A manufacturer of women€™s shoes wishes to compare the distribution of defects found in the shoes produced by the three shifts of workers in his plant. A sample of shoes with defects is classified as to type of defect and production shift.

a. Would the proportions of the four defects being the same for all three shifts imply that defects are independent of shift? Explain why or why not.
b. What would it imply if the proportions vary from shift to shift? Explain.
c. Do the data above show that the proportions vary significantly from shift to shift at the a = 0.01 level of significance? Explain, stating your decision, conclusion, and evidence very carefully.

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Type of Defect Shift 6 a.m. 2 p.m. 10 p.m. AB 17 27 31 43 23 37 19 17 53 18 nA