Question

Your company manufactures face masks and are concerned about the scrap rates of your 3 different plants. Particularly, you need to know is there is a difference in scrap rates per 1000 units produced by each Plant. You collect a sample of 4 observations per each Plant. The results are as follows:

Plant A Plant B Plant C

11.4 11.1 10.2

12.5 14.1 9.5

10.1 16.8 9.0

13.8 13.2 13.3

You need to run a test with α = 0.05 Show full procedure

Answer 1

	Mean	n	Std. Dev
Plant A	11.95	4	1.576
Plant B	13.80	4	2.362
Plant C	10.50	4	1.930
Total	12.08	12	2.281

ANOVA table
Source	SS	df	MS	F	p-value
Treatment	21.887	2	10.9433	2.78	.1145
Error	35.370	9	3.9300
Total	57.257	11

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

Test Statistic :-
f = MS treatment / MS error = 2.7846

Test Criteria :-
Reject null hypothesis if f > f(α , a-1 , N-a )
Critical value f(0.05, 2 , 9 ) = 4.2565 (From F table)
Since 2.7846 < 4.2565, we fail to reject H0
Conclusion = Treatment means are same

There is insufficient evidence to support the claim that  there is a difference in scrap rates per 1000 units produced by each Plant.