Problem
A new agency publishes results of a recent poll. It reports that a certain candidate has a 9-points stronger support in town A than in town B because 38% of the poll participants in town A and 29% of the poll participants in town B supported the candidate. Notice that 400 randomly selected registered voters participated in the poll in each town, and the reported margins of error correspond to 90% confidence interval.
i. What is the margin of error should the news agency report for the listed estimate 38%?
ii. What is the margin of error should the news agency report for the listed estimate 9%?