Answer
$F_0=2.599$
Work Step by Step
$x ̅=\frac{73+82+82+81+97+67+77+66+67+83+72+80+87+77+96}{15}=79.1333$
$x ̅_1=\frac{73+82+82+81+97}{5}=83$
$x ̅_2=\frac{67+77+66+67+83}{5}=72$
$x ̅_3=\frac{72+80+87+77+96}{5}=82.4$
$s_1^2=\frac{(73-83)^2+(82-83)^2+(82-83)^2+(81-83)^2+(97-83)^2}{5-1}=75.5$
$s_2^2=\frac{(67-72)^2+(77-72)^2+(66-72)^2+(67-72)^2+(83-72)^2}{5-1}=58$
$s_3^2=\frac{(72-82.4)^2+(80-82.4)^2+(87-82.4)^2+(77-82.4)^2+(96-82.4)^2}{5-1}=87.3$
$SST=n_1(x ̅_1-x ̅)^2+n_2(x ̅_2-x ̅)^2+n_3(x ̅_3-x ̅)^2=5(83-79.1333)^2+5(72-79.1333)^2+5(82.4-79.1333)^2=382.5333$
$MST=\frac{SSE}{k-1}=\frac{382.5333}{3-1}=191.2667$
$SSE=(n_1-1)s_1^2+(n_2-1)s_2^2+(n_3-1)s_3^2=(5-1)75.5+(5-1)58+(5-1)87.3=883.2$
$MSE=\frac{SSE}{n-k}=\frac{883.2}{15-3}=73.6$
$F_0=\frac{MST}{MSE}=\frac{191.2667}{73.6}=2.599$
