A production line operates with a mean filling weight of 16 ounces per container. Overfilling or underfilling presents a serious problem and when detected requires the operator to shut down the production line to readjust the filling mechanism. From past data, a population standard deviation σ = .8 ounces is assumed. A quality control inspector selects a sample of 30 items every hour and at that time makes the decision of whether to shut down the line for readjustment. The level of significance is α = .05.

a. State the hypothesis test for this quality control application.

b. If a sample mean of x = 16.32 ounces were found, what is the p-value? What action would you recommend?

c. If a sample mean of x = 15.82 ounces were found, what is the p-value? What action would you recommend?

d. Use the critical value approach. What is the rejection rule for the preceding hypothesis testing procedure? Repeat parts (b) and (c). Do you reach the same conclusion?