A manufacturer wishes to determine the effectiveness of four types of

Question

A manufacturer wishes to determine the effectiveness of four types of machines (A, B, C and D) in the production of bolts. To accumulate this, the numbers of defective bolts produced for each of two shifts in the results are shown in the following table:

Machine	First Shift	Second Shift
Machine
A	6	4	5	5	4	5	7	4	6	8
B	10	8	7	7	9	7	9	12	8	8
C	7	5	6	5	9	9	7	5	4	6
D	8	4	6	5	5	5	7	9	7	10

Perform an analysis of variance to determine at 5% level of significance, whether there is a difference (a) Between the machines and (b) Between the shifts.

22 Apr 2024

Answer :

Word Count : 302

To analyze whether there is a significant difference between the machines and between the shifts at a 5% level of significance, we perform a Two-Way Analysis of Variance (ANOVA) without interaction. --- ### Step 1: Define the Hypotheses #### (a) Testing for Difference Between Machines - Null Hypothesis (H₀₁): There is no significant difference in the number of defective bolts ________ ______ ___ ____ ____ _________ _______ ____ ____ ______.
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Village	$N_{1}$	$\bar{X}_{1}$	${S}_{1}^{2}$
Collage A	400.	60	20
Collage B	200	120	80

Plot No.	Group 1	Group 2	Group 3	Group 4	Group 5	Group 6
1	8	6	18	13	17	12
2	13	5	8	7	15	15
3	11	16	6	13	10	11
4	26	5	10	6	21	17
5	13	16	16	7	20	8
6	31	5	20	2	25	10

Machine	First shift					Second Shif
Machine	M	T	W	Th	F	M	T	W	Th	F
A	6	4	5	5	4	5	7	4	6	8
B	10	8	7	7	9	7	9	12	8	8
C	7	5	6	5	9	9	7	5	4	6
D	8	4	6	5	5	5	7	9	7	10

age	22	25	22	21	22	25	24	23	22	21	20	21
22	23	25	23	24	22	24	24	21	20	23	21	22
20	20	21	22	25

age	22	25	22	21	22	25	24	23	22	21	20	21
22	23	25	23	24	22	24	24	21	20	23	21	22
20	20	21	22	25

age	22	25	22	21	22	25	24	23	22	21	20	21
22	23	25	23	24	22	24	24	21	20	23	21	22
20	20	21	22	25