Question

A health researcher was interested in comparing three methods of weight loss: low-calorie diet, low-fat diet, and high-exercise regimen. He selected 15 moderately overnight subjects and randomly assigned 5 to each weight-loss program. The following weight reductions (in pounds) were observed after a one-month period: Low-fat diet: 7,6,8,8,6 low Calorie diet: 7,7,5,4,5 high exercise: 7,8,7,9,8  

a) Test the null hypothesis that the extent of weight reduction does not differ by type of weight-loss program. (Set α=.01 level) (10 points) b) If the result at a) rejects the null hypothesis, use an appropriate multiple comparison procedure and determine where the significant differences occur. (5 points) c) Calculate the correlation ratio and interpret the result. (3 points)

Answer 1

Ho:extent of weight reduction does not differ by type of weight-loss program

Ha: extent of weight reduction differ by type of weight-loss program

	A	B	C
count, ni =	5	5	5
mean , x̅ i =	7.000	5.60	7.80
std. dev., si =	1.000	1.342	0.837
sample variances, si^2 =	1.000	1.800	0.700
total sum	35	28	39		102	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	6.80
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	0.040	1.440	1.000
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	0.200	7.200	5.000		12.4
SS(within ) = SSW = Σ(n-1)s² =	4.000	7.200	2.800		14.0000

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   15
df within = N-k =   12
  
mean square between groups , MSB = SSB/k-1 =    6.2000
  
mean square within groups , MSW = SSW/N-k =    1.1667
  
F-stat = MSB/MSW =    5.3143

anova table
	SS	df	MS	F	p-value	F-critical
Between:	12.40	2	6.20	5.31	0.0222	6.93
Within:	14.00	12	1.17
Total:	26.40	14
					α =	0.01
			conclusion :	p-value>α , do not reject null hypothesis

conclusion :

p-value>α , do not reject null hypothesis

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