A systems engineer is experimenting with a system that has traditionally produced an average quality index of 10 and a standard
deviation of 10. She is experimenting with a new method, and she will produce n outputs that are normally distributed with a new mean and the same standard deviation of 10. A standard Single Sample Z Test will be used. You would like to find a value of n such that the type I error rate is less than 5% and the type II error rate is less than 10% if the population mean of the new method is 8. Try the following values for n: 100, 200, 300, 400 and 500. Which ones meet the criteria? Which one would you choose considering that samples cost money?
