The makers of High Life Dog Food have an automated filling machine that can be set at any targeted fill level between 10 and 40 pounds. At the end of every shift (eight hours), 16 bags are selected at random and the mean and standard deviation of the sample are computed. Based on these sample results, the production control manager determines whether the filling machine needs to be readjusted or whether it remains all right to operate. Previous data suggest the fill level has a normal distribution with a standard deviation of 0.65 pounds. Use α = 0.05. At the end of a run of 20-pound bags, a sample of 16 bags was taken and tested using a two-sided test to determine if the mean fill level was equal to 20 pounds.
a. Calculate the probability that the test procedure will detect that the average fill level is not equal to 20 pounds when in fact it equals 20.5 pounds.
b. On the basis of your calculation in part a, would you suggest a change in the test procedure? Explain what change you would make and the reasons you would make this change.