6.Suppose a pet supplies company uses three manufacturing centers for the production of its cat toys. The defect classification for item production contains three levels: no defects, minimal defects but still acceptable for use, and significant defects where the item does not meet quality standards.
Connor, a quality assurance specialist at the pet supplies company, plans to run a chi-square test of homogeneity to determine if the proportion of cat toy items in each defect category is the same across the three manufacturing centers. He sets the significance level for the test at =0.05.
He randomly selects 388 items from Center A, 406 items from Center B, 274 items from Center C, and records the defect classification of each item.
The sample results are summarized in the contingency table.
--value =________________ (Round to 3 decimal places)
Select the accurate statement regarding Connor's hypothesis test decision and conclusion.
INCORRECT Connor should reject the null hypothesis because there is sufficient evidence (-value < 0.05) to reject the null. Thus, Connor should conclude that the manufacturing center used is not independent of the defective rate.
Connor should fail to reject the null hypothesis because there is insufficient evidence (--value < 0.05) to reject the null. Thus, Connor should conclude that the frequency distribution for each defect classification is the same across the manufacturing centers.
Connor should fail to reject the null hypothesis because there is insufficient evidence (--value > 0.05) to reject the null. Thus, Connor should conclude that defect classification proportions are uniform across the manufacturing centers.
Connor should reject the null hypothesis because there is sufficient evidence (-value < 0.05) to reject the null. Thus, Connor should conclude that there is homogeneity in the defect classification proportions across the manufacturing centers.
Connor should reject the null hypothesis because there is sufficient evidence (-value < 0.05) to reject the null. Thus, Connor should conclude that at least one of the proportions for a defect classification is different among the three manufacturing centers.
