Answers & Solutions to questions paper

, 0*- w% AN0+ts (?)r-.rr=Jmarks) h=Yt+tTrt=@tK='@ X ecotogist wishes to investigate the levels of mercury pollution in four laKes. ne citches 4 fish from lake 1, 7 fish from lake 2, 5 fish from lake 3, and 5 fish from lake 4. The following table gives a summary of measurements (in parts per million) for each of four samples. Lake (treatment) Sample data 1 2 -l 4 tli 4 7 5 5 n. t' 1.,.. - T. ? ,'ll I ./ =l 52 69 7t 6t n. I z .i=1 2 1' . . 753 798 t248 9t2 Assume that concentr.tions of mercury in all fish in a lake constitute the population of values. Assume that all three populations are normal and have common variance. a. Construct the ANOVA table for the sample data. use the rest of page for the calculations required for ANovA table. b. Test at 5yo significance level to determine if the data provide sufficient evidence to indicate a difference in larr'-population means. lf required, use Tukey' method to determine which means differ' c. construct an individ ual g|%o confidence interva! for the difference between mean concentrations of mercury in the fish from lake # 2 and lake # 1. Write the solutions for questions b. and c. on the following page' OVA T Source of variation Degrees of freedom Sums of squares Mean squares F ratio Treatment (-l=3 60, t, gf LO, l6t 0. 16 q Error h* f. -- l1 60t. 1 rt 3S. Y 33 Tota I h-t=20 5 6 Z-. 9SZ Ffr =-- ?'5 Er+';g, "Y-s;,;:@ + a'a d7r r{h;,-: _--- ss; =rtd-+'z-3?rr E ry=@ ntJ- , ? ^- tlc, ssrr=E# #={.q*rF-q 9sE = sST- SSI-r = aqz,tg+ o

b. Test at 5% significance level to determine if the data provide sufficient evidence to indicate a difference in four population means. lf required, use Tukey' method to determine which means differ. a. State null and alternative hypotheses. (0.5 mark) F{o: F,= lrr = ft = 1, , I{,: 6+ ArAryI' *ru r"tun iE il1'tr1*t'* W W Yl4'trtt b. State the calculated value of test statistic and criticalvalue of test. (1 mark) .f*,. = 0. S59 f-.- !-o-o.sr3f l? =3.zt c. Decide whether null hypothesis is true and make the conclusions. lf required, use Tukey's procedure. (0.5 mark) Lrrrq l*. z ?, we da vuv+ W lfin. a+ sL = O'os- \t1,g ti,'"w[[iu.uN+ W wi)a'uu l4^/* ('u/+L a'&d''[4t'w PPru"'** ttt^'artq T,r4"" W te vw+ w,ywiva4. c. Construct an individ ual gil%confidence interval for the difference between.mean concentrationsofmercuryinthefishfromlake#1andIake#z.Lz,niin>".I- -f [,. = * = * = B t tr . =+" =+ = s-sb i F-[r.= 3.[Y, t_ to, zsllr MtE[*,*frJ = 2,uD @e4,s7- =l,ll0

":r fi.= [l.ht, ) Tr.=[st)6= t06t T.z.=-!9s)y=YY0, Il.=(F0)6=?a0 T,, =fl.nTz.*T3. : s 0o t yyo r 3 og :@ ) 5 SIr cnn ^$(. f,ut ,,i i" 1ry0 wu.atf,. @ ssrr- t#,- F_- -h*-#,H- F= #-#.y-w:- 5\t+09.8 t- 5qt806 - 9Y,?0t,8 = luo.za i',.=F=W=F2.3^ - Lake (treatment) sa m p re o ari'-------------- 1 2 a J tti 6 8 6 i. 51 55 50 s. I 5.4 4.9 5.2 Assume that concentrations of mercury in allfish in a lake constitute the population of values. Assume that all three populations are normal and have common variance. a. Construct the ANOVA table for the sample data. Use the rest of page for the calculations required for ANOVA table. b. Test at 5%o significance level to determine if the data provide sufficient evidence to indicate a difference in three population means. lf required, use Tukey' method to determine which means differ. c. Construct an individ ual95% confidence interval for the difference between mean concentrations of mercury in the fish from lake # 2 and lake # 1. Write the solutions for questions b. and c. on the following page. ANOVA TABLE Source of variation Degrees of freedom Sums of squares Mean squares F ratio Treatment lc-t = / t0 0, Lo F0, t0 4.{0 Error h-Kal+ o,{r. o} 26, 4z Total [1-] = l! s\s, ?\" SLSS-52.il2 + 6LST-sZ.3l2 = lo0,L q000 _ \Z . tJl = 15,605 +-Zyrlsotl o s sTr =Z,n;L[;-8, S 9l'r = 6 Ll t- SZ. 3)z + . SsE = Jt,.(n;-f) t=l "= S;,{1(s) * t{.gt(?) r ;.ZL(,s) =Vyg.O+ @

