CheatSheet_Final_12 Dec 06

CheatSheet_Final_12 Dec 06 - Authorized Reference Sheet for...

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Authorized “Reference Sheet” for IENG 213 Final Exam © 2004-2006 Steven E. Guffey, PhD, CIH 1/5 12/12/2006 Confidence Intervals Confidence interval, single mean, variance known: /2 1 ZZ PX X nn αα σσ µ α −< < + = ⎜⎟ 2 Z n e σ ⎛⎞ ⎝⎠ = 5 . 0 2 / n Z e Confidence interval, single mean, variance NOT known: 1 tS Px x < + = υ = n 1 -1 Tolerance Limits: (1−γ )% confidence that the given limits contain at least the proportion (1 – α) of the measurements: µ ± k σ x ± k s Difference between 2 means, both variances known: () 22 12 / 2 1 2 / 2 1 Px x z x x z µα ⎡⎤ −− + < < −+ + = ⎢⎥ ⎣⎦ 2 2 2 1 2 1 2 1 n n x x + = Difference between 2 means, variances NOT known, but assumed EQUAL: / 2 / 2 11 ( ) 1 pp P x xt s x s +<− <−+ + = 2 ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 2 + + = n n S n S n S p υ = n 1 + n 2 – 2 Difference between 2 means, variances NOT known, but assumed UN EQUAL: / 2 / 2 ( ) 1 ss Px x t x x t + = ( ) 2 11 22 1 2 // 1 1 snsn sn n n υ + = +−
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Authorized “Reference Sheet” for IENG 213 Final Exam © 2004-2006 Steven E. Guffey, PhD, CIH 2/5 12/12/2006 Confidence Interval for Mean of Differences of Paired Data: /2 1 dd d ts Pd d nn αα µ α ⎧⎫ −< < + = ⎨⎬ ⎩⎭ µ d = µ 1 µ 2 d = x 1 – x 2 ( ) 2 12 1 1 n d d i xx s n = −− = υ = df = n pairs – 1
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CheatSheet_Final_12 Dec 06 - Authorized Reference Sheet for...

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