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hw6sol_F10 - Business Statistics Lecture Sections(Prof...

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Business Statistics Lecture Sections (Prof. Inchi HU) Assignment 6 Solution (Problem Sheet 5 #4, 7 - 10 and an extra question) 4. (a) H 0 : p = 0.5 vs H 1 : p > 0.5 55 . 0 100 55 ˆ = = p Test statistic 1 100 ) 5 . 0 )( 5 . 0 ( 5 . 0 55 . 0 ˆ = - = - = n pq p p z obs And z α = z 0.05 = 1.645. Since z < z 0.05 , we cannot reject H o at 0.05 level of significance. No evidence shows % of UST graduates who receive more than one job offer greater than 50%. (b) Let m 1 be the population average monthly salary among those with one job offer. Let m 2 be the population average monthly salary among those with three jobs offer. H 0 : m 1 - m 2 = 0 vs H 1 : m 1 - m 2 0 Test statistic ( 29 1011 . 2 30 1500 40 1200 0 11000 10300 ) ( ) ( 2 2 2 2 2 1 2 1 2 1 2 1 - = + - - = + - - - = n s n s x x z obs m m p -value = ( 29 ( 29 ( 29 0358 . 0 0179 . 0 2 4821 . 0 5 . 0 2 1011 . 2 2 = = - = - Z P . Since p -value < a = 0.05, reject H 0 at 0.05 level of significance. Mean salary for the two groups are not the same. 7. a = P(Reject H 0 | H 0 is true) = P( X > 200 when m = 0) = ( 29 0384 . 0 4616 . 0 5 . 0 7678 . 1 50 800 0 200 = - = = - Z P Z P p -value = ( 29 0 4194 . 4 50 800 0 500 = - Z P Z P 9. Let 1 p and 2 p
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