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 μ0=500\mu_0 = 500. A sample of 247247 packages filled by the machine are collected. The sample mean y‾\bar{y} is equal to 521.3521.3 and the sample variance sn−12s^2_{n-1} is equal to 527.08527.08.

    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: t=y‾−μ0sn−12n=521.3−500527.08247=14.581. \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.