proportional confidence intervals We will measure a single stastistic from a large population, and call it the point estimate. This is usually denoted as \hat{p}. Given a proportion \hat{p} (“95% of sample), the range which would possibly contain it as part of its 2\sigma range is the 95\% confidence interval. Therefore, given a \hat{p} the plausible interval for its confidence is:

where, n is the sample size, \hat{p} is the point estimate, and z*=1.96 is the critical value, the z-score denoting 95\% confidence (or any other desired confidence level). conditions for proportional confidence interval There are the conditions that make a proportional confidence interval work distribution is normal n\hat{p} and n(1-\hat{p}) are both >10 we are sampling with replacement, or otherwise sampling <10\% of population (otherwise, we need to apply a finite population correction value confidence intervals The expression is:

where t* is the t score of the desired power level with the correct degrees of freedom; s the sample standard deviation, n the sample size, and \har{x} the mean.