\begin{question}
A machine fills milk into $500$ml packages. It is suspected that the
machine is not working correctly and that the amount of milk filled differs
from the setpoint $\mu_0 = 500$. A sample of $226$ packages
filled by the machine are collected. The sample mean $\bar{y}$ is equal to
$517.2$ and the sample variance $s^2_{n-1}$ is equal to
$262.56$.
Test the hypothesis that the amount filled corresponds on average to the
setpoint. What is the absolute value of the $t$~test statistic?
\end{question}
\begin{solution}
The $t$~test statistic is calculated by:
\begin{eqnarray*}
t & = & \frac{\bar y - \mu_0}{\sqrt{\frac{s^2_{n-1}}{n}}}
= \frac{517.2 - 500}{\sqrt{\frac{262.56}{226}}}
= 15.958.
\end{eqnarray*}
The absolute value of the $t$~test statistic is thus equal to
$15.958$.
\end{solution}
%% META-INFORMATION
%% \extype{num}
%% \exsolution{15.958}
%% \exname{t statistic}
%% \extol{0.01}