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Unformatted text preview: Data analysis Gaussian distribution t test Q test Confidence interval Statistics gives us tools to accept conclusions that have a high probability of being correct and to reject conclusions that do not. N(0,0.2) Gaussian Distribution y z = z y z = 2 Mean Standard deviation Variance Gaussian or normal distribution ( ) ( ) 2 2 1 , , e x p 2 2 x f y = x z = The standardized normal deviate z x n = Confidence interval: Interval within which the true value almost certainly lies! Confidence intervals z x n = Z= 1.96 Z= 2.58 Z= 0.67 Students distribution Sample mean 1 n i i x x n = = 2 1 ( ) 1 n i i x x s n = = Sample standard deviation ts x n = Confidence interval W.S. Gosset (1908), a distribution for a sample. The quantity t has a known distribution: x x t s = Applications Example : Daily level of an impurity in a reactor has a mean 4.0 and = 0.3....
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 Spring '11
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