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IEOR 165 Lecture 10 June 16 2009 Homework 3 Review

# IEOR 165 Lecture 10 June 16 2009 Homework 3 Review -...

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Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry Hypothesis test ,…, x1 xn sample data = , = , , Test whether mean μ not greater or less than value Two Cases: - know σ2 variance - Do not know variance - 1 st Case We know the variance: - TEST 1 with Confidence Intervals - = H0 μ μ0 = H1 μ not μ0 - - ~ , xbar μσn N0 1 : Using confidence intervals - % : 1 α100 CI - < - < = - P zα2 xbar μσn zα2 1 α - > Reject H0 if xbar μσn zα2 - If it was in the interval, then we CANNOT REJECT H0 - - Test 2 with P Value - - = - p value 2PZ xbar μσn - Reject H0 at any significance level > p-value - - 2 nd Case: We DON’T KNOW VARIANCe - S2sample variance - = H0 μ μ0 H1 μ μ0 - - ~ - xbar μSn tn 1 - - , - * , + , - * xbar tα2 n 1 Sn xbar tα2 n 1 Sn - = - ≥ - p value 2Ptn 1 xbar μ0Sn - - 2 distributions - ,… x1 xn sample data : means of 2 normal distributions ,…, ,…, x1 xn and y1 ym - - Known variance: - - - - + ~ ( , ) xbar ybar μx μyσx2n σy2m N 0 1 - : = H0 μx μy : = H1 μx not μy - TEST 1 Use confidence intervals:

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Lecture Notes IEOR 165 | George Shanthikumar Tu W Th 2-4:30 pm | 3113 Etcheverry - - % : ( - - + , - + + 1 α100 CI
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