When the Gallup Organization conducted the poll introduced in Example 1, 54.9% of those surveyed considered the amount of federal income tax they have to pay as fair. Gallup reported its “survey methodology” as follows:

Results are based on telephone interviews with a random sample of 1016 national adults, aged 18 and older. For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is 4 percentage points.

Determine and interpret the confidence interval for the proportion of Americans aged 18 and older who believe the amount of federal income tax they have to pay is fair.

Approach Confidence intervals for a proportion are of the form point estimate ± margin of error. So add and subtract the margin of error from the point estimate to obtain the confidence interval. Interpret the confidence interval, “We are 95% confident that the proportion of Americans aged 18 and older who believe that the amount of federal income tax they have to pay is fair is between lower bound and upper bound.”

Data from Example 1

The Gallup Organization conducted a poll in which a simple random sample of 1016 Americans 18 and older were asked, “Do you consider the amount of federal income tax you have to pay is fair?” Of the 1016 adult Americans surveyed, 558 said yes. Obtain a point estimate for the proportion of Americans 18 and older who believe the amount of federal income tax they pay is fair.