Question

A sports researcher gave a standard questionnaire of eating habits to 12 randomly selected male professional athletes, four each from baseball, football, and basketball. The results were:

Baseball: 34, 18, 21, 65

Football: 27, 28, 67, 42

Basketball: 35, 44, 47, 61

Is there a significant difference in eating habits among professionals in the three sports? (Use the .05 sig level.)

Answer 1

H0: μ1 = μ2 = μ3

H1: There is at least one mean difference among the populations.

Applying one way ANOVA:

	Baseball	Football	basketball
	34	27	35
	18	28	44
	21	67	47
	65	42	61
count ni=	4	4	4
Average==ΣXi/ni=	34.5000	41.0000	46.7500
Total=ΣX2i   =	6146.000	7766.0000	9091.0000
SS=ΣX2i -(Σxi)2/ni=	1385.000	1042.0000	348.7500
Grand average Xgrand =∑xi/N =		489/8=	40.7500

i	ni	x̅i	ni*(Xi-Xgrand)2	SS=(ni-1)*s2
treatment 1	4	34.5000	156.250	1385
treatment 2	4	41.0000	0.250	1042
treatment 3	4	46.7500	144.000	348.75
Total	12		300.500	2775.7500
			SSTr	SSE
df treatments =	number of treatments-1=			2
df error =	N-k=	12-3=		9
df total=	N-1=	12-1=		11
MS(treatment) =SSTr/df(Tr)=300.5/2=			150.25000
MS(error) =SSE/df(error)=2775.75/9=			308.41667
test statistic F =MSTr/MSE =150.25/308.42=			0.487

for (2,11) degree of freedom and 0.05 level  critical value =4.26

since test statistic < critical value, we fail to reject null hypothesis

we do not have significant evidence to conclude that  there is a significant difference in eating habits among professionals in the three sports