Each item produced by a production system goes through a quality inspection process to be classified as non-defective (ND), partially defective (PD), or totally defective (TD). Over the past several years, category percentages for a certain item produced by this system have stabilized at 85% non-defective (ND), 10% partially defective (PD), and 5% totally defective (TD). The company has purchased a new machine for producing this item. A sample of size 200 items produced by the new machine yielded 180 non-defective (ND), 16 partially defective (PD), and 4 totally defective (TD) items. We are interested to perform a goodness of fit test to determine whether the sample of 200 items produced by the new machine is consistent with the historical distribution of the number of items in each of the three categories. Let PND = probability that an item produced is non-defective (ND) PPD = probability that an item produced is partially defective (PD) PTD = probability that an item produced is totally defective (TD). Required:
a. What is the expected frequency for non-defective category?
b. What is the chi square test statistic?
c. What is the p-value obtained from the chi-square?