\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 value of the $t$~test statistic?
\begin{answerlist}
\item $ 1.275$
\item $-13.070$
\item $-53.309$
\item $ 9.888$
\item $ 14.581$
\end{answerlist}
\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 $t$~test statistic is thus equal to
$14.581$.
\begin{answerlist}
\item False
\item False
\item False
\item False
\item True
\end{answerlist}
\end{solution}
%% META-INFORMATION
%% \extype{schoice}
%% \exsolution{00001}
%% \exname{t statistic}