Problem 14 required testingwhether the process was in control using a p chart. Test the hypothesis that the value of p is the same each day using classical statistical methods. That is, test the hypothesis H0: p1 p2 pk versus H1: Not all the pi are equal, where k is the number of days in the data set (k 23 in this case) and pi is the true proportion of defectives for day i. Define xi as the number of rolls of film rejected in day i and p as the estimate of p obtained from the data [p was computed in Problem 14(a)]. The test statistic is given by the formula

where n is the number of items sampled each day (n 25 in this case). The test is to reject H0 if 2 2 ,k1, where 2 ,k1 is a number obtained from a table of the 2 distribution. For .01 (which is larger than the value that yields 3 limits on a p chart), 2 .01,22 40.289. Based on this value of , does the 2 test indicate that this process is out of control? If the answer you obtained is different from that of Problem 14(b), how do you account for the discrepancy? Which method is probably better suited for this application?

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x = (x;- np') np'(1-p')'