A multinational corporation employing several thousand workers at its campus in a large city in the southwestern United States would like to estimate the proportion of its employees who commute to work by any means other than an automobile. The company hopes to use the information to develop a proposal to encourage more employees to forgo their automobiles as a part of their commute. A pilot study of 100 randomly sampled employees found that 14 commute to work by means other than an automobile.
a. How many more employees must the company randomly sample to be able to estimate the true population of employees who commute to work by means other than an automobile with a margin of error of ± 0.03 and a level of confidence of 90%?
b. Suppose that after the full sample is taken, it was found that 50 employees commute to work by means other than an automobile. Construct a 90% confidence interval estimate for the true population of employees who commute to work using means other than an automobile.