HW_2_Solution - Homework#2 Solution 1 pts BME 423 Fall 2007...

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Homework #2 Solution BME 423 Fall 2007 1. ( pts) Null hypothesis: There is no significant difference between the surgical and medical treatments for the narrowing of carotid arteries. 5729 . 0 96 / 55 ˆ = = s p 7656 . 0 64 / 49 ˆ = = m p Pooled estimate under null hypothesis 6500 . 0 64 96 49 55 ˆ = + + = p Yates correction 3344 . 2 ) 64 1 96 1 )( 65 . 0 1 ( 65 . 0 ) 64 1 96 1 ( 5 . 0 7656 . 0 5729 . 0 ) 1 1 )( ˆ 1 ( ˆ ) 1 1 ( 5 . 0 ˆ ˆ = + - + - - = + - + - - = m s m s m s n n p p n n p p z 960 . 1 ) ( 3344 . 2 05 . 0 = = t z 3263 . 2 ) ( 3344 . 2 02 . 0 = = t z Conclusion: Reject null hypothesis. There is a sufficient evidence to show that one treatment is better than the other (p<0.02).
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2. ( pts) Null hypothesis: There is no significant difference between the surgical and medical treatments for the narrowing of carotid arteries. Observed results: Therapy Recurrence Recovery Total Surgical 55 41 96 Medical 49 15 64 Total 104 56 160 Expected contingency table if there is no difference between the two treatments: Therapy Recurrence Recovery Total Surgical 62.4 33.6 96 Medical 41.6 22.4 64 Total 104 56 160 - = expected ) observed expected ( 2 2 χ 4 . 22 ) 5 . 0 4 . 22 15 ( 6 . 33 ) 5 . 0 6 . 33 41 ( 6 . 41 ) 5 . 0 6 . 41 49 ( 4 . 62 ) 5 . 0 4 . 62 55 ( 2 2 2 2 2 - - + - - + - - + - - = χ 4499 . 5
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