1) The data given below is milk yield of 28 daughters of 4 sires in 3 herds Herd Sire Milk Yield 1 1 157, 160, 138 2 96, 110, 115, 120 3 82, 65 4 120, 130,110 2 1 140, 142, 145 2 122, 117, 98 3 70, 94 3 2 112, 125, 105 3 110, 92 4 116, 129, 131 With a variance components analysis on Minitab, which statement is correct? a) The analysis cannot be carried out because it is an unbalanced design. b) The milk yield is an independent variable. c) “Herd” contributed more variability than “Sire”. d) “Sire” contributed more variability than “Herd”. e) All of above. f) None of above. (Problem#2~6) The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in °F) for that month. The past year’s usage and temperature are shown in the following table: Month Temp. Usage /1000 Month Temp. Usage /1000 Jan. 22 185.79 July 68 621.55 Feb. 24 214.47 Aug. 72 675.06 Mar. 32 288.03 Sept. 62 562.03 Apr. 45 424.06 Oct. 50 452.93 May 51 454.58 Nov. 41 369.95 June 59 539.03 Dec. 31 273.98 Let y = steam usage and x = monthly average temperature. 2) What is the correlation coefficient between x and y? a) Close to 1.00 b) Close to -1.00 c) Close to 0.50 d) Close to -0.50 e) None of above 3) Find a 99% confidence interval for ß1 a) (7.01, 11.90) b) (8.01, 10.90) c) (9.01, 9.90) d) (9.21, 9.70) e) None of above 4) Find a 99% confidence interval for ß0 a) (-49.16, -14.84) b) (-39.16, -4.84) c) (-29.16, 4.84) d) (-49.16, 14.84) e) None of above 5) Find a 95% confidence interval on mean steam usage when the average temperature is 55°F a) (497.20, 508.71) b) (487.20, 518.71) c) (477.20, 528.71) d) (467.20, 538.71) e) None of above 6) What is the distribution of the residuals? a) N(0, 7.90) b) N(0, 62.45) c) N(46.42, 16.87) d) N(46.42, 284.63) e) None of above (Problem #7) The Regression Equation is Tons mined = 4.359 + 0.000310 Personnel hours S = 0.0559431 R-Sq = 39.2% R-Sq(adj) = 33.1% Source DF SS MS F P Regression 1 0.0201823 0.0201823 6.45 0.029 Error 10 0.0312964 0.0031296 Total 11 0.0514787 7) Which two statements are correct for the Regression Analysis displayed above? a) The regression analysis based on the “p-value” is statistically significant at 95 % confidence. b) The independent variable is “Tons mined.” c) The regression is statistically insignificant as the R 2 value is < 80 %. d) the dependent variable is “tons mined.” e) the input “personnel hours” has a significant impact on “tons mined.” 8) given the following incomplete anova table, what is the sum of squares caused by the level? source df ss ms f p level 3 0.011425 error 64 44270.29 691.72 a) 52550 b) 15390 c) 8280 d) 2760 e) none of above 9) when conducting an anom, determine the lower and upper decision lines with ? and =2.00 if a significant level of 0.05 is desired. there are 5 levels, where each has 7 observations. a) ldl=7.14, udl=12.86 b) ldl=7.73, udl=12.27 c) ldl=8.16, udl=11.83 d) ldl=8.37, udl=11.62 e) none of above (problem #10) a meteorologist has measured the amount of rain in four cities for six months. she wants to know if there are different amounts of rain in the four cities. following is a result from kruskal-wallis test. kruskal-wallis test: rain versus city kruskal-wallis test on rain city n median ave rank z 1 6 90.50 15.5 1.20 2 6 88.00 15.4 1.17 3 6 69.00 6.1 -2.57 4 6 80.00 13.0 0.20 overall 24 12.5 h = 7.07 df = 3 p = 0.070 10) what conclusion could be made ( ? a) fail to reject the null hypothesis that all means are equal. b) the null hypothesis that all means are equal should be rejected. c) fail to reject the null hypothesis that all medians are equal. d) the null hypothesis that all medians are equal should be rejected. e) none of above (problem #11) aircraft primer paints are applied to aluminum surface by two methods: dipping and spraying. a factorial experiment was performed to investigate the effect of primer type and application method on paint adhesion. the resulting anova table is as follows, two-way anova: adhesion versus primer_type, apply_method source df ss ms f p primer_type 2 4.5811 2.29056 27.86 0.000 apply_method 1 4.9089 4.90889 59.70 0.000 interaction 2 0.2411 0.12056 1.47 0.269 error 12 0.9867 0.08222 total 17 10.7178 s = 0.2867 r-sq = 90.79% r-sq(adj) = 86.96% 11) what conclusion could not be made ( ? a) primer type is statistically significant. b) application method is statistically significant. c) the interaction is not statistically significant. d) all of above. e) none of above (problem #12) a collector is considering to buy one of 3 classical violins. he asked 10 musicians to play the violins and evaluate the violins on a scale 1~10 (10 is the best). following is a result from friedman