(Solved): I don't understand when we reject H0. What exactly is f? and How do we find the p-value, can you ill ...

In order to test ${\mathrm{H}}_0:{?}_1=?={?}_k$, we define the following test statistic: $F=\frac{{?}_{j=1}^k{n}_j{\left({\stackrel{?}{X}}_{?j}?\stackrel{?}{X}\right)}^2/(k?1)}{{?}_{j=1}^k{?}_{i=1}^{n_j}{\left(X_{ij}?{\stackrel{?}{X}}_{?j}\right)}^2/(n?k)}=\frac{B/(k?1)}{W/(n?k)}.$ Under ${\mathrm{H}}_0,F?F_{k?1,n?k}$. We reject ${\mathrm{H}}_0$ at the $100?\%$ significance level if: $f>F_{?,k?1,n?k}$ where $F_{?,k?1,n?k}$ is the top $100?$ th percentile of the $F_{k?1,n?k}$ distribution, i.e. $P\left(F>F_{?,k?1,n?k}\right)=?$, and $f$ is the observed test statistic value. 315 10. Analysis of variance (ANOVA) The $p$-value of the test is: $p\text{-value }=P(F>f).$ It is clear that $f>F_{?,k?1,n?k}$ if and only if the $p$-value $<?$, as we must reach the same conclusion regardless of whether we use the critical value approach or the $p$-value approach to hypothesis testing.