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 ${\mathit{\mu}}_{0}=500$. A sample of $247$ packages
filled by the machine are collected. The sample mean $\stackrel{\u203e}{y}$ is equal to
$521.3$ and the sample variance ${s}_{n-1}^{2}$ 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?