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 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

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.

06 Mar 2024

Answer :

Word Count : 727

To solve the problem and analyze whether there is a significant difference between the machines and between the shifts at a 5% level of significance, we will perform Two-Way Analysis of Variance (ANOVA). The steps are as follows:

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### 1. Organize the Data
The data is provided for four machines (A, B, C, D) and two shifts (First Shift, Second Shift). Let us summarize the data:

#### First Shift:
- Machine A: 6, 4, 5, 5, 4
- Machine B: 10, 8, 7, 7, 9
- Machine C: 7, 5, 6, 5, 9
- Machine D: 8, 4, 6, 5, 5

#### Second Shift:
- Machine A: 5, 7, 4, 6, 8
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Village	Ni	$\bar{X}$ i	$S_{i}^{2}$
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
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5	13	16	16	7	20	8
6	31	5	20	2	25	10