The Eaton Company sells breakable china through a mail-order system that has been very profitable. One of its major problems is freight damage. It insures the items at shipping, but the inconvenience to the customer when a piece gets broken can cause the customer not to place another order in the future. Thus, packaging is important to the Eaton Company.
In the past, the company has purchased two different packaging materials from two suppliers. The assumption was that there would be no difference in the proportion of damaged shipments resulting from use of either packaging material. The sales manager recently decided a study of this issue should be done. Therefore, a random sample of 300 orders using shipping material 1 and a random sample of 250 orders using material 2 were pulled from the files. The number of damaged parcels, x , was recorded for each material as follows:

a. Is the normal distribution a good approximation for the distribution of the difference between the sample proportions? Provide support for your answer.
b. Based on the sample information and a = 0.03, what should the Eaton Company conclude?