Statistics

A television poll. A television news program conducts a call-in poll about the salaries of business executives. Of the 2372 callers, 1921 believe that business executives are vastly overpaid and that their pay should be substantially reduced. The station, following recommended practice, makes a confidence statement: “81% of the Channel 13 Pulse Poll sample believe that business executives are vastly overpaid and that their pay should be substantially reduced. We can be 95% confident that the true proportion of citizens who believe that business executives are vastly overpaid and that their pay should be substantially reduced is within 1.6% of the sample result.” The confidence interval calculation is correct, but the conclusion is not justified. Why not?