EXAMPLE 1 Should children be vaccinated?

The proportion of all American adults who feel childhood vaccinations are extremely important is a parameter describing the population of 258 million adults. Call it p, for “proportion.” Alas, we do not know the numerical value of p. To estimate p, Gallup took a sample of 1015 adults. The proportion of the sample who favor such an amendment is a statistic. Call it , read as “p-hat.” It happens that 548 of this sample of size 1015 said that they feel childhood vaccines are extremely important, so for this sample,

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Because all adults had the same chance to be among the chosen 1015, it seems reasonable to use the statistic as an estimate of the unknown parameter p. It’s a fact that 54% of the sample feel childhood vaccines are extremely important—we know because we asked them. We don’t know what percentage of all American adults feel this way, but we estimate that about 54% do.