Question

Scenario 1:
A researcher wants to determine if different forms of regular exercise alter HDL levels in obese middle aged males between the ages of 35 and 45.  Participants in the study are randomly assigned to one of four exercise groups – No Exercise, Resistance 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.

Exercise Group	N	Mean	Std Dev
No exercise (TV watching 60 min/day)	40	45.1	9.8
Resistance Training 60min/day	40	51.2	10.2
Aerobic Exercise 60min/day	40	46.3	11.1
Stretching/Yoga 60min/day	40	47.1	12.5

1. What is the null hypothesis equation for this experiment?

2. Specify the ν_nnumerator degrees of freedom? Please paste your data output file in the space below.

3. Specify the ν_ddenominator degrees of freedom?  

4. Identify the F-critical value at P<0.05 from the F distribution table 3-1 from the Primer of Biostatistics 7^thEd.

5. Identify the F-critical value at P<0.01 from the F distribution table 3-1 from the Primer of Biostatistics 7^thEd.

6. Specify whether you accept or reject the null hypothesis at P<0.05?

7. Specify whether you accept or reject the alternate hypothesis at P<0.05?

Answer 1

1)

null hypothesis : mean HDL levels is same for all forms of excercise

_{no excercise} =_{ressitance training} =_Aerobic =_stretching

2)

nnumerator degrees of freedom =groups -1=k-1=4-1=3

3)

denominator degrees of freedom =N-k =160-4=156

4)

F-critical value at P<0.05 is =2.663

5)

F-critical value at P<0.01 is 3.910

6)

population	ni	x̅i	S2i	ni*(Xi-Xgrand)2	(ni-1)*S2i
no excersice	40	45.100	96.040	216.225	3745.56
resistance	40	51.200	104.040	570.025	4057.56
Aerobic	40	46.300	123.210	50.625	4805.19
stretching	40	47.100	156.250	4.225	6093.75
	grand mean=	47.425		841.100	18702.06
				SSTr	SSE
Source of variation		SS	df	MS	F
between		841.1000	3	280.37	2.339
within		18702.0600	156	119.89
total		19543.1600	159

as f test statistic 2.339 is belw crtiical value we accept the null hypothesis

7)

as f test statistic 3.910 is belw crtiical value we accept the null hypothesis