3. A factory manufactures batches of an electronic component. Each component is manufactured in one of three shifts. A component may have one of two types of defect, \(D _ { 1 }\) or \(D _ { 2 }\), at the end of the manufacturing process. A production manager believes that the type of defect is dependent upon the shift that manufactured the component. He examines 200 randomly selected defective components and classifies them by defect type and shift. The results are shown in the table below.
| \backslashbox{Shift}{Defect type} | \(D _ { 1 }\) | \(D _ { 2 }\) |
| First shift | 45 | 18 |
| Second shift | 55 | 20 |
| Third shift | 50 | 12 |
Stating your hypotheses, test, at the \(10 \%\) level of significance, whether or not there is evidence to support the manager's belief. Show your working clearly.