hypothesis testing and internal control Sampling from a Normal population provides a caricature of quality controI.

Suppose a machine is operating according to tolerances, is "in control" or is "out of controI." If it is out of control, it is necessary to intervene and correet whatever problem has surfaced. Suppose an in control machine produces items with a critical dimension that follows a Normal distribution with a mean of 4.5 inches and a standard deviation of .1 inch. A random sample of 10 units is selected. The sample average dimension is 4.438 inches. What is the probability of observing this or a lower sample average, assuming the machine is in control?

Suppose we expand the above story. It costs so mueh to inspect a unit of output, it costs so much to readjust the machine, and faulty units eventually cost so much in subsequent failure and repair cost. Building on these specifications, we design an optimal quality inspection program for the machine in question. Carefully discuss how this quality control analogy applies and does not apply to internai controI.

AppendixLO1