You may use your books, notes, and a calculator. Write your answers in the space provided. Total score is 30 points.

Transcription

1 ECON/ST AT 495 Fall, 26 FNAL Name:5( ~-hovl-- (print: first last) nstructins: Yu may use yur bks, ntes, and a calculatr. Write yur answers in the space prvided. Ttal scre is 3 pints. Ouestin 1 A survey was taken t see if a persn's purchases based n infmercials n televisin differed by the level f several different factrs. One study cnsideredthe tw factrs. One study cnsidered the tw factrs"husehld incme" and "marital status." Husehld incme was categrized int 4 categries:(1) under $3K, (2) $3K- $5K, (3) $5K- $look,and (4) ver $1K. Marital status was categrized int 3 levels: A, single (never married); B, married; and C, divrced/separated/widwed.fr each f the 12 cells, tw peple were surveyed and reprted their estimatedpast purchases per year that were based n infmercialsn televisin. The data are in the fllwingtable: Husehld incme Marital status A 35,27 39,53 37,23 43,53 B 43,39 45,51 33,37 57,43 C 39,45 51, 45 35,49 59,39 (a) [1 pint] Which statistical tl wuld yu use if yu wish t see hw a persn's purchase depends n their martial status? A. Multiple regressin B. One-way Anva C. Tw-way Anva D. Categricaldata analysis C y::: ('v').j 1-\ -t (V\1' 1- { \'"' 23 - BC (b) [3 pints] Suppsethe data were randmly selec~e dwn the first mdel yu will use t analyze the data. Define all ntatins yu use. k+h bs\h..t,'n f ~l ;Lt +." + ~j + 'YC:j + C-J.)' :j~k p~"~ f"'c;(j3)..m = Dver"ll\ m~ n _ J -;) 2) -:,,4 )<::::'.>2 d" ::. cli~,,-h'd -t.ffec.t.f {V'\~tlT~ \ s~.lca.s-== e,j -= /1 " 1 husehld 1V1Q)f)\e=d_ 1.-, -::: i nler- A'~'Yl Q-ffic.t ~ r>1<1n~.j sk-w! 't ~J. "J htasehld rt1cbm~ a E:;\t +t erry -h?r( 1

2 (c) [2 ~ints] State the a~sumptinsf the mdel yu chse in (b) and describe hw yu will verify these assumptons. Answer~ j(, J?l"" ::nrmj d..i'shi ~. will UQ.Jl+Lu n{)l"ro-j. pl'dba.b;/i~ pc+~res..&wj!> ~ nrm~ +.e~ -t \JQvi~ V&ln-OLMUS f 'Jk. -(2 ~ ~fj,j. L Wl'\ UQ.J1+~ re.sidla.r& -plo+-)p red..-.jt~j. \/4/ ~ ll.s. res,c:h D.J ~ L~V4t'\~ +est- + Ve-{\f:j -+W'S. (d) [2 pints] Draw a plt t shw the interactinbetween husehld incme and marital status. Cmment n the plt whether r nt the interactineffect is significant. Me.. (\ PlArC~~se. 4~ 41-35f)+- ---A XxXB C 3fY Ī 1 t / \ ~ - 3> 4. husehld ly\cme 2

3 (e) [1 pint] Based n yur answer in (d), is the mdel in (b) still an apprpriate ne? f yes, explain why. f nt, please write dwn the next mdel yu will use t fit the data. N, S,f(JL /f;} =!r C)Y CJJ-,~\. ~ assu.~. ~ Wlw ry'ade-{wl.\\ ~ ~ij\<. -::)A+ d-i +~j 4- l'.~i~ fv' J., \-\ (t) [2 pint] ~~J "11)'''''' ""rflr-" (:j,predict the purchase amunt fa single persn whse husehld incme is abut $4K based n infmercials n televisin. ~4 k ::;- leve\ 2..; S\...t'\~ Le :: A T t sa.m pr >'Y\.t<U'\ "f Q1lASehd ~~~me ~ 2) g Si (la (. :::: ~g+-53d = 4-6D ~ tjitl 'JAJl f 46D + p~d-f~r t~ p\j.r~a..s-t ~MOUt1T. Questin 2 [2 pints] Julie is interested in assessing humr and thus develps a lo-questinsurvey. A randm sample f 1 cllege students is asked t respnd t each questin n a 5-pint scale with 1 indicating "disagree" and 5 indicate "agree." What statistic methd (anva, regressin, r thers) shuld Julie use t analyze her data? What is the gal f the methd? rndr A~ri.., T~ 3J S-,;reku d~ frdm ~drjrs (tl~~) -k:>.i mp~ toy ~ur. 3

