In a shop study, a set of data was collected to determine whether or not the proportion of defectives produced was the same for workers on the day, evening, or night shifts. The data were collected and shown in the following table. Shift Day Evening Night Defectives 50 60 70 Non-defectives 950 840 880 (a) Use a 0.05 level of significance to determine if the proportion of defectives produced is the same for all three shifts. (10%) (b) Let X=0 and X=1 denote the "defective" and "non-defective" events, and Y=1,2,3 denote the shift of "Day", "Evening" and "Night", respectively. Use a 0.05 level of significance to determine whether the variables X and Y are independent. (10%) (c) What is the relationship between problems (a) and (b)? (5%)