EXAMPLE 21 Sample size for estimating when is known

Refer to Example 20. Suppose that the Gallup Organization now wanted to estimate the population proportion of those who think there should be a law that would ban the possession of handguns to within a margin of error of with 95% confidence. How large a sample size is needed?

Solution

From Example 20, we have the sample proportion . The confidence level of 95% implies that our , and the desired margin of error is . Thus, the required sample size is

469

Rounding up, this gives us a minimum required sample size of 8955. The smaller margin of error requires a larger sample size.