# For H 0 </msub> : &#x03C0;<!-- π --> = 0.20 , for instance, the score test sta

For ${H}_{0}:\pi =0.20$, for instance, the score test statistic is $Z\left(s\right)=-2.50$, which has two-sided P-value $0.012<0.05$, so $0.20$ does not fall in the interval.
It is understood that the score test statistic is $-2.5$ using $n=25$ and $\stackrel{^}{\pi }=0$ (in the previous description), but the part where the P-value is $0.012$ is not understood.
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charringpq49u
The $2$-sided P-value is double the probability below $-2.5$ under the standard normal density curve; that is,$P\left(|Z|>2.5\right)=P\left(Z<-2.5\right)+P\left(Z>2.5\right)=2P\left(Z<-2.5\right)\phantom{\rule{0ex}{0ex}}=2\left(0.0062\right)=0.0124<0.05=5\mathrm{%},$
so the null hypothesis is rejected at the $5\mathrm{%}$ level.
In $R$, where $\mathtt{p}\mathtt{n}\mathtt{o}\mathtt{r}\mathtt{m}$ is a normal CDF:
$\mathtt{p}\mathtt{n}\mathtt{o}\mathtt{r}\mathtt{m}\mathtt{\left(}\mathtt{-}\mathtt{2.50}\mathtt{\right)}$

Or use printed standard normal CDF tables (usually limited to $4$-place accuracy).