An Accountemps survey asked workers to identify what behavior of coworkers irritates them the most. Forty-one percent of the workers surveyed said that sloppy work is the most irritating behavior. Suppose that this percentage is based on a random sample of 500 workers.
a. Construct a 95% confidence interval for the proportion of all workers who will say that sloppy work is the most irritating behavior of their coworkers.
b. Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Discuss all possible alternatives. Which alternative is the best?