a) number of levels of factor A =df(A)+1 =3+1 =4
number of levels of factor B =df(B)+1 =1+1 =2
b)
number of observation for each combination =(total df+1)/(level of factor A*level of factor B) =24/(4*2)=3
c)
Source | df | SS | MS | F |
A | 3 | 2.25 | 0.75 | 5.00 |
B | 1 | 0.95 | 0.95 | 6.33 |
A*B | 3 | 0.9 | 0.30 | 2.00 |
error | 16 | 2.4 | 0.15 | |
total | 23 | 6.5 |
d)
for 0.1 level and (3,16) df , crtiical value =2.46
since test statistic F=5 is higher than critical value, factor A is significant
for 0.1 level and (1,16) df , crtiical value =3.05
since test statistic F=6.33 is higher than critical value, factor B is significant
for 0.1 level and (3,16) df , crtiical value =2.46
since test statistic F=2 is not higher than critical value, interaction is not significant
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