exam1 - E c o n 3 2 1 E x a m 1 M a rtin S c h m id t S u m...

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Unformatted text preview: E c o n 3 2 1 E x a m 1 M a rtin S c h m id t S u m m e r 2 0 1 0 P le a s e a n s w e r a ll o f th e q u e s tio n s b e lo w (1 0 q u e s tio n s w o r th 2 7 p o in ts ) . P le a s e m a k e s u r e th a t y o u e x p la in h o w y o u a r r iv e d a t y o u r a n s w e r s . P le a s e b e a w a r e th a t I w ill r e w a r d p r e c is e a n d d e ta ile d a n s w e r s w h ile p e n a liz in g a n s w e r s th a t a r e a m b ig u o u s o r to o g e n e r a l. G o o d lu c k . T h is e x a m is a c lo s e d b o o k e x a m . M o r e o v e r , o n ly th e s im p le s t, n o n ­ s ta tis tic a l c a lc u la to r s a r e a llo w e d . D is r e g a r d in g th e s e r u le s w ill r e s u lt in z e r o p o in ts . 1 0 q u e s tio n s 1 . I n c o m in g s tu d e n ts a t a la w m e d ic a l s c h o o l h a v e a n a v e ra g e L S A T (L a w S c h o o l A p titu d e T e s t) s c o re o f 1 5 8 a n d a n S D o f 1 2 . T o m o rr o w , o n e o f th e s e s tu d e n ts w ill b e p ic k e d a t ra n d o m . Y o u h a v e to g u e s s th e s c o r e n o w ; th e g u e s s w ill b e c o m p a re d w ith th e a c tu a l s c o r e to s e e h o w fa r o ff it is . E a c h p o in t o ff w ill c o s t a d o lla r. (F o r e x a m p le , if th e g u e s s is 1 6 5 a n d th e s c o re is re a lly 1 6 1 y o u w ill h a v e to p a y $ 4 ) . (a ) W h a t is th e b e s t g u e s s a n d w h y is th is th e b e s t g u e s s ? (b ) T h e r e is a b o u t 1 c h a n c e in 2 to lo s e m o r e th a n a c e rta in a m o u n t o f d o lla rs ? W h a t is th is a m o u n t o f d o lla rs a n d h o w d o y o u a rr iv e a t th is a m o u n t? (c ) N o w a w h o le s e rie s o f s tu d e n ts is c h o s e n . T h e r .m .s . s iz e o f y o u r lo s s e s s h o u ld b e a ro u n d w h a t a m o u n t? P le a s e e x p la in h o w y o u a r riv e a t th is a m o u n t. (2 p o in t s ) 2 . P le a s e d e s c rib e th e d o m a in o f d e s c rip tiv e s ta tis tic s a n d p re s e n t a t le a s t 4 to o ls th a t d e s c rip tiv e s ta tis tic s u s e s to e x tra c t in fo r m a tio n o u t o f la rg e d a ta s e r ie s ? W h y a re th e s e to o ls n e c e s s a r y a t a ll? W h a t a r e th e lim ita tio n s o f d e s c rip tiv e s ta tis tic s ? (2 p o in t s ) 3 . P le a s e d e s c r ib e a g e n e ra l s ta tis tic a l a p p ro a c h to in fe r c a u s a l e ffe c ts . P le a s e e x p la in w h y th is a p p ro a c h m a k e s s e n s e a n d w h y it h a s s h o r tc o m in g s . P le a s e u s e a n e x a m p le to illu s tr a te w h a t y o u a r e s a y in g . (2 p o in t s ) 4 . B re a s t c a n c e r is o n e o f th e m o s t c o m m o n m a lig n a n c ie s a m o n g w o m e n in th e U .S . If it is d e te c te d e a rly e n o u g h b e fo re th e c a n c e r s p re a d s c h a n c e s o f s u c c e s s fu l tr e a tm e n t a re m u c h b e tte r. D o s c r e e n in g p r o g r a m s s p e e d u p d e te c tio n b y e n o u g h to m a tte r? T h e firs t la rg e ‐ s c a le tria l w a s ru n b y th e H e a lth In s u ra n c e P la n o f G re a te r N e w Y o rk , s ta rtin g in 1 9 6 3 . T h e s u b je c ts (a ll m e m b e rs o f th e p la n ) w e r e 6 2 ,0 0 0 w