Question

A clinical trial is run to assess the effects of different forms of regular exercise on HDL levels in persons between the ages of 18 and 29. Participants in the study are randomly assigned to one of three exercise groups - Weight training, Aerobic exercise or Stretching/Yoga – and instructed to follow the program for 8 weeks. Their HDL levels are measured after 8 weeks and are summarized below

Weight Training	Aerobic Exercise	Stretching/Yoga
48	38	56
49	41	57
51	42	60
53	37	55
45	39	58
47	44	64
54	43	61
49	42	62
50	36	60
47	34	56
48	33	55
45	35	59
44	38	61
55	40	62
52	34	63
55	32	67
50	35	64

Is there a significant difference in mean HDL levels among the exercise groups? Run the test at a 5% level of significance. (10 points)

1. Hypotheses(1 points)

           H_O:                                                        vs.      H_A

2. Summary statstics(2 points)

Group	Exercise Group	N	Mean	Std Dev
1	Weight Training
2	Aerobic Exercise
3	Stretching/Yoga

3. MSB(1 points)

      MSB=

4. MSW(1 points)

      MSW=

5. Compute F-stat(3 points)

F-stat=

6. P-value(1 points)
7. Conclusion(1 points)(circle one )

            Accept H0                                                                  Reject H0

Answer 1

Applying one way ANOVA:

Source of Variation	SS	df	MS	F
Between Groups	4184.588	2	2092.294118	164.9896
Within Groups	608.7059	48	12.68137255
Total	4793.294	50

a)

Ho: μ_{weight training} =μ_Aerobic =μ_stretching

Ha:at least two means differs from each other

b)

Groups	N	Average	std deviation
Weight Training	17	49.5294	3.4481
Aerobic Exercise	17	37.8235	3.7289
Stretching/Yoga	17	60.0000	3.5000

c)

MSB =2092.2941

d)

MSW =12.6814

e)

F stat =164.9896

f) p value =0.0000

g) reject Ho