Confidence Intervals: Summary of Formulas 1.5 2008/06/06 16:39:36 GMT-5 2008/07/21 03:01:13.108 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics General form of a confidence interval ( lower value , upper value ) = ( point estimate - error bound , point estimate + error bound ) To find the error bound when you know the confidence interval error bound = upper value - point estimate OR error bound = upper value - lower value 2 Single Population Mean, Known Standard Deviation, Normal Distribution Use the Normal Distribution for Means EBM = z α 2 ⋅ σ n The confidence interval has the format ( x - EBM , x + EBM ) . Single Population Mean, Unknown Standard Deviation, Student-t Distribution Use the Student-t Distribution with degrees of freedom df = n - 1 . EBM = t α 2 ⋅ s n Single Population Proportion, Normal Distribution Use the Normal Distribution for a single population proportion p ' = x n EBP = z α 2 ⋅ p ' ⋅ q ' n p ' + q ' = 1 The confidence interval has the format ( p ' - EBP , p ' + EBP ) . Point Estimates x is a point estimate for μ p ' is a point estimate for ρ s is a point estimate for σ