Answer
$F_0=2.04$
Work Step by Step
$x ̅=\frac{28+23+30+27+22+25+17+23+25+24+19+30}{12}=24.4167$
$x ̅_1=\frac{28+23+30+27}{4}=27$
$x ̅_2=\frac{22+25+17+23}{4}=21.75$
$x ̅_3=\frac{25+24+19+30}{4}=24.5$
$s_1^2=\frac{(28-27)^2+(23-27)^2+(30-27)^2+(27-27)^2}{4-1}=8.6667$
$s_2^2=\frac{(22-21.75)^2+(25-21.75)^2+(17-21.75)^2+(23-21.75)^2}{4-1}=11.5833$
$s_3^2=\frac{(25-24.5)^2+(25-24.5)^2+(25-24.5)^2+(25-24.5)^2}{4-1}=20.3333$
$SST=n_1(x ̅_1-x ̅)^2+n_2(x ̅_2-x ̅)^2+n_3(x ̅_3-x ̅)^2=4(27-24.4167)^2+4(21.75-24.4167)^2+4(24.5-24.4167)^2=55.1667$
$MST=\frac{SSE}{k-1}=\frac{55.1667}{3-1}=27.5833$
$SSE=(n_1-1)s_1^2+(n_2-1)s_2^2+(n_3-1)s_3^2=(4-1)8.6667+(4-1)11.5833+(4-1)20.3333=121.75$
$MSE=\frac{SSE}{n-k}=\frac{121.75}{12-3}=13.5278$
$F_0=\frac{MST}{MSE}=\frac{27.5833}{13.5278}=2.04$
