a. Simulate the following process for 20 days: Each day, 200 calculators are manufactured with a 5% rate of defects, and the proportion of defects is recorded for each of the 20 days. The calculators for one day are simulated by randomly generating 200 numbers, where each number is between 1 and 100. Consider an outcome of 1, 2, 3, 4, or 5 to be a defect, with 6 through 100 being acceptable. This corresponds to a 5% rate of defects.

b. Construct a p chart for the proportion of defective calculators, and determine whether the process is within statistical control. Since we know the process is actually stable with p = 0.05, the conclusion that it is not stable would be a type I error; that is, we would have a false positive signal, causing us to believe that the process needed to be adjusted when in fact it should be left alone.

c. The result from part (a) is a simulation of 20 days. Now simulate another 10 days of manufacturing calculators, but modify these last 10 days so that the defect rate is 10% instead of 5%.

d. Combine the data generated from parts (a) and (c) to represent a total of 30 days of sample results. Construct a p chart for this combined data set. Is the process out of statistical control? If we concluded that the process was not out of statistical control, we would be making a type II error; that is, we would believe that the process was okay when in fact it should be modified to correct the shift to the 10% rate of defects.