of Different Sizes
The data in the following table can be used, under an assumption of simple random sampling, to calculate the confidence interval around estimates based on samples of different sizes. It is based on a sample that is evenly divided in two halves on a measure, that is, 50 percent each. This produces the maximum confidence interval. The confidence interval would be smaller for proportions that are more extreme or divided, say 80 percent to 20 percent, in an equivalent sample of the same size. These calculations also assume that the samples are drawn from a population of at least 10,000.
Suppose a survey based on a simple random sample of 1,500 respondents reports that 52 percent support Al Gore and 48 percent support George W. Bush. Using this table, you could conclude that 95 percent of the time, the proportion of people in the population who support Gore lies between 49.5 percent and 54.5 percent (52 percent ±2.5 percent).
It is important to remember that analysis of subsamples implies that a different row of the table must be referenced for the appropriate confidence interval. For example, the typical sample of adults in the United States would include about half male and half female respondents. So a sample of 1,500 respondents would consist of approximately 750 males and 750 females. While the confidence around an estimate of Gore support in the entire sample should be ±2.5 percentage points, for the subsample of either men or women, it would be ±3.6 percentage points.