Question: In a poll to estimate presidential popularity, each person in a random sample of 1,000 voters was asked to agree with one of the following statements:

1. The President is doing a good job.

2. The President is doing a poor job.

3. I have no opinion.

A total of 560 respondents selected the first statement, indicating they thought the President was doing a good job.

a. Construct a 95 percent confidence interval for the proportion of respondents who feel the President is doing a good job.

b. Based on your interval in part (a), is it reasonable to conclude that a majority (more than half) of the population believes the President is doing a good job?