EXAMPLE 19 Understanding the News

Here’s what the TV news announcer says: “A new Gallup poll on American exercise habits finds that 45% of adults are not engaging in vigorous sports or physical activities. The margin of error for the poll was 3 percentage points.” Plus or minus 3%, starting at 45%, is 42% to 48%. People with minimal statistics knowledge may think that the truth about the entire population must be in that interval, but now we know better!

This is the full background Gallup actually gives: “For results based on this sample, one can say with 95% confidence that the maximum error attributable to sampling and other random effects is 3 percentage points. in addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.” That is, Gallup tells us that the margin of error works only for 95% of all its samples; “95% confidence” is shorthand for that longer fact. The news report left out the “95% confidence.” in fact, almost all margins of error in the news are for 95% confidence. if you don’t see the confidence level in a scientific poll, it’s usually safe to assume 95%.