Question

A sports researcher gave a standard written test of eating habits to 12 randomly selected professionals, four each from baseball, football, and basketball. The results were as follows:

Eating Habit Scores

Baseball Players: 34, 18, 21, 65

Football Players: 27, 28, 67, 42

Basketball Players: 35,44,47,41

Is there a difference in eating habits among professionals in the three sports (using the 0.05 significance level)?

Please use the 5 steps to solve this equation.

Please include the S^2 between / S^within, graphs, and all information neceissary to compute this problem

Answer 1

count, ni =	4	4	4
mean , x̅ i =	34.500	41.00	41.75
std. dev., si =	21.486	18.637	5.123
sample variances, si^2 =	461.667	347.333	26.250
total sum	138	164	167		469
grand mean , x̅̅ =	Σni*x̅i/Σni =	39.08

square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	21.007	3.674	7.111
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	84.028	14.694	28.444		127.1667
SS(within ) = SSW = Σ(n-1)s² =	1385.000	1042.000	78.750		2505.7500

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 =    63.5833
  
mean square within groups , MSW = SSW/N-k =    278.4167
  
F-stat = MSB/MSW =    0.2284
P value =   0.8003

------------------------

Ho: µ1=µ2=µ3
H1: not all means are equal

	SS	df	MS	F	p-value	F-critical
Between:	127.17	2	63.58	0.23	0.8003	4.26
Within:	2505.75	9	278.42
Total:	2632.92	11
					α =	0.05
			conclusion :	p-value>α , do not reject null hypothesis

There is insufficient evidence that means are different.