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Unformatted text preview: Confidence Intervals Definition . Level C confidence inter val (C.I.) for θ is interval ( L,U ) where L,U obtained from data, such that P ( L ≤ θ ≤ U ) = C no matter what θ. Typically, C = 0 . 90 , . 95 , . 99 . C.I. is interval estimator, represents set of plausible estimates for θ , unlike a point estimator which is only one value and doesn’t take into account sampling error. 1 C.I. Normal Mean & Known Variance Let θ = μ population mean. Point es timator ˆ Θ = ¯ X is unbiased. Sampling distribution is ¯ X ∼ when population is normal. 2 How to find C.I. • Standardize: Z = • Find from normal table value z * with P ( ) = C 3 • Substitute P ( ) = C • Rearrange inequalities 4 • Hence C.I. has structure ¯ X ± = point estimate ± ME where margin of error ME = z * σ √ n 5 Suppose C = 0 . 90 , 1 C 2 = . 10 2 = 0 . 05 ,. Look up z * corresponding to 1 1 C 2 = 1 . 05 = 0 . 95 . Get z * = 1 . 645 ....
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 Fall '10
 drera
 Normal Distribution, µ, 90%

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