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Class meeting 13

# Class meeting 13 - CHEN 3010 Applied Data Analysis Class...

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1 CHEN 3010 Applied Data Analysis Class Meeting #13 Tuesday, Oct. 12 th Today's Topics Reading for Thursday: pages 172-177 Homework #6 due Thursday P-values OC curves and sample size formulas The "variance unknown" case: hypothesis testing confidence intervals

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2 Normal Distribution with Two-sided Critical Region 0.00E+00 1.00E+00 2.00E+00 3.00E+00 4.00E+00 5.00E+00 6.00E+00 39.6 39.7 39.8 39.9 40 40.1 40.2 40.3 40.4 xbar f(xbar) P-values threshold rejection probability values x P in this case, P is the probability that a value of or lower would occur, given the distribution centered at μ=40 x If we chose α=P, the H0/H1 decision would be borderline
3 OC Curves for Normal Distribution, alpha = 0.01 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 3.5 sigma shift beta 3 5 7 10 20 n=10 for beta = 20% at sigma shift of 1 These curves depend on the distribution (normal here) and the α value. With Excel, curves can be "live" and readjust for different α's. OC curves give a better "feel" for selection of n than the formulas (used in the text). OC Curves

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4 Sample size formulas for one-sided hypothesis test 2 10 zz n αβ δ µµ δσ +  = =   σ shift in μ in terms of number of σ's for two-sided hypothesis test 2 2 n +
5 Example calculation from Workshop #12 0.01 α= 0.2 β= 1 δ σ = z 2.33 α = z 0.84 β = one-sided n 2 2.33 0.84 n 10.04 10 1 +  = =   two-sided n 2 z 2.58 = 2 2.58 0.84 n 11.7 11 1 + = = same as graph

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6 4-5 Inference on the Mean of a Population, Variance Unknown 4-5.1 Hypothesis Testing on the Mean
7 Variance ( & std dev ) must be estimated from sample

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Class meeting 13 - CHEN 3010 Applied Data Analysis Class...

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