o m e n a g e 4 0 to 6 4 . T h e s e w o m e n w e re d iv id e d a t ra n d o m in to tw o e q u a l g ro u p s . In th e tre a tm e n t g r o u p , w o m e n w e r e e n c o u ra g e d to c o m e in fo r a n n u a l s c re e n in g , in c lu d in g e x a m in a tio n b y a d o c to r a n d X ‐ ra y s . A b o u t 2 0 ,2 0 0 w o m e n in th e tre a tm e n t g ro u p d id c o m e in fo r th e s c re e n in g ; b u t 1 0 ,8 0 0 re fu s e d . T h e c o n tro l g r o u p w a s o ffe re d u s u a l h e a lth c a r e . A ll th e w o m e n w e re fo llo w e d fo r m a n y y e a rs . R e s u lts fo r th e fir s t 5 y e a rs a r e s h o w n in th e ta b le b e lo w (“H IP ” is th e u s u a l a b b re v ia tio n fo r th e H e a lth In s u r a n c e P la n ) : C a u s e o f D e a th B r e a s t c a n c e r A ll o th e r Number R a te Number R a te T r e a tm e n t group E x a m in e d 20200 23 1 .1 428 21 R e fu s e d 10800 16 1 .5 409 38 T o ta l 31000 39 1 .3 836 27 C o n tr o l 31000 63 2 .0 879 28 group E p id e m io lo g is ts w h o w o rk e d o n th e s tu d y fo u n d th a t (i) s c re e n in g h a d little im p a c t o n d is e a s e s o th e r th a n b re a s t c a n c e r; (ii) p o o r e r w o m e n w e re le s s lik e ly to a c c e p t s c re e n in g th a n ric h e r o n e s ; a n d (iii) m o s t d is e a s e s fa ll m o re h e a v ily o n th e p o o r th a n th e ric h . P le a s e a n s w e r th e fo llo w in g q u e s tio n s : (a ) D o e s s c re e n in g s a v e liv e s ? W h ic h n u m b e rs in th e ta b le a re e v id e n c e fo r th is p o in t? (b ) W h y is th e d e a th r a te fro m a ll o th e r c a u s e s in th e w h o le tre a tm e n t g ro u p ( "e x a m in e d " a n d " re fu s e d " c o m b in e d ) a b o u t th e s a m e a s th e r a te in th e c o n tro l g ro u p ? (c ) B re a s t c a n c e r ( lik e p o lio , b u t u n lik e m o s t o th e r d is e a s e s ) a ffe c ts th e ric h m o re th a n th e p o o r. W h ic h n u m b e rs in th e ta b le c o n fir m th i s a s s o c ia tio n b e tw e e n b re a s t c a n c e r a n d in c o m e ? (d ) T h e d e a th ra te ( fro m a ll c a u s e s ) a m o n g w o m e n w h o a c c e p te d s c re e n in g is a b o u t h a lf th e d e a th ra te a m o n g w o m e n w h o re fu s e d . D id s c re e n in g c u t th e d e a th ra te in h a lf? If n o t, w h a t e x p la in s th e d iffe r e n c e in d e a th ra te s ? (e ) T o s h o w th a t s c re e n in g re d u c e s th e ris k fro m b r e a s t c a n c e r , s o m e o n e w a n ts to c o m p a r e th e ra te s 1 .1 a n d 1 .5 . Is th is a g o o d c o m p a r is o n ? Is it b ia s e d a g a in s t s c r e e n in g ? F o r s c re e n in g ? (f) S o m e o n e c la im s th a t e n c o u ra g in g w o m e n to c o m e in fo r b r e a s t c a n c e r s c re e n in g in c re a s e s th e ir h e a lth c o n s c io u s n e s s , s o th e s e w o m e n ta k e b e tte r c a re o f th e m s e lv e s a n d liv e lo n g e r fo r th a t re a s o n . Is th e ta b le c o n s is te n t o r in c o n s is te n t w ith th e c la im ? (g ) In th e firs t y e a r o f th e H IP tria l, 6 7 b re a s t c a n c e r s w e re d e te c te d in th e "e x a m in e d " g ro u p , 1 2 in th e " re fu s e d " g ro u p , a n d 5 8 m th e c o n tr o l g ro u p . T ru e o r fa ls e , a n d e x p la in : s c re e n in g