4. [25 points] The PCB concentration of a sh caught in a lake is measured by a technique that is known to result in an error of measurement. Suppose the results of 5 independent measurements of this sh are 11.2, 12.4, 10.8, 11.6, 12.5 in ppm (parts per million). (a) You are given that the standard deviation of the error of measurement is 0.3 ppm. Construct a 95% condence interval of the true PCB concentration. What assumptions are required? (b) Using the information provided in part (a), determine the minimum sample size needed to obtain a margin of error for the true PCB concentration within 0.01 ppm with 90% condence. What assumptions are required? (c) Repeat parts (a) and (b), but without using any information about the standard deviation of the error of measurement provided in part (a). In repeating part (b), the minimum sample size needed now refers to the additional size beyond the 5 measurements that are already taken. (d) Again without using any information in part (a), construct a 95% condence interval for the standard deviation of the error of measurement. What assumptions are required