Question

a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 405 - gram setting. is there sufficient evidence at the 0.1 level that the bags are underfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.

Explanation:

Step1: Define null hypothesis

The null hypothesis ($H_0$) is that the machine is working correctly, so the mean weight $\mu$ is equal to the setting.
$H_0:\mu = 405$

Step2: Define alternative hypothesis

The alternative hypothesis ($H_a$) is that the bags are under - filled, so the mean weight $\mu$ is less than 405.
$H_a:\mu<405$

Answer:

$H_0:\mu = 405$
$H_a:\mu<405$