Records show that in a random sample of 100 hours a machine produced an hourly average of 678 articles with a standard deviation of 25. After a safety device was installed, in a random sample of 500 hours the machine produced an hourly average of 674 articles with a standard deviation of 5. Pointing to the drop of 4 articles per hour in the sample mean, management claimed the safety device was reducing production. The union countered that the drop of 4 articles was "merely statistical fluctuation."

(a) To objectively summarize the evidence on whether production is left unchanged, calculate the prob-value.

(b) If the arbitration board decides that a = 1 % is a fair level of significance (type I error), do they rule in favor of management or union?