Homework SourseA company operates four machines during three shifts each da
A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift.
Machine
Shift
A
B
C
D
1
41
20
12
16
2
31
11
9
14
3
15
17
16
10
| Machine | ||||
| Shift | A | B | C | D |
| 1 | 41 | 20 | 12 | 16 |
| 2 | 31 | 11 | 9 | 14 |
| 3 | 15 | 17 | 16 | 10 |
Solution
A company operates four machines during three shifts each day. From production records, the data in the table below were collected. At the .05 level of significance test to determine if the number of breakdowns is independent of the shift. Machine Shift A B C D 1 41 20 12 16 2 31 11 9 14 3 15 17 16 10
A.The number of breakdowns is dependent on the shift, because the test value 11.649 is less than the critical value of 12.592.
B.The claim that the number of breakdowns is independent of the shift cannot be rejected, because the test value 11.649 is less than the critical value of 12.592.
C.The number of breakdowns is dependent on the shift, because the p-value is .07.
D.The number of breakdowns is independent of the shift, because the test value 12.592 is greater than the critical value of 11.649.
Chi-Square Test
Observed Frequencies
Column variable
Row variable
A
B
C
D
Total
1
41
20
12
16
89
2
31
11
9
14
65
3
15
17
16
10
58
Total
87
48
37
40
212
Expected Frequencies
Column variable
Row variable
A
B
C
D
Total
1
36.5236
20.1509
15.5330
16.7925
89
2
26.6745
14.7170
11.3443
12.2642
65
3
23.8019
13.1321
10.1226
10.9434
58
Total
87
48
37
40
212
Calculations
fo-fe
4.4764
-0.1509
-3.5330
-0.7925
4.3255
-3.7170
-2.3443
1.7358
-8.8019
3.8679
5.8774
-0.9434
(fo-fe)^2/fe
0.5486
0.0011
0.8036
0.0374
0.7014
0.9388
0.4845
0.2457
3.2549
1.1393
3.4125
0.0813
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
4
Degrees of Freedom
6
Results
Critical Value
12.592
Chi-Square Test Statistic
11.649
p-Value
0.0703
Do not reject the null hypothesis
| Chi-Square Test | |||||
| Observed Frequencies | |||||
| Column variable | |||||
| Row variable | A | B | C | D | Total |
| 1 | 41 | 20 | 12 | 16 | 89 |
| 2 | 31 | 11 | 9 | 14 | 65 |
| 3 | 15 | 17 | 16 | 10 | 58 |
| Total | 87 | 48 | 37 | 40 | 212 |
| Expected Frequencies | |||||
| Column variable | |||||
| Row variable | A | B | C | D | Total |
| 1 | 36.5236 | 20.1509 | 15.5330 | 16.7925 | 89 |
| 2 | 26.6745 | 14.7170 | 11.3443 | 12.2642 | 65 |
| 3 | 23.8019 | 13.1321 | 10.1226 | 10.9434 | 58 |
| Total | 87 | 48 | 37 | 40 | 212 |
