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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's-t distribution

Use the Student's-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

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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