EXAMPLE 4 What is the margin of error?

The Gallup Poll in Example 1 interviewed 1015 people. The margin of error for 95% confidence will be about

Gallup announced a margin of error of 4%, and our quick method gave us 3.1%. Our quick and approximate method can disagree a bit with Gallup’s for two reasons. First, polls usually round their announced margin of error to the nearest whole percent to keep their press releases simple. Second, our rough formula works for an SRS. We will see in the next chapter that most national samples are more complicated than an SRS in ways that tend to slightly increase the margin of error. In fact, Gallup’s survey methods section for this particular poll included the statement, “Each sample of national adults includes a minimum quota of 50% cellphone respondents and 50% landline respondents, with additional minimum quotas by time zone within region. Landline and cellular telephone numbers are selected using random-digit-dial methods.” While these methods go beyond what we will study in the next chapter, the complexity of collecting a national sample increases the value of the margin of error.