hours of exercise 11 hours of exercise Average 5 5 25 4.5 5 50 10 12 5 65 13 11 ANOVA SS df F P-value Fcrit 163.3333 2 MS 81.6667 9.1667 8.9091 0.0042 Source of Variation Between Groups Within Groups Total 3.8853 110 12 273.3333 14