EXAMPLE 3 Understanding the news

Here’s what the TV news announcer says: “A new Gallup Poll finds that a slight majority of 54% of American adults feel it is extremely important that parents vaccinate their children. The margin of error for the poll was 4 percentage points.” Plus or minus 4% starting at 54% is 50% to 58%. Most people think Gallup claims that the truth about the entire population lies in that range.

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This is what the results from Gallup actually mean: “For results based on a sample of this size, one can say with 95% confidence that the error attributable to sampling and other random effects could be plus or minus 4 percentage points for American adults.” That is, Gallup tells us that the margin of error includes the truth about the entire population for only 95% of all its samples—“95% confidence” is shorthand for that. The news report left out the “95% confidence.”