test. friedman test: score versus violin blocked by player s = 9.95 df = 2 p = 0.007 est sum of violin n median ranks 1 10 8.083 26.5 2 10 7.167 21.0 3 10 6.000 12.5 grand median = 7.083 12) what conclusion could be made ( ? a) fail to reject the null hypothesis that all violins are the same. b) the null hypothesis that all violins are the same should be rejected. c) violin #1 is the best. d) violin #3 is the best. e) none of above 13) in selecting factors to be included in the regression model, we could use “best subset” analysis. what criteria we should consider? a) look for the highest r-sq value with the same number of predictors. b) look for the highest adj. r-sq value with different number of predictors. c) look for the smallest mallow’s and close to the number of parameters in the model. d) look for the smallest (std. deviation about the regression). e) all of above. (problem #14~16) a fractional factorial design was used to study 4 factors in a chemical process. the factors are a=temperature, b=pressure, c=concentration, and d=stirring rate, and the response is filtration rate. the design and the data are as follows, run a b c d response 1 45 2 100 3 45 4 65 5 75 6 60 7 80 8 96 14) what is the resolution of this doe? a) iii b) iv c) v d) v+ e) none of above 15) what is the estimated effect of a? a) 141.50 b) 78.00 c) 70.75 d) 19.00 e) none of above 16) what is the estimated magnitude of contrast column a dispersion effects? a) -0.0905 b) -0.1810 c) 0.0905 d) 0.1810 e) none of above 17) which of the following statements is false of the pareto chart effects diagram output shown by minitab above? a) there are 5 factors varied in this experimental effort. b) factor “b” has the highest effect on the output measured in this experiment. c) three-way interaction effects have a significant effect on the output. d) factor “c” has the lowest effect on the output measured in this experiment. e) two-way interactions and main effects are to be pursued in further trials. 18) for a doe with 6 2-level factors, resolution iv design, write down the contrast column numbers. 19) write down the 2-factor interaction confounding in the contrast column of the previous question. 20) construct a 5x5 latin square design using factors a, b, c, d, and e 80="" %.="" d)="" the="" dependent="" variable="" is="" “tons="" mined.”="" e)="" the="" input="" “personnel="" hours”="" has="" a="" significant="" impact="" on="" “tons="" mined.”="" 8)="" given="" the="" following="" incomplete="" anova="" table,="" what="" is="" the="" sum="" of="" squares="" caused="" by="" the="" level?="" source="" df="" ss="" ms="" f="" p="" level="" 3="" 0.011425="" error="" 64="" 44270.29="" 691.72="" a)="" 52550="" b)="" 15390="" c)="" 8280="" d)="" 2760="" e)="" none="" of="" above="" 9)="" when="" conducting="" an="" anom,="" determine="" the="" lower="" and="" upper="" decision="" lines="" with="" and="2.00" if="" a="" significant="" level="" of="" 0.05="" is="" desired.="" there="" are="" 5="" levels,="" where="" each="" has="" 7="" observations.="" a)="" ldl="7.14," udl="12.86" b)="" ldl="7.73," udl="12.27" c)="" ldl="8.16," udl="11.83" d)="" ldl="8.37," udl="11.62" e)="" none="" of="" above="" (problem="" #10)="" a="" meteorologist="" has="" measured="" the="" amount="" of="" rain="" in="" four="" cities="" for="" six="" months.="" she="" wants="" to="" know="" if="" there="" are="" different="" amounts="" of="" rain="" in="" the="" four="" cities.="" following="" is="" a="" result="" from="" kruskal-wallis="" test.="" kruskal-wallis="" test:="" rain="" versus="" city="" kruskal-wallis="" test="" on="" rain="" city="" n="" median="" ave="" rank="" z="" 1="" 6="" 90.50="" 15.5="" 1.20="" 2="" 6="" 88.00="" 15.4="" 1.17="" 3="" 6="" 69.00="" 6.1="" -2.57="" 4="" 6="" 80.00="" 13.0="" 0.20="" overall="" 24="" 12.5="" h="7.07" df="3" p="0.070" 10)="" what="" conclusion="" could="" be="" made="" (="" a)="" fail="" to="" reject="" the="" null="" hypothesis="" that="" all="" means="" are="" equal.="" b)="" the="" null="" hypothesis="" that="" all="" means="" are="" equal="" should="" be="" rejected.="" c)="" fail="" to="" reject="" the="" null="" hypothesis="" that="" all="" medians="" are="" equal.="" d)="" the="" null="" hypothesis="" that="" all="" medians="" are="" equal="" should="" be="" rejected.="" e)="" none="" of="" above="" (problem="" #11)="" aircraft="" primer="" paints="" are="" applied="" to="" aluminum="" surface="" by="" two="" methods:="" dipping="" and="" spraying.="" a="" factorial="" experiment="" was="" performed="" to="" investigate="" the="" effect="" of="" primer="" type="" and="" application="" method="" on="" paint="" adhesion.