Lecture+4

# Lecture+4 - Data analysis • Gaussian distribution • t...

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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 μ σ − = z y z μ σ − = μ σ 2 σ Mean Standard deviation Variance Gaussian or normal distribution ( ) ( ) 2 2 1 , , e x p 2 2 x f y μ μ σ σ σ π ⎛ ⎞ − = − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ x z μ σ − = The standardized normal deviate z x n σ μ = ± Confidence interval: Interval within which the true value almost certainly lies! Confidence intervals z x n σ μ = ± Z= 1.96 Z= 2.58 Z= 0.67 Student’s 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 μ = ± 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 σ = 0.3....
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Lecture+4 - Data analysis • Gaussian distribution • t...

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