Question: Every 10 years, the United States takes a census. The census tries to count every resident. There are two forms, known as the "short form," answered by most people, and the "long form," slogged through by about one in six or seven households chosen at random. According to the Census Bureau (www.census.gov),". each estimate based on the long form responses has an associated confidence interval."
Why is this so? For example, why should a confidence interval for the mean amount families spend monthly on housing be wider for a sparsely populated area of farms in the Midwest than for a densely populated area of an urban center? How does the formula show this will happen? To deal with this problem, the Census Bureau reports long-form data only for " geographic areas from which about two hundred or more long forms were completed-which are large enough to produce good quality estimates. If smaller weighting areas had been used, the confidence intervals around the estimates would have been significantly wider, rendering many estimates less useful."