Statistical Hypothesis Testing and Regression Analysis - Prof. Pei Xiao, Exams of Statistics

Download Statistical Hypothesis Testing and Regression Analysis - Prof. Pei Xiao and more Exams Statistics in PDF only on Docsity! STAT 3704Exam#2 Tuesday, November 18th, 2008 100 points possible Form B Inslructions'. You may use your calculator and the Jront and back ofyour formula sheet. .4ppropriate probebility lables haw been provided. Read each question care/ lly. Partial credit will be giwn so it k in J)ow best intercsl to make sure your qnswe$ ate clear and detailed, Turn in your formula sheet with the exemwhen you are done. lfyou hare any queslions, please raise vour hand and I v,ill do my best to answer them. Good llrck! Undergraduate Honor Pledse: I have neither given nor received unauthorized assistance on this exam. Name Signature Part A, Show all your work for each question, Question I A tire manufacturcr claims that their tires have an average lifespan of40.000 miles with a sample standard deviation of328l miles. An independent consumer group wishes to test if thei clam is tme or if the actual ifespan is dift,"erl from 40.000 miles. l hcy collect he following data on l0 tires: 49000 41000 40500 45000 40000 39000 38000 41000 39500 43000 a. What are the Null and Altemative Il)pothescs? [ ' l . t r r ' (O'oC6 nni les, , " r l+ - t ul qo ' ooo n4; ta5\w / b. What is the nrean sample lil-espan? r= 1\ooo + s!p66 +-.+t3,oo6 = 41, Goo to c. What is the obsened test statistic?Compute the test statistic. 4 "obs - t - lL-- -------tr- ^ e. What is the p-value fbr lhis test? 1.r;d*l 9(6> C"r") = .{0*!. : ft l lFo:qro,oo=\sqi l € d. What is the critical lalue or the rejection region: (Assume o : 0.0 5) , +"b61 >a.a6> 92"=.oaS6Ulc }-sideo / /- \ I ' €n-,1"= e.e;? /4 - U_ -l1e q ar"> f. What conclusion can be dra\l'n liom this test? ,ac2 .b 'l V!!i:: L- :^ t',3l'sq fu f3,.ro ' - uJ.tr- Ts \<o-5 e' A|^oI\ 'oS, ..$s . -$,u.rsl r'+t q ''1 neF$incz'6oga it [c-ss+h"r\ a,]6e brre cairr )a:l |o czlcrt tl. Y"\. trr.<rrLcnre bast! "* *.c-dqi +" coul^tre \'\""* l\leeNot,4 i;; -;."^ is A;&&6tllr{B,br'. !o,ooo. Queltion 3 A statistics tercher believes they can predict he second test s€orcs for a class bosed on their Iirst tGst scor€s. The Minitab output is shown below. Ragratllon Andyala: 8coE2 vanua Scottl Pre.licto! coef sE coef r 9 P Constant L,M7 0.1093 10.23 10.000 scole1 a,a.167 o.o7740 - to.oooS = 0,12?419 R-Sq - 95.?t R-3q(adj) = 95. l t B Analysis of var iance Soulce DF SS l ,S Reelesslon 1 PrlS]q 2, s{ 1e Residual Error l L-_-_____Lo . 0152 Total I 2.5555'- \ P 0.000 0nusual Obselvat ions obs Scorel 3co!€2 F1t sE Fl t ReslduaL St Re31d 9 ?.50 2.5000 2.?502 0.0519 -4.2502 -2.15R R denotes an oblelvat lon wi th a tarEe standardi .z€d !€sidua]. a, What ar€ the values for the missing portions ofthe output? & ^= a.6556- a. tq l? =. t [3? o c= .3U!l = \t.s'6lt . 6\rlqo b. What is the vatue of R2 for this model and how is it inteDr€ted? Si,\cr v\.',s 5tR,,Rl = 95.?a 9s'lz of {^e ua-ra|'l^ in Scorcs "ot h "rptt'".J b\ \t- oalr'd{t\ i^ Ec.re\.Tft.-s, i^frcafcs {-l t\. r I tL S;t)hto&,et -,s * o.ttr Ftc.s!= 156.901 p-u\=o3* , ,_ - . ,\ ., -:\*rrr z- +o concfrrAe o, \L 'OfRerec\ +\^r n ̂ \.-\tc". a cao.5\ a,'fu1!3 t,* - . -t:- l* -*"*.n*4" tdr $$ o-rJ.clru'eLrp exiJ\ Provide the test ofoverall model significance. Is the model fit significant at the .05 significance l rel? rBe sure to include the hlpothels. p-raJue and conclusiont \t '. l\ .:6 (no r cGl'oshl P ) '*it'g,n o (.cLclry'el"lP e*nts) t-te>] =-Cre!- = la.s6?8 5e(c"cf) g-,rJ*" = O (>06 (Extra Credit) Two different e-st statistics jn the output are related under certain special circumstances in this problem. Name the two tests. specily the relationship between them and the special circumstances ofthis problem that allou'for the relationship to exist. {>= F) (r>. soti l}= tsc ?oe Oat.< tt." ',.t $g caee ot- 6LR. The statistics teacher finds out that the prediction equation was not copied liom the 1op of the Minitab output. Thankfirlly it can be recreated using the output that $as copicd. What is the equation for the model fit? \= t, l t f l +.Iw6? &"o1- Perfom a test of slope significance. Be sure to include the hypothescs, t-statistics. p- value and conclusion. Ho,F,= o Ho:p,*o ,t \e< \\an- \l* l"u"[ *&)i vtr-e \{c'c ><rdu€ ',6 ^-\ siq r{i1i icorrce C,CS/ ote O.,^d$[rb c6ndx4P wf^s- oreL-t)sv ct? lcsre}' co.N t-qej}-\I.€-b n.r.\\ \*lrcsj, 6r.ore I is e. S\v.i{ iq^l- \l g. Finally the statistics teacher wants to chcck to scc if hc has violated any ofthe assunptioDs of simplc linear regression. What are the 4 assumptions discussed in class ofsimplc Iincar regression? From the residual plot belo$'. have any ofthc assunrptions bccn violated. ifso. how? nurnber ofobscn'ations or rc\ls ol'data are in this sample. what is thc maxirrunr # trl' predictors he can includc and still get a l'ull set ol oulpul? -1144 ma-lc L(r-6( \est€-1 A f,Q 8"" $- ."1.ts snvrt raao&el cL lSrmal Probability Plot Residual Plots for Score2 VeFus Fits I 90 g l0 0 15 0,00 015 0,30 Histoga-am 0.25 0.20 {.15 {,10 -0,05 0.00 ReCd€l 34567 I qrzbjcxors.