
\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 $247$ packages 
filled by the machine are collected. The sample mean $\bar{y}$ is equal to 
$521.3$ and the sample variance $s^2_{n-1}$ is equal to 
$527.08$.

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{521.3 - 500}{\sqrt{\frac{527.08}{247}}}
  = 14.581.
\end{eqnarray*}
The absolute value of the $t$~test statistic is thus equal to
$14.581$.
\end{solution}

%% META-INFORMATION
%% \extype{num}
%% \exsolution{14.581}
%% \exname{t statistic}
%% \extol{0.01}
