Step 1 :Given that the sample size n = 100 and the proportion of workers who are satisfied with their job p = 0.12.
Step 2 :Calculate the value of \(n p^{\wedge}\left(1-p^{\wedge}\right)\) to verify if it is greater than or equal to 10.
Step 3 :The calculated value of \(n p^{\wedge}\left(1-p^{\wedge}\right)\) is 10.56, which is greater than 10.
Step 4 :Therefore, the sample size is large enough to perform a hypothesis test.
Step 5 :Final Answer: \(\boxed{10.56}\)