实验设计与方差分析 HW6_Solution

1. Solution:(a) Factor A: bottle type ,low level for the glass type and high for the plastic. Factor B: worker ,low level for the first and high for the second.(b) Data structure:FactorReplicateAB1st2nd3rd4thTotal-5.124.894.98519.99+-4.954.434.274.2517.9-+6.656.245.495.5523.93+5.284.914.754.7119.65(c) (d) 2. Solution:(a) Data structure:FactorReplicateABCD1st2ndTotal-9093183+-7478152-+-8185166+-8380163-+-7778155+-+-8180161-+-8882170+-7370143-+9895193+-+7276148-+-+8783170+-+8586171-+9990189+-+7975154-+8784171+8080160(b)FactorSSdfMSContributionA657.03131657.03130.403714B13.78125113.781250.008468C57.78125157.781250.035504D124.03131124.03130.076211AB132.03131132.03130.081127AC3.7812513.781250.002323AD38.28125138.281250.023522BC2.5312512.531250.001555BD0.2812510.281250.000173CD22.78125122.781250.013998ABC215.28131215.28130.13228ABD175.78131175.78130.108009ACD7.0312517.031250.00432BCD7.0312517.031250.00432ABCD47.53125147.531250.029206Error122.5167.65625Total1627.46931(c)ANOVA tableFactorSSdfMSFA657.03131657.031385.81633B13.78125113.781251.8C57.78125157.781257.546939D124.03131124.031316.2AB132.03131132.031317.2449AC3.7812513.781250.493878AD38.28125138.281255BC2.5312512.531250.330612BD0.2812510.281250.036735CD22.78125122.781252.97551ABC215.28131215.281328.11837ABD175.78131175.781322.95918ACD7.0312517.031250.918367BCD7.0312517.031250.918367ABCD47.53125147.531256.208163Error122.5167.65625Total1627.46931Because ,the effect of A,D,AB,ABC,ABD is important at 1% significance level.(d) (e)Basic FactorGeneratorABCD=ABCTotalABACAD-1-1-1-1(1)901111-1-11ad72-1-11-11-11bd87-11-111-1-1ab831-1-1-1-111cd991-1-11-11-1ac81-11-1-111-1bc88-1-111111abcd80111FactorSSdfContributionA288164.28571429B210.446428571C3217.142857143D210.446428571AB72116.07142857AC210.446428571AD50111.16071429From the contribution column, we can regard the effects of B, D, AC as error. The ANOVA table is as follow:FactorSSdfMSFA2881288144C3213216AB7217236AD5015025Error632Total4487The regression model is:3. (a) basic factors: A, B, C, D. Generators: E=BCD, F=ACD, G=ABC, H=ABD. (b) I=BCDE=ACDF=ABCG=ABDH=ABEF=ADEG=ACEH=BDFG =BCFH=CDGH=CEFG=EFDH=BEGH=AFGH=ABCDEFGH (c) 1 overall mean, main factor effect of A, B, C, D, E, F, G, H, interaction effect AB, AC, AD,A