Applied Statistics Qualifier Examination

Transcription

1 Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng these problems. (3) You re on the double honor system to not consult wth ny ndvdul bout ths exmnton untl fter the exmnton s over. Wth double honor system, you re requred to only consult books, journls nd clss notes for help n solvng these problems nd you re requred to report ny voltons of ths polcy tht you observe n ny other student who s tkng ths test. (4) Prnt your nme nd the problem number on every pge you turn n. Number every pge nd stple pges for ech soluton together. Then use pper clp to ttch ll your solutons to ths cover sheet. Plce the entre fle n n envelope. (5) Plese fll n the nformton below nd submt hrd copy of your solutons n person to Dr. Nncy Mendell n Mth Tower Room - by FRIDAY, June 6 t AM or 4 hours fter you receve the exm (should you receve t lte for some specl reson). Plese be sure to fll n the pproprte nformton below: I m submttng solutons to QUESTIONS,, nd of the ppled sttstcs qulfer exmnton. There re pges of wrtten solutons. Plese red the followng sttement nd sgn below: Ths s to certfy tht I hve tken the ppled sttstcs qulfer nd hve used no other person s resource. (Sgnture) Prnt your nme here.

2 Queston. There re two ndependent rndom smples, both followng the norml dstrbuton. Tht.. d... d. s, X,, X n ~ N, nd,, n ~, Y Y N. () Plese derve test, t the sgnfcnce level α, for H : 3 versus : H 3 () Suppose tht 3, plese derve test, t the sgnfcnce level α, for H : 3 versus H : 3 (3) Suppose tht 3, plese derve the (-α)% confdence ntervl for

3 Queston. Rndom vrbles Yj re observed ccordng to the one-wy ANOVA model... where ~ d N, j. Y j j,,, k, j,, n, () Plese show tht the lkelhood rto test of H : k s gven by the usul ANOVA F test. () For the cse of equl number of observtons on ech tretment, tht s, n n,,, k, plese show tht t test of H : ' versus H : ' k P Y. Y S '. cn be bsed on the sttstc t', where S nd S s the S P / n k vrnce of the th smple. (3) For the equl vrnce cse llustrted n (), plese show tht the usul ANOVA F test cn be consdered n verge t-test, tht s, t F kk '., ' (4) To determne det qulty, mle wenng rts were fed dets wth vrous proten levels. Ech of 5 rts ws rndomly ssgned to one of three dets, nd ther weght gn n grms ws recorded s follows. Det proten level Low Medum Hgh Plese llustrte the reltonshp between the t nd F sttstcs, gven n () nd (3) bove, usng the dt set gven bove. 3

4 Queston 3 The dt set contns ten columns. The leftmost column s the ID of subject (rngng from to,). It should be uncorrelted wth the dependent vrble. Next re three contnuous ndependent vrbles. There re lso fve ndctor vrbles. Ech ndctor represents whether the subject hs genetc llele tht could be ssocted wth chnge n the dependent vrble. Fnlly, there s the dependent vrble. The dt s smulted. Prepre four pge report tht focuses on whether ny of the vrbles s ssocted wth the dependent vrble. Mke sure tht your report ncludes fnl model nd the nlyss of vrnce tble for ths model. Include sttement of whether or not ech of the genetc lleles ppers to be ssocted wth the dependent vrble. Below re lsted the vlues for the frst 5 cses. The entre dtset s on the fles qxjune8.txt nd qxjune8.xls

5 Queston 4. A study s done to determne whether prevous pregnncy complctons n the mother re ssocted wth behvor problems n the subsequent chldren. The comprson s between mothers of chldren who hd been referred by ther techers s behvor problems nd mothers of control chldren. Ech mother s hstory of nfnt losses (for exmple, stllbrths) pror to the brth of the chld ws recorded. Snce these loss rtes mght be ssocted wth the number of prevous pregnnces we nclude ths vrble s well. Below we gve tble showng the frequences of the responses for Chld Behvor (B) Problem vs. Control for ech of the Number of Prevous Pregnnces (P) nd Pregnncy Loss ctegores. (P)Prevous (B)Chld (L)Pregnncy Loss Pregnnces Behvor Yes No Totl Problem 8 Control Problem Control Problem 7 49 Control () (b) (c) Obtn the ln(odds) of chld wth behvor problem for ech prevous pregnnces (P) nd pregnncy loss hstory (L) combnton. Mke tble or plot tht summrzes the reltonshp between Chld Behvor (B) nd these two predctors. Indcte how you thnk behvor s ffected by prevous pregnncy loss nd the number of prevous pregnnces. Indcte whether these log odds nd log odds rtos ndcte nterctons between (L) nd (P) on (B). Indcte f you see ny evdence of n ssocton between pregnncy number (P) nd pregnncy loss (L). Use logstc regresson to ft model for predctng the odds of chld wth behvor problems s functon of the number of prevous pregnnces (P) nd pregnncy loss (L). Test for the presence of two wy ntercton (L*P) of these fctors on chld behvor. () If sgnfcnt two wy ntercton s observed between L nd P then nlyze the three prevous pregnncy ctegores seprtely for ssocton between (L) nd (B). () If the two wy ntercton between L nd B s non sgnfcnt: test for mn effects of (P) nd (L) on Behvor (B). (d) Obtn fnl model. Report relevnt odds rto estmtes. (e) Repet the nlyss usng loglner models. Test for 3 wy ssocton nd then test for two wy ssoctons. Indcte wht you lern bout the ssoctons between B nd L from ths nlyss. Wht would be good pth dgrm to summrze the prwse ssoctons between these three vrble? (f) Wrte short report on your fndngs. Qul_june_8 5