Question
========
A machine fills milk into 500ml 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?

Solution
=========
The t-test statistic is calculated by:
$$
\begin{aligned}
  t = \frac{\bar y - \mu_0}{\sqrt{\frac{s^2_{n-1}}{n}}}
    = \frac{521.3 - 500}{\sqrt{\frac{527.08}{247}}}
    = 14.581.
\end{aligned}
$$
The absolute value of the t-test statistic is thus equal to
14.581.

Meta-information
================
extype: num
exsolution: 14.581
exname: t statistic
extol: 0.01