MidTermExamEquations

# MidTermExamEquations - Related Information Quadratic...

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Related Information Quadratic Equation: if ax 2 + bx + c = 0 , then x = - b ± b 2 - 4 ac 2 a Standard Deviation: s = r ( x i - x ) 2 N - 1 Error Propagation Equation: σ 2 y ( u, v,. .. ) = σ 2 u ± dy du ² 2 + σ 2 v ± dy dv ² 2 + ··· t-tests: True Mean Comparison: x 1 - x 2 = ± ts/ N Measured Means Comparison (when σ 2 1 = σ 2 2 ): x 1 - x 2 = ± ts pooled r N 1 + N 2 N 1 N 2 s pooled = s s 2 1 ( N 1 - 1) + s 2 2 ( N 2 - 1) N 1 + N 2 - 2 Measured Means Comparison (when σ 2 1 6 = σ 2 2 ): | x 1 - x 2 | = ± t p s 2 1 /N 1 + s 2 2 /N 2 ν = ( s 2 1 /N 1 + s 2 2 /N 2 ) 2 ( s 2 1 /N 1 ) 2 N 1 + 1 + ( s 2 2 /N 2 ) 2 N 2 + 1 - 2 Degrees of Freedom, ν t(90%) t(95%) t(99%) 1 6.314 12.706 63.657 2 2.920 4.303 9.925 3 2.353 3.182 5.841 4 2.132 2.776 4.604 5 2.015 2.571 4.032 6 1.943 2.447 3.707 7 1.895 2.365 3.500 8 1.860 2.306 3.355 9 1.833 2.262 3.250 10 1.812 2.228 3.169 1.64 1.96 2.576 Table 1: Values of t for ν degrees of freedom for 95% conﬁdence levels. ν = N - 1 = degrees of freedom, and conﬁdence limit = x ± ts N . 11

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F Distribution F = s 2 A s 2 B . (1) Note that critical F values in the two-tailed F -test table with probability p/ 2 can be found in the one-tailed table F -test with probability p . ν 1 =1 2 3 4 5 6 7 8 9 10 12 15 20 ν 2 1 161.4 199.5 215.7 224.6 230.2 234.0 236.8 238.9 240.5 241.9 243.9 245.9 248.0 254.3 2 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.43 19.45 19.50 3 10.13 9.552 9.277 9.117 9.013 8.941 8.887 8.845 8.812 8.786 8.745 8.703 8.660 8.53 4 7.709 6.944 6.591 6.388 6.256 6.163 6.094 6.041 5.999 5.964 5.912 5.858 5.803 5.63 5 6.608 5.786 5.409 5.192 5.050 4.950 4.876 4.818 4.772 4.735 4.678 4.619 4.558 4.36 6 5.987 5.143 4.757 4.535 4.387 4.284 4.207 4.147 4.099 4.060 4.000 3.938 3.874 3.67 7 5.591 4.737 4.347 4.120 3.972 3.866 3.787 3.726 3.677 3.637 3.575 3.511 3.445 3.23 8 5.318 4.459 4.066 3.838 3.687 3.581 3.500 3.438 3.388 3.347 3.284 3.218 3.150 2.93 9 5.117 4.256 3.863 3.633 3.482 3.374 3.293 3.230 3.179 3.137 3.073
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## This note was uploaded on 07/17/2008 for the course CHEM 121 taught by Professor Wyzlouzil during the Fall '07 term at Ohio State.

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MidTermExamEquations - Related Information Quadratic...

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