Using samples of 194 credit card statements, an auditor found the following:
Sample 1 2 3 4
With errors 4 6 5 8
a. Determine the fraction defective in each sample
b. If the true fraction of defective for this process is unknown, what is your estimate of it?
c. What is your estimate of the mean and standard deviation of the sampling distribution of fractions defective for this sample size?
d. What control limits would give an alpha risk of 0.03 for this process?
e. What alpha risk would control limits of 0.047 and 0.012 provide?
f. Using control limits of 0.047 and 0.12, is the process in control?
g. Suppose that the long term fraction defective of the process is known to be 2%. What are the values of the mean and the standard deviation of the sampling distribution?
h. Construct a control chart for the process, assuming a fraction defective of 2%, using two-sigma control limits. Is the process in control?