Section9 - Anna Lee Jery Stedinger Fall 2006 CEE 304...

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Anna Lee & Jery Stedinger Fall 2006 CEE 304 – Section 9 Handout ( Two Sample Hypothesis Tests) 1. Are men taller than women as is often believed? Look at the following data on heights (with units of inches) that was collected by former CEE 304 students. N Mean Median Stdev Women 4 65.146 64.500 2.441 Men 12 71.258 71.000 2.889 Let us consider these students to be a random sample of Cornell engineering students. Use a t-test appropriate for small n. Women’s height Men’s height __ __ y = 71.258 x = 65.146 s x = 2.441 s y = 2.889 n x = 4 n y = 12 σ x , σ y UNKNOWN, small samples Æ Use t-test, __ __ 2 2 ( ) ( ) x y y x x y X Y T s s n n μ μ = + (i) What are the appropriate hypotheses? Null Hypothesis H o : μ x = μ y Alternative Hypothesis: H a : μ x < μ y Æ lower-tailed test (ii) At the 1% level, what would be the rejection region for the test? α = 1 % Degrees of freedom: 2 2 2 4 2 4 2 1 1 y x x y y y x x x y s s n n s n s n n n ν + = + = 6 6 , 01 . 0 , t t = ν α = -3.143 So, H o is rejected if ν α , t t test < = -3.143 (lower tailed t test).
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