The production control manager at Ashmore Manufacturing is interested in determining whether there is a difference in standard deviation of product diameter for part #XC-343 for units made at the Trenton, New Jersey, plant versus those made at the Atlanta plant. The Trenton plant is highly automated and thought to provide better quality control. Thus, the parts produced there should be less variable than those made in Atlanta.

A random sample of 15 parts was selected from those produced last week at Trenton. The standard deviation for these parts was 0.14 inch. A sample of 13 parts was selected from those made in Atlanta. The sample standard deviation for these parts was 0.202 inch.

a. Based on these sample data, is there sufficient evidence to conclude that the Trenton plant produces parts that are less variable than those of the Atlanta plant? Test using a  0.05.

b. Consider the scenario that the Trenton plant is discovered to have a smaller variability than the Atlanta plant. Management, on this basis, decides that they must expend a large amount of money to upgrade the machinery in Atlanta. Suppose also that, in reality, the difference in the observed variability between the two plants is a result of sampling error. Specify the type of error associated with hypothesis testing that was made. How would you modify the hypothesis procedure to guard against such an error?