Question

Problem 1

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

What is your conclusion?

Select one:

a. Plant A has a higher scrap rate than Plant B

b. All Plants have the same mean scrap rate

c. Can't reach a conclusion without more information

d. Not all the Plants have the same scrap rate

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 :- Not all the Plants have the same scrap rate