Question

With all the fad diets advertised on TV, a researcher wanted to know if there was a significant difference in weight loss depending on which new fad diet you were on. Over the course of 2 weeks, a total of 12 male volunteers who weighed the same and had similar lifestyles were broken up into 3 groups: Diet 1, Diet 2, and Diet 3. Conduct an ANOVA on the following table with alpha = 0.5 to determine if at least one of the diets has significantly different weight loss compared to the other two. Diet 1 -1 5 3 4 Diet 2-13 12 8 3 Diet 3-6 2 1 2 1. What are the null and alternative hypotheses? What is the critical value? (Round to 4 decimal places) a. 3.8853 b. 3.9823 c. 4.2565 d. 3.5874

Answer 1

	diet 1	diet 2	diet 3
count, ni =	4	4	4
mean , x̅ i =	3.25	9.00	2.75
std. dev., si =	1.71	4.55	2.22
sample variances, si^2 =	2.917	20.667	4.917
total sum	13	36	11		60	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =				5.00
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	3.0625	16.00	5.0625
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	12.25	64.00	20.25		96.5
SS(within ) = SSW = Σ(n-1)s² =	8.75	62.00	14.75		85.5

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   12
df within = N-k =   9
  
mean square between groups , MSB = SSB/k-1 =    48.250
  
mean square within groups , MSW = SSW/N-k =    9.500
  
F-stat = MSB/MSW =    5.079
P value =   0.033

anova table
	SS	df	MS	F	p-value	F-critical
Between:	96.5	2	48.3	5.08	0.033	4.2565
Within:	85.5	9	9.5
Total:	182.0	11

F-criitical = 4.2565(answer)