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 $226$ 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 value of the t-test statistic?
Answerlist
----------
* $-9.853$
* $30.505$
* $-22.761$
* $-2.894$
* $15.958$
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 t-test statistic is thus equal to
$15.958$.
Answerlist
----------
* False
* False
* False
* False
* True
Meta-information
================
extype: schoice
exsolution: 00001
exname: t statistic