QUESTION $4(10$ MARKS$)$

Four different types of carbon materials were tested, and the surface roughness was measured, as listed below:

$\backslash$table$[[$Carbon Material Type,Surface roughness$],[$Type $1,0\mathrm{.}51,0\mathrm{.}53,0\mathrm{.}36,0\mathrm{.}50,,,],[$Type $2,0\mathrm{.}32,0\mathrm{.}28,0\mathrm{.}20,0\mathrm{.}48,0\mathrm{.}31,0\mathrm{.}30,],[$Type $3,0\mathrm{.}22,0\mathrm{.}28,0\mathrm{.}25,0\mathrm{.}32,0\mathrm{.}24,,],[$Type $4,0\mathrm{.}10,0\mathrm{.}16,0\mathrm{.}13,0\mathrm{.}12,,,]]$

Assume the surface roughness is normally distrusted, test if the type of carbon material has a significant effect on the mean surface roughness? Use $=0\mathrm{.}01.$

$(10$ marks$)$

QUESTION $5(10$ MARKS$)$

Contact resistance of a brake$-$only relay was investigated for different silver$-$based alloys. The Microsoft Excel output shows the following result:

$\backslash$table$[[$Anova: Single Factor,,,,$],[,,,,],[$SUMMARY$,,,,],[$Groups$,$Count,Sum,Average,Variance$],[$Type $1,10,971,97\mathrm{.}1,3\mathrm{.}4333],[$Type $2,10,1019,101\mathrm{.}9,3\mathrm{.}4333],[$Type $3,10,1178,117\mathrm{.}8,31\mathrm{.}7333],[$Type $4,10,974,97\mathrm{.}4,1\mathrm{.}6000],[$Type $5,10,1026,102\mathrm{.}6,0\mathrm{.}9333],[$Type $6,10,1000,100,4\mathrm{.}2222]]$

ANOVA

$\backslash$table$[[$Source of Variation,SS$,df,$MS$,F,P-$value$],[$Between Groups,$2953\mathrm{.}4,,590\mathrm{.}6800,78\mathrm{.}1399,1\mathrm{.}77E-23$