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At an umbrella manufacturing facility, umbrella handles are measured and then removed from the assembly line if they don't meet specifications. A daily report indicates how many rejected handles were produced by each of three presses at the facility during each of three shifts. A quality engineer wants to determine whether press and shift are associated.
The engineer performs a chi-square test for association to determine whether the press and the shift that produced the rejected handles are associated.
For this data, the Pearson chi-square statistic is 11.788 (p-value = 0.019) and the likelihood ratio chi-square statistic is 11.816 (p-value = 0.019). Both p-values are less than the significance level of 0.05. Thus, the engineer concludes that the variables are associated and that the performance of the presses varies depending on the shift.
The first shift produces the most rejected handles (160), and a large proportion of the bad handles come from press 2 (76). The number of bad handles produced on press 2 during shift 1 is much larger than would be expected if the variables were independent. The engineer uses this information to investigate the rejected handles from Press 2, made on the first shift.
| 1st shift | 2nd shift | 3rd shift | All | |
|---|---|---|---|---|
| 1 | 48 | 47 | 48 | 143 |
| 56.08 | 46.97 | 39.96 | ||
| 1.1637 | 0.0000 | 1.6195 | ||
| 2 | 76 | 47 | 32 | 155 |
| 60.78 | 50.91 | 43.31 | ||
| 3.8088 | 0.2998 | 2.9530 | ||
| 3 | 36 | 40 | 34 | 110 |
| 43.14 | 36.13 | 30.74 | ||
| 1.1809 | 0.4151 | 0.3468 | ||
| All | 160 | 134 | 114 | 408 |
| Chi-Square | DF | P-Value | |
|---|---|---|---|
| Pearson | 11.788 | 4 | 0.019 |
| Likelihood Ratio | 11.816 | 4 | 0.019 |
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