Question: The personnel manager for a large airline has claimed that, on average, workers are asked to work no more than 3 hours overtime per week. Past studies show the standard deviation in overtime hours per worker to be 1.2 hours. Suppose the union negotiators wish to test this claim by sampling payroll records for 250 employees. They believe that the personnel manager's claim is untrue but want to base their conclusion on the sample results.

a. State the research, null, and alternative hypotheses and discuss the meaning of Type I and Type II errors in the context of this case.

b. Establish the appropriate decision rule if the union wishes to have no more than a 0.01 chance of a Type I error.

c. The payroll records produced a sample mean of 3.15 hours. Do the union negotiators have a basis for a grievance against the airline? Support your answer with a relevant statistical procedure.