Stat 3500 Section 7 Question 3. A study was carried out to compare the writing D

Question

Stat 3500 Section 7 Question 3. A study was carried out to compare the writing Due: 4/ G lifetimes of four brands of pens. It was thought might affect lifetime, so three different surfaces were randomly selected. her wise homogeneous. Consider the A writing machine was used to ensure that conditions were ot following data table: Surface 1 Surtace 2 Surface 3 Brand 1 781, 785760, 763 728, 721 Brand 2 739, 743 773, 776 766, 761 Brand 3 719, 724 712, 712 724, 727 Brand 4 754, 758 747, 742 757, 755 (a). Complete the ANOVA table. You must show your work. MS Source A(Brand) B(Surface) DF 6128.12 136.17 93.89 101.5 Error Total 1·126696 × 1 04

Explanation / Answer

Since give data is two way anova with interaction

A,B are the given data

since the data is distributed 4*3*2 form

i.e 4 rows ,3 columns,2 in each of these

Degrees of freedom total is 23 since 4*3*2-1

for A=4-1=3

for B=3-1=2

for Interaction= (4-1)*(3-1)=6

error=12

since from the give data

SS(A)=6128.12

TSS=11266.96

SSE=101.5

MSB=136.17

F statistic of Interaction is 93.89

since MSE=SSE/Df=101.5/12=8.458

i) for A

MSA= SSA/DF=6128.12/3=2042.707

F statistic is MSA/MSE=2042.7/8.458=241.73

ii)for B

SSB=2*MSB=272.34

F statistic is=MSB/MSE=272.34/8.458=32.19

for Interaction

MSI=MSE*93.89=93.89*8.45=782.54

SSI=MSI*6= 782.54*6=4695.23

hence the reqiured anova table is

source DF ss ms F A 3 6128.12 2042.7 241.73 B 2 272.333 136.17 32.19 INTERACTION 6 4695.23 782.54 93.89 ERROR 12 101.5 8.45 TOTAL 23 1.126696

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