4. Your factory makes umbrellas. You know from past experience that 2% are defective. You think, however, that the process may have changed since you hired a bunch of new employees ten days ago. In the 10 days previous to the new hires arriving you observed 25 defects out of a batch of 1000. In the 10 days since, there have been 29 defects out of 1000. At the 5% level, using two-sided tests, do the following: (a) Test Ho : P1 = 0.02 based on the first 10 days of data. (b) Test Ho : p2 = 0.02 based on the last 10 days of data. (c) Test Ho : p = 0.02 based on all the data combined. (d) Test Ho : P1 - P2 = 0 by comparing data from the two samples. (e) Explain in words the discrepancy between the various tests