Question

Samples were drawn from three populations. The sample sizes were n1 = 6, n2 = 9, and n3 = 8. The sample means were =1.52, < x 2 >=1.62 , and < x 3 >=1.65. The sample standard deviations were s1 = 0.50, s2 = 0.36, and s3 = 0.48. The grand mean is = 1.604348 . Compute the value of the test statistic F.

Answer 1

popn	sample size (given)	sample mean (given)	sample var (given)	SS = Sample_var*(n-1)
1	6	1.52	0.5	0.5*(6-1) =	2.5
2	9	1.62	0.36	0.36*(9-1) =	2.88
3	8	1.65	0.48	0.48*(8-1) =	3.36

k=3
n = 6+9+8 = 23
Xbar =    1.604348 (given)

SS_between =    (6*(1.52-1.604348)^2)+(9*(1.62-1.604348)^2)+(8*(1.65-1.604348)^2) = 0.0616
SS_within =    2.5+2.88+3.36 = 8.7400
SS_total =    =0.0616+8.74 = 8.8016

ANOVA table:

source	df	SS	MSS	F
between	3-1	0.06	0.0616/2	=(0.0616/2)/(8.74/20)
within	23-3	8.74	8.74/20
total	23-1	8.80	8.8016/22

source	df	SS	MSS	F
between	2	0.0616	0.0308	0.0705
within	20	8.74	0.44
total	22	8.8016	0.40