c a u s e s b re a s t c a n c e r . (5 p o in ts ) 5 . T ru e o r fa ls e , a n d e x p la in p le a s e : (a ) If y o u s u b tra c t 2 fro m e a c h e n try o n a lis t, t h a t d e c re a s e s th e a v e ra g e b y 2 . (b ) If y o u s u b tra c t 2 fro m e a c h e n try o n a lis t, th a t d e c r e a s e s th e S D b y 2. (c ) If y o u h a lf e a c h e n try o n a lis t, th a t h a lv e s th e a v e r a g e . (d ) If y o u h a lf e a c h e n try o n a lis t, th a t h a lv e s th e S D . (e ) If y o u c h a n g e th e s ig n o f e a c h e n try o n a lis t, th a t c h a n g e s th e s ig n o f th e a v e ra g e . (f) If y o u c h a n g e th e s ig n o f e a c h e n try o n a lis t, th a t c h a n g e s th e s ig n o f th e S D . (2 p o in ts ) 6 . O n th e M a th S A T , m e n h a v e a d is tin c t e d g e . In 2 0 0 5 , fo r in s ta n c e , th e m e n a v e ra g e d a b o u t 5 3 8 , a n d th e w o m e n a v e ra g e d a b o u t 5 0 4 . Y o u m a y a s s u m e th a t th e h is to g ra m s fo llo w e d th e n o rm a l c u rv e , a n d th a t b o th S D s w e re a b o u t 1 2 0 . (a ) P le a s e e s tim a te th e p e r c e n ta g e o f m e n g e ttin g o v e r 7 0 0 o n th is te s t in 2 0 0 5 , a n d s h o w h o w a n d w h y y o u a rriv e a t th e r e s u lts . (b ) P le a s e e s tim a te th e p e rc e n ta g e o f w o m e n g e ttin g o v e r 7 0 0 o n th is te s t in 2 0 0 5 , a n d s h o w h o w a n d w h y y o u a rriv e a t th e re s u lts (2 p o in ts ) 7 . P le a s e p r o v e th a t ‐ 1 ≤ r(x ,y ) ≤ 1 (e v e ry e q u a lity o r in e q u a lity n e e d s e x p la n a tio n ) . (3 p o in ts ) 8 . P le a s e d ra w th e s c a tte r d ia g ra m a n d c a lc u la te a ll 5 c o m m o n s u m m a r y s ta tis tic s fo r th e d a ta s e t b e lo w . P le a s e w rite d o w n th e g e n e ra l fo rm u la s fo r th e s u m m a r y s ta tis tic s . W h a t a s p e c t o f th e d a ta s e r ie s d o th e 5 s u m m a ry s ta tis tic s try to c a p tu re ? x 1 1 1 2 2 2 3 4 y 5 3 7 3 1 1 1 1 (5 p o in ts ) 9. W h a t d o e s e c o lo g ic a l c o rre la tio n m e a n ? Is e c o lo g ic a l c o rr e la tio n p re s e n t in th e d a ta o f q u e s tio n 8 a n d , if s o , w h a t is th e lik e ly e ffe c t? D o th e d a ta o f q u e s tio n 8 in d ic a te a c a u s a l e ffe c t o f x o n y ? (2 p o in ts ) 1 0 . T h e fig u re ( a d a p te d fro m a 1 9 9 2 n e w s p a p e r a rtic le ) s h o w s th e d is trib u tio n o f A m e ric a n fa m ilie s b y in c o m e . R a n g e s in c lu d e th e le ft e n d p o in t b u t n o t th e rig h t. F o r e x a m p le , 3 .7 % o f th e fa m ilie s h a d in c o m e s in th e r a n g e $ 0 ‐ $ 4 ,9 9 9 , 5 .8 % h a d in c o m e s in th e r a n g e $ 5 ,0 0 0 ‐ $ 9 ,9 9 9 , a n d s o fo rth . T ru e o r fa ls e , a n d p le a s e e x p la in : (a ) A lth o u g h A m e ric a n fa m ilie s a re n o t s p r e a d e v e n ly o v e r th e w h o le in c o m e ra n g e , th e fa m ilie s th a t e a r n b e tw e e n $ 1 0 ,0 0 0 a n d $ 3 5 ,0 0 0 a re s p re a d fa irly e v e n ly o v e r th a t r a n g e . (b ) T h e fa m ilie s th a t e a r n b e tw e e n $ 3 5 ,0 0 0 a n d $ 7 5 ,0 0 0 a re s p r e a d fa irly e v e n ly o v e r th a t ra n g e . (c ) T h e g ra p h is a h is to g ra m . (2 p o in ts ) ...
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