Question

A company has three manufacturing plants, and you want to determine whether there is a difference in the average age of workers at the three locations. The following data are the ages of five randomly selected workers at each plant. Perform a test to determine whether there is a significant difference in the mean ages of the workers at the three plants. Use α = 0.01 . Interpret on your findings.
Plant A Plant B Plant C
29 31 27
27 32 26
30 30 27
27 33 27
28 29 28

Answer 1

	Mean	n	Std. Dev
Plant A	28.2	5	1.30
Plant B	31.0	5	1.58
Plant C	27.0	5	0.71
Total	28.7	15	2.09

ANOVA table
Source	SS	df	MS	F	p-value
Treatment	42.13	2	21.067	13.45	.0009
Error	18.80	12	1.567
Total	60.93	14

To Test :-
H0 :- µ1 = µ2 = µ3 = 0  
H0 :- µ1 = µ2 = µ3 ≠ 0  

Test Statistic :-
f = MS treatment / MS error = 13.4468

Test Criteria :-
Reject null hypothesis if f > f(α , a-1 , N-a )
Critical value f(0.01, 2 , 12 ) = 6.9266 (From F table)
Since 13.4468 > 6.9266, we reject H0
conclusion = Treatment means differs

Decision based on P value
P value = 0.0009
Reject null hypothesis if P value < α = 0.01
Since P value = 0.0009 < 0.01, hence we reject the null hypothesis
Conclusion :- Treatment means differs  

There is sufficient evidence to support the claim that  there is a significant difference in the mean ages of the workers at the three plants.