Exam 1

1. 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.