A small regional dairy uses four machines to fill gallon jugs with milk. The qua
ID: 3238358 • Letter: A
Question
A small regional dairy uses four machines to fill gallon jugs with milk. The quality control manager is concerned that the proportion of underfilled jugs differs depending upon the machine used to do the filling. Random sampling is done 100 times for each machine and the following results were recorded: Machine 1: 5% were underfilled Machine 2: 7% were underfilled Machine 3: 9% were underfilled Machine 4: 2% were underfilled Is there evidence, at a 10% significance level, that the proportion of underfilled jugs differs depending on the machine that was used to do the filling? The p-value for this test is...
Explanation / Answer
Answer:
A small regional dairy uses four machines to fill gallon jugs with milk. The quality control manager is concerned that the proportion of underfilled jugs differs depending upon the machine used to do the filling. Random sampling is done 100 times for each machine and the following results were recorded: Machine 1: 5% were underfilled Machine 2: 7% were underfilled Machine 3: 9% were underfilled Machine 4: 2% were underfilled Is there evidence, at a 10% significance level, that the proportion of underfilled jugs differs depending on the machine that was used to do the filling? The p-value for this test is...
Ho: the proportion of underfilled jugs not differs depending on the machine that was used to do the filling.
H1: the proportion of underfilled jugs differs depending on the machine that was used to do the filling
Calculated chi square =4.936
P value = 0.1765
Since calculated P= 0.1765 > 0.10 level, there is no evidence that the proportion of underfilled jugs differs depending on the machine that was used to do the filling.
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
C4
Total
fo-fe
R1
5
7
9
2
23
-0.75
1.25
3.25
-3.75
R2
95
93
91
98
377
0.75
-1.25
-3.25
3.75
Total
100
100
100
100
400
Expected Frequencies
Column variable
Row variable
C1
C2
C3
C4
Total
(fo-fe)^2/fe
R1
5.75
5.75
5.75
5.75
23
0.0978
0.2717
1.8370
2.4457
R2
94.25
94.25
94.25
94.25
377
0.0060
0.0166
0.1121
0.1492
Total
100
100
100
100
400
Data
Level of Significance
0.1
Number of Rows
2
Number of Columns
4
Degrees of Freedom
3
Results
Critical Value
6.2514
Chi-Square Test Statistic
4.9360
p-Value
0.1765
Do not reject the null hypothesis
Chi-Square Test
Observed Frequencies
Column variable
Calculations
Row variable
C1
C2
C3
C4
Total
fo-fe
R1
5
7
9
2
23
-0.75
1.25
3.25
-3.75
R2
95
93
91
98
377
0.75
-1.25
-3.25
3.75
Total
100
100
100
100
400
Expected Frequencies
Column variable
Row variable
C1
C2
C3
C4
Total
(fo-fe)^2/fe
R1
5.75
5.75
5.75
5.75
23
0.0978
0.2717
1.8370
2.4457
R2
94.25
94.25
94.25
94.25
377
0.0060
0.0166
0.1121
0.1492
Total
100
100
100
100
400
Data
Level of Significance
0.1
Number of Rows
2
Number of Columns
4
Degrees of Freedom
3
Results
Critical Value
6.2514
Chi-Square Test Statistic
4.9360
p-Value
0.1765
Do not reject the null hypothesis
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