finalsoln

finalsoln - S TAT 8 200 F inal E xam - Decmber 9 , 2 010 S...

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STAT 8200 Final Exam - Decmber 9, 2010 SHOW ALL WORK! Name, ,4nswQI kef 1. The State Board of EducatlOn has adopted basic skills tests for high school gradu- ation. One of these is a writing test. The state employs 25 professional graders to grade all the tests taken each year within the state. To determine whether these 25 graders are grading to the same standard, an experiment was conducted as follows. Thirty writing samples were randomly selected from last year's collection of tests; each writing sample is assigned to be graded by five graders. Thus each grader will grade six samples, and each pair of graders will have one sample in common. The data from this experiment are given below. , J i ; a. (6 pts.) Keeping in mind the goals of this experiment, identify (i) the treatment factor(s), (ii) the blocking factor(s), (iii) the experimental units, and (iv) the overall experimental design (be very specific) . .1 -f· L~.-l r. ' \..-"' r '-. .. J e r 7Y '1 ~\.C.iU. ri . [ ' / /./,U_ ,,j loe kl jf ret c T()r' ex C/Lv'Vl } ex1 'f~ I U1' f. ..,. . e CcL L. exC>wc fA) he", tt lot de d 6;1 a lJc. ./7!'- J / eJ Y~fv 7> exr 'h,I Uo,j (~e ire ),)0 of 'C/) ~ j-v\ ;,/1 t"-) I J iloek S ;Y/l 1
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See the attached SAS program graders.sas and its output, graders.lst. The analyst who wrote graders.sas was interested in testing whether or not the graders all graded to the same standard and in estimating the mean score given by each grader, but was not sure how to implement the appropriate analyses, so he tried more than one approach in graders.sas. b. (6 pts.) Write down an appropriate model for the analysis of these data and write down the hypothesis that the analyst is interested in testing in formal terms (that is, in terms of model quantities). Test this hypothesis at a = 0.05 and state the appropriate conclusion. OJ ' ,/-or: _ /." } 1 v' -::: re J'~-/j 5c (~jrc;",-J. e C;:'i.ve~ j ".1 ItC; (-' ':7rooIC/ iJ~ J e '":'J.-( I ' lI. . II·' 0 . 7 //' U c,) i I) t I c~,?I'lt~ u. ~) 25" -c::! ~o ('-., C?ft C''- C I /lO /'Z. .t J. - e X{Z11Vl ') (':; ,) '. - . ) .J .j J ..' ) i \ (nD! oj/ DosS I .;/e (r:.l,"Vt~i.tlC;.-lJ1J 01' () J c:·.re <5 6.st/ Ve cL) /\/J. I!L I 7 .,.' J (' 2.. ) '_ I .. LD ~ . r -, . , t. l ,I -'~~. . ~ -- i ./' i ' '.' _ -+ J.+ 2>' + e. '-' 1 E':,' 'J r---J N u [; 2- or -= 0 L. & --= 0 .-- ,M <:71 [ r J lJ) lJ )') . I ). I J ft LI c. ,j ///1,. /'7 I .' ..J I /'-,' ,( OV'0.~" I ~ /'= SIl. c,de/' . \..) e eXt:"',";'" /~d J I('i) 3. \, /0'Jcll1.s 15, ': H; d 1;=-'" :::: o{z.-::C 0 ,~~v"- ~ (if!. {/ rU,.1 r-/ 'J C J Uf) i//~ 0.- J e feci E t KL Lj . A ::::- -.' := A.A } <- Dr 1,o~l"'\I- / £-,. . -~ L(, '1 f b A 2 L( 7{; d.l LJ LJi2 ',U =- /llA'f c>« ~;-0:3 ({C,Jz/ l , F / - j D -< .. 0 0 01 _~ ) ;2e;}2 C -; lb, ,b-r c 1.<.J£.r s } y;/-/ 1/ , v:v~£:~-;eI eXcc.V'o15 J (') /JDJ ';( f';-,. [)} e -h ,/'1.( J&vc>( Sl:,:V\.d~d" j CY } "J ) :'/ ~- (C~ 01'"\ C.j If c. (4 pts.) Estimate the mean score that grader number 3 assigns when j, c;; v{' Jc;~Vh€. grading writing samples of this kind and give a 95% confidence interval for /J ~ ) this quantity. /l/[.cL/{ SC,L/e - ;: b:J)( 62 / L/ C' JJJ cL of (0,(D)~ C7,95/Y) > .-.~r" 2
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so (J/'/sl d. (4 pts.) Why do you think that 30 writing samples were used for this experiment? That is, assuming that each sample is evaluated by 5 graders and without changing the total number of graders (25), could we have used the same experimental design with fewer than 30 }yriting Ja~ples?
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finalsoln - S TAT 8 200 F inal E xam - Decmber 9 , 2 010 S...

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