hw7sol_F10 - ISOM 111 Business Statistics M Lecture...

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ISOM 111 - Business Statistics Lecture Sections (Prof. Inchi HU) Assignment Solution (Problem Sheet 6 #1, and two extra questions) 1. (a) ( 29 ( 29 1 . 44 1 10 2136 . 2 1 2 2 = - = - = n s S x xx ( 29 ( 29 1 . 164 1 10 2701 . 4 1 2 2 = - = - = n s S y yy 1 . 77 10 107 107 1222 = × - = - = n y x xy S xy 7483 . 1 1 . 44 1 . 77 ˆ 1 = = = xx xy S S b ( 29 0068 . 8 7 . 10 7483 . 1 7 . 10 ˆ ˆ 1 0 - = - = - = x y b b Interpretation: For a 1% increase in the market return, the average return on Dalton Company tends to increase by 1.7483%. (b) 1 : 1 0 = b H vs 1 : 1 0 b H ( 29 3061 . 29 1 . 44 1 . 77 1 . 164 2 2 = - = - = xx xy yy S S S SSE , 9140 . 1 6633 . 3 2 10 3061 . 29 2 = = - = - = n SSE s Since the test statistic 860 . 1 5963 . 2 1 . 44 9140 . 1 1 7483 . 1 ˆ 05 . 0 ; 8 ; 2 1 1 0 = = = - = - = - t t S s t n xx obs a b b , we reject 0 H at 5% significance level. Hence, there s sufficient evidence that Dalton Company is sensitive. (c) A 90% prediction interval for an individual y is given as ( 29 ( 29 ( 29 1 . 44 7 . 10 5 . 10 10 1 1 9140 . 1 860 . 1 5 . 10 7483 . 1 0068 . 8 1 1 ˆ 2 2 2 ; 2 - + + × ± × + - = - + + ± - xx p n S x x n s t y a ( 29 4.0856 1 , 6151 . 6 7353 . 3 3503 . 10 = ± = (d) % 14 . 82 or 8214 . 0 9063 . 0 2 = = R r (e) A 98% confidence interval for the average is given as ( 29 ( 29 ( 29 1 . 44 7 . 10 14 10 1 9140 . 1 896 . 2 14 7483 . 1 0068 . 8 1 ˆ 2 2 2 ; 2 - + × ± × + - = - + ±
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