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
$\stackrel{\u203e}{y}$ is equal to
$517.2$ and the sample variance
${s}_{n-1}^{2}$ is equal to
$262.56$.
Test the hypothesis that the amount filled corresponds on average to the
setpoint. What is the value of the
$t$ test statistic?