Confidence Intervals for Correlation and Proportion

We make these corrections because we approximate a discrete distribution with a continuous one. 

Because the confidence interval ranges from 51% to 59%, the newspaper must have found that 55% of their sample prefer Candidate A. 

Because the confidence interval extends 4% in both directions, the margin of error is 4%. The standard error is sqrt[(.4)(.6)/100] = .0490. The correction = .5/100 = .005. Thus, the upper limit of the 95% confidence interval is: .4 + (1.96)(.049) + .005 = .501. Clearly, there is a large margin of error.