Question: A production line for a popular soft drink 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 in order to readjust the filling

mechanism. From historical data, a population standard deviation of 0.8 ounces is assumed

for the individual containers. A quality control inspector selects a sample of 36 items at

regular intervals. Afterward, this individual makes the decision of whether or not to shut

down the line for readjustment. Suppose that a particular selection of 36 containers results

in a sample mean of 16.32 ounces. The company uses a level of significance of 0.05.

(a) Formulate the appropriate null and alternative hypotheses.

(b) Provide the critical value(s) and clearly present the rejection and nonrejection regions.

(c) Compute the value of the appropriate test statistic.

(d) Combine your results in (b) and (c) to make a decision. I’d like you to provide a graphic representation of your results. Also, state specifically what your decision is. Provide the mathematical reason for making this decision.

(e) At the 5% level of significance, what is your conclusion about the need to readjust?

(f) Calculate the p-value(s). Make the appropriate comparison. Then, make a decision.