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 226226 packages filled by the machine are collected. The sample mean y\bar{y} is equal to 517.2 and the sample variance sn12s^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: t=yμ0sn12n=517.2500262.56226=15.958. \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.