Quiz 3

# Quiz 3 - Inference on the Means of 2 Populations, Variances...

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Inference on the Means of 2 Populations, Variances Known Assumptions: Both samples are random samples, independent, and are normal (if not normal, C.L.T. apply) E(Xbar1 – Xbar2) = E(Xbar1) – E(Xbar2) = μ1-μ2 V(Xbar1-Xbar2)=V(Xbar1)+V(Xbar2)= + σ12n1 σ22n2 = - -( - ) + Z X1 X2 μ1 μ2 σ12n1 σ22n2 Hypothesis Testing on the Difference in Means, Variances Known Null hypothesis: μ1-μ2 = delta_0 Test stat: = - - + Z0 X1 X2 ∆0σ12n1 σ22n2 Alternative Hyp: != delta_0—P-value: P above Z_0 and P below –Z_0, P = 2[1-phi(|Z_0|)] Rejection: Z_0 > Z_a/2 or Z_0 < -Z_a/2 Hyp > Delta_0—P-value: P above Z_0, P = 1-phi(Z_0), reject Z_0 > Z_a Hyp < Delta_0—P-value: P below Z_0, P = phi(Z_0), reject Z_0 < Z_a Type II Error and Choice of Sample Size Sample Size for 2-sided Alt Hyp. On Difference in Means, Variances known, n1=n2 = + ( + )( - ) n Zα2 Zβ2 σ12 σ22 Δ Δσ 2 For one-sided: = + ( + )( - ) n Zα Zβ2 σ12 σ22 Δ Δ0 2 = - - + - - - - + β ϕZα2 Δ Δ0σ12n1 σ22n2 ϕ Zα2 Δ Δ0σ12n1 σ22n2

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## This note was uploaded on 09/17/2008 for the course IEE 380 taught by Professor Anderson-rowland during the Spring '06 term at ASU.

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Quiz 3 - Inference on the Means of 2 Populations, Variances...

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