b. Test at 5% significance level to determine if the data provide sufficient evidence to indicate a difference in three population means. lf required, use Tukey' method to determine which means differ. ' -" State null and alternative hypotheses. (0.5 mark) F[: dr{- at W V+a,k uul '*kf,[+al WWyY State the calculated value of test statistic andtiiticalvalrie of test. (1 mark) f*= to.og,zrtL=3,50' Ff,: tlU= lh.=Vt ' *ltu"dr .fut, = 4, g0 Decide whether null hypothesis is true and make the conclusions. lf required, use Tukey's procedurs. iron '5 mark) t Jto.oqrr 2b.\rc(lrt) @_Jg: t*.,we Aav'olyw( ltro a**= o,oy d,vd w,t/),",rq il^rr* l4/'ptL r9 w d4[41^r/^/L &ful(/)^ la4puw@^/L wtA,t^^' Inr,&r,t' L Wdilrt,ls no4 wry.,rc/. c.Constructan,no,,',,ffinceinterva!forthedifferencebetweenmean concentrations of mercury in the fish from lake # 2 and lake # 1' tt- tl b L,ll _,1"g6 , ltr^ ! I *rhr*,) L6 ,tro (f +f) . l, - !, , ss-sl t z .,r

, $tnf -1n&r{ A[r|$17A , M ril/vi{1/^^k4 d-vian. 6)t, +3+2=(,r;;;"" --"T*'['=63," vt= 5+t{ +r=11' 0 \#order to study the differences in operation cost of different types of machines, an engineer examined the operation costs for three different types of machines. Random samples of operation costs (in $ per hour) were obtained for each type of machine. The data obtained by the engineer are represented in the table below. one observation is missed, not all sample sizes are the same. 1, 2 3 4 5 [, Type I machine L0.4 9.9 10.6 8.9 1,1,.0 50"8 Type ll machine 8.8 1,1,.6 L0.9 1,1,.4 Yz,a Type lll machine L1,.2 13.4 11,.9 13.3 13.1 62.5 Itb.Y h 9u= t0, ft ff2, = 10.6t k ,= lz'58 $$rl:1 77462 7,, '" SgT= 9SIr = 9$E= l4gh = IV'I9E = l6 r0?,1,' a 6. oll if ti-+= r3t 6:l v *t-t,= Er h; h L = [t. 3g g. Ir a. Construct ANOVA table. Leave 3 digits after decimal point for the values of SSTr, SSE, SST, MSTr, MSE, and 2 digits for the value of F ratio. Use the rest of page for the calculations required for ANOVA table. b. Test at 5% significance level to determine if differences exist in mean operation costs of 3 types of machines. lf required, use Tukey's method to determine which means differ. Use a = 0.05. c. Construct 90 % individual confidence interval for the difference in mean operation costs for Type I machine and Type 2 machine. Write the solutions for question b. - c. on the following two pages. ANOVA TABLE Source of variation Degrees of freedom Sums of squares Mean squares F ratio Treatment K-l:t t6,ozt f ,ou +,+\ Error h-tl- =11 ,1. e ,E 1,03r Total 1a-1 = l3 z+. t{09 lT+Y" 6L - lE6. Y I -. l4 = L+, rlo 3 5!-C*\z.lz r hr* 156.Y-t = lb, r,zt. #lr{ sgr - 5e. f(-l sE_ h -tu ssrr = L+.rurl-!'itliu = rt ,388 =. l.0et (0