4 Ouestin 3 The paper "Shuld Dentists Advertise?" cmparedthe attitudes f cnsumers and dentists tward the advertisingf dental services. Separate randm samples f 11cnsumers and 124 dentists were asked t respnd t the fllwing statement:" favr the use f advertising by dentists t attract new patients." ~?;luthrs were interested in determiningwhether the tw grupscnsumersand dentist~fered in their attitudes tward advertising. (a) [2 pints] State prper null and alternative hyptheses in wrds. \-\ () ~ JnSlAyY'\e'f$ & derrt\s-k -&..v.q~ ~CU'YlJ}tlff;~ + ~..J vev--j1 ;11" <1 L (b) [2 pints] What test wuld yu use t test the hyptheses in (a)? A. Tw-sample t-test B. Tw-sample z-test C. Paired t-test D. Chi-square test D (c) [1pints] Suppse that the p-value f the test in (b) is.1, state yur test cnclusin in wrds. RDj ec..l H a..'t,d CtMcl ~~i-t~h.j.. VQ +fs \Vu\.. U 4

5 Ouestin 4 Sil and sediment adsrptin, the extent t which chemicals cllect in a cndensed frm n the surface, is an imprtant characteristic because it influencesthe effectiveness f pesticides and varius agricultural chemicals. We are interested in hw the adsrptin (Y) changes as the amunt f extractable irn (Xl) and the amunt f extractablealuminum (X2) change. A regressinmdel Y = bo + b 1*X 1 + b2*x2 + errr is fitted. (a) [2 pints] Based n the fllwing scatter plts, what signs wuld yu expect fr b and b2? <8 8 & N >< Q) er ;1 '3 <1' x, X2 (b) [1 pint] Frm the matrix f crrelatins,which ne, the amunt f irn r aluminum, is mre crrelatedwith adsrptin? Crrelatins X1 X2 y X1 Pearsn Crrelatin 1.794*.98* 5ig. (2-tailed).1. N X2 Pearsn Crrelatin.794* 1.935* 5ig. (2-tailed).1. N y Pearsn Crrelatin.98* ('.935* 1 5ig. (2-tailed). -: N **. Crrelatin is significant at the.1 level (2-tailed). 5

6 (c) [3 pints] Write dwn the fitted regressin mdel using the attached utput. Hw well des this mdel fit the data? (d) [2 pints] Which independent variables are statistically significant at a=o.l O? Use the attached utput. (e) [2 pints] One assumptin is dubtable based n the residual plt belw. dentify this assumptinandstatewhatyuwill dt try t fixthe prblem?. Dependent Variable: Y Cii "iii CD a: "Cl CD N =e ns "Cl c J! Cl) -1 C iii U!! Cl -2 CD a: -2-1 Regressin Standardized Predicted Value Vtt.""; a+1 ~ C{~umJ>frY1, CUT? nt-e~j. 1 T 2 w ()(.,t(cf dd ~ y tnalr' f) 11 ;v:r)c i+_ 6

7 (t) [2 pints] The fllwing plt is the residual plt f anther mdel. D yu think the prblem identified in (e) fixed? s there anther prblem in this plt? Dependent Variable: L Y ';;j :J "C "iii Cl) a::: "C ~ "E 'll "C -1 C J! rn c "iii -2 U!! Cl ~ Regressin Standardized Predicted Value -r~ vm-it1!.mt.as 4r'P fr"/)fe el$1 nr...j, H(),.Jeve~ Q Dui-ter ".(!tjytef(~cfy'cfll l,~).. 7

8 The REG Prcedure Dependent Variable: Y Number f Observatins Read Number f Observatins Used Analysis f Variance Surce Mdel Errr Crrected Ttal Sum f Mean DF Squares Square F Value Pr > F < Rt MSE R-Square.9485 Dependent Mean Adj R-Sq.9382 Ceff Var Parameter Estimates Parameter Standard Variable DF Estimate Errr t Value Pr > t ntercept t X1 1 O X