3. P343. 13. A sociologist is interested in surveying workers in computer-related jobs to estimate the proportion of such workers who has changed jobs within the past years. (a) In the absence of preliminary data, how large a sample must be taken to ensure that a 95% con dence interval will specify the proportion to within 0:05? (b) In a sample of 100 workers, 20 of them had changed jobs within the past year. Find a 95% con dence interval for the proportion of workers who have changed jobs within the past year. (c) Based on the data in part (b), estimate the sample size needed so that the 95% con dence interval will specify the proportion to within 0:05.