Section 8.3 Summary

1. The sample proportion of successes

   is a point estimate of the population proportion .

2. The confidence interval for the population proportion is given by

   where is the sample proportion of successes , is the sample size, and depends on the confidence level. The interval for may be constructed only if both the following conditions apply: and (alternatively, and ).

3. Note that the confidence interval for takes on the form

   where is the point estimate of and is the margin of error.

4. Suppose we want to estimate the population proportion to within a margin of error with confidence . If is known, then the required sample size needed is given by

   If is not known, then the required sample size needed is given by