="" the="" resulting="" anova="" table="" is="" as="" follows,="" two-way="" anova:="" adhesion="" versus="" primer_type,="" apply_method="" source="" df="" ss="" ms="" f="" p="" primer_type="" 2="" 4.5811="" 2.29056="" 27.86="" 0.000="" apply_method="" 1="" 4.9089="" 4.90889="" 59.70="" 0.000="" interaction="" 2="" 0.2411="" 0.12056="" 1.47="" 0.269="" error="" 12="" 0.9867="" 0.08222="" total="" 17="" 10.7178="" s="0.2867" r-sq="90.79%" r-sq(adj)="86.96%" 11)="" what="" conclusion="" could="" not="" be="" made="" (="" a)="" primer="" type="" is="" statistically="" significant.="" b)="" application="" method="" is="" statistically="" significant.="" c)="" the="" interaction="" is="" not="" statistically="" significant.="" d)="" all="" of="" above.="" e)="" none="" of="" above="" (problem="" #12)="" a="" collector="" is="" considering="" to="" buy="" one="" of="" 3="" classical="" violins.="" he="" asked="" 10="" musicians="" to="" play="" the="" violins="" and="" evaluate="" the="" violins="" on="" a="" scale="" 1~10="" (10="" is="" the="" best).="" following="" is="" a="" result="" from="" friedman="" test.="" friedman="" test:="" score="" versus="" violin="" blocked="" by="" player="" s="9.95" df="2" p="0.007" est="" sum="" of="" violin="" n="" median="" ranks="" 1="" 10="" 8.083="" 26.5="" 2="" 10="" 7.167="" 21.0="" 3="" 10="" 6.000="" 12.5="" grand="" median="7.083" 12)="" what="" conclusion="" could="" be="" made="" (="" a)="" fail="" to="" reject="" the="" null="" hypothesis="" that="" all="" violins="" are="" the="" same.="" b)="" the="" null="" hypothesis="" that="" all="" violins="" are="" the="" same="" should="" be="" rejected.="" c)="" violin="" #1="" is="" the="" best.="" d)="" violin="" #3="" is="" the="" best.="" e)="" none="" of="" above="" 13)="" in="" selecting="" factors="" to="" be="" included="" in="" the="" regression="" model,="" we="" could="" use="" “best="" subset”="" analysis.="" what="" criteria="" we="" should="" consider?="" a)="" look="" for="" the="" highest="" r-sq="" value="" with="" the="" same="" number="" of="" predictors.="" b)="" look="" for="" the="" highest="" adj.="" r-sq="" value="" with="" different="" number="" of="" predictors.="" c)="" look="" for="" the="" smallest="" mallow’s="" and="" close="" to="" the="" number="" of="" parameters="" in="" the="" model.="" d)="" look="" for="" the="" smallest="" (std.="" deviation="" about="" the="" regression).="" e)="" all="" of="" above.="" (problem="" #14~16)="" a="" fractional="" factorial="" design="" was="" used="" to="" study="" 4="" factors="" in="" a="" chemical="" process.="" the="" factors="" are="" a="temperature," b="pressure," c="concentration," and="" d="stirring" rate,="" and="" the="" response="" is="" filtration="" rate.="" the="" design="" and="" the="" data="" are="" as="" follows,="" run="" a="" b="" c="" d="" response="" 1="" 45="" 2="" 100="" 3="" 45="" 4="" 65="" 5="" 75="" 6="" 60="" 7="" 80="" 8="" 96="" 14)="" what="" is="" the="" resolution="" of="" this="" doe?="" a)="" iii="" b)="" iv="" c)="" v="" d)="" v+="" e)="" none="" of="" above="" 15)="" what="" is="" the="" estimated="" effect="" of="" a?="" a)="" 141.50="" b)="" 78.00="" c)="" 70.75="" d)="" 19.00="" e)="" none="" of="" above="" 16)="" what="" is="" the="" estimated="" magnitude="" of="" contrast="" column="" a="" dispersion="" effects?="" a)="" -0.0905="" b)="" -0.1810="" c)="" 0.0905="" d)="" 0.1810="" e)="" none="" of="" above="" 17)="" which="" of="" the="" following="" statements="" is="" false="" of="" the="" pareto="" chart="" effects="" diagram="" output="" shown="" by="" minitab="" above?="" a)="" there="" are="" 5="" factors="" varied="" in="" this="" experimental="" effort.="" b)="" factor="" “b”="" has="" the="" highest="" effect="" on="" the="" output="" measured="" in="" this="" experiment.="" c)="" three-way="" interaction="" effects="" have="" a="" significant="" effect="" on="" the="" output.="" d)="" factor="" “c”="" has="" the="" lowest="" effect="" on="" the="" output="" measured="" in="" this="" experiment.="" e)="" two-way="" interactions="" and="" main="" effects="" are="" to="" be="" pursued="" in="" further="" trials.="" 18)="" for="" a="" doe="" with="" 6="" 2-level="" factors,="" resolution="" iv="" design,="" write="" down="" the="" contrast="" column="" numbers.="" 19)="" write="" down="" the="" 2-factor="" interaction="" confounding="" in="" the="" contrast="" column="" of="" the="" previous="" question.="" 20)="" construct="" a="" 5x5="" latin="" square="" design="" using="" factors="" a,="" b,="" c,="" d,="" and="">