EXAMPLE 6 2012 election polls

In 2012, shortly before the presidential election, SurveyUSA, a polling organization, asked voters in several states who they would vote for. In Minnesota they asked a random sample of 574 likely voters, and 50% said they would vote for Barack Obama and 43% said Mitt Romney. SurveyUSA reported the margin of error to be plus or minus 4.2%. In Georgia they sampled 595 likely voters, and 44% said they would vote for Obama and 52% said Romney. The margin of error was reported to be plus or minus 4.1%.

There you have it: the sample of likely voters in Georgia was slightly larger, so the margin of error for conclusions about voters in Georgia is slightly smaller (4.1% compared to 4.2%). We are 95% confident that between 39.9% (that’s 44% minus 4.1%) and 48.1% (that’s 44% plus 4.1%) of likely voters in Georgia would vote for Obama. Note that the actual 2012 election results for Georgia were 45.5% for Obama, which is within the margin of error.