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 $226$ packages
filled by the machine are collected. The sample mean $\bar{y}$ is equal to
517.2 and the sample variance $s^2_{n-1}$ is equal to
262.56.
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:
$$
\begin{aligned}
t = \frac{\bar y - \mu_0}{\sqrt{\frac{s^2_{n-1}}{n}}}
= \frac{517.2 - 500}{\sqrt{\frac{262.56}{226}}}
= 15.958.
\end{aligned}
$$
The absolute value of the t-test statistic is thus equal to
15.958.
Meta-information
================
extype: num
exsolution: 15.958
exname: t statistic
extol: 0.01