Question

23.8 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?

Answer 1

The estimated proportion is  .

The width of confidence interval is

The width of 95% CI is

Within 1.6% of the sample result means the width of the CI should be

Since , we cannot 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.