Benson Manufacturing is considering ordering suppliers. The suppliers may differ
ID: 3227607 • Letter: B
Question
Benson Manufacturing is considering ordering suppliers. The suppliers may differ terms of quality in that the proportion or percentage of defective components may differ among the suppliers. To evaluate the proportion of defective components for the suppliers, Benson has requested a sample shipment of 500 components from each suppliers. The number of defective components and the number of good components found in each shipment are as follows. Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers. Using a .05 level of significance, conduct the hypothesis test. What is the p-value what is your conclusion? Conduct a multiple comparison test to determine if is an overall best supplier if one supplier can be eliminated because of poor quality.Explanation / Answer
Answer:
Ho: P1=P2=P3
H1: At least one pair of proportions are different.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
A
B
C
Total
fo-fe
Defective
15
20
40
75
-10
-5
15
Good
485
480
460
1425
10
5
-15
Total
500
500
500
1500
Expected Frequencies
Column variable
Row variable
A
B
C
Total
(fo-fe)^2/fe
Defective
25
25
25
75
4.0000
1.0000
9.0000
Good
475
475
475
1425
0.2105
0.0526
0.4737
Total
500
500
500
1500
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
14.73684
p-Value
0.000631
Reject the null hypothesis
Calculated chi square = 14.7368, P=0.00063 which is < 0.05 level.
Ho is rejected. We conclude that defective proportions are different.
Marascuilo Procedure
Level of Significance
0.05
Square Root of Critical Value
2.447746831
Sample Proportions
Group 1
0.03
Group 2
0.04
Group 3
0.08
MARASCUILO TABLE
Proportions
Absolute Differences
Critical Range
| Group 1 - Group 2 |
0.01
0.028440248
Not significant
| Group 1 - Group 3 |
0.05
0.035080576
Significant
| Group 2 - Group 3 |
0.04
0.03663452
Significant
Multiple comparison tests show that supplier C is different from suppliers A and B.
By comparing the proportion of defects, supplier A is best supplier and C is of poor quality.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
A
B
C
Total
fo-fe
Defective
15
20
40
75
-10
-5
15
Good
485
480
460
1425
10
5
-15
Total
500
500
500
1500
Expected Frequencies
Column variable
Row variable
A
B
C
Total
(fo-fe)^2/fe
Defective
25
25
25
75
4.0000
1.0000
9.0000
Good
475
475
475
1425
0.2105
0.0526
0.4737
Total
500
500
500
1500
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
3
Degrees of Freedom
2
Results
Critical Value
5.991
Chi-Square Test Statistic
14.73684
p-Value
0.000631
Reject the null hypothesis
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