Question

a manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 438 - gram setting. is there sufficient evidence at the 0.02 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 $H_0$ assumes the machine is working correctly. So, it is that the mean weight $\mu$ of the bags is equal to the setting of 438 grams.
$H_0:\mu = 438$

Step2: Define alternative hypothesis

The alternative hypothesis $H_a$ is what we are testing for. Since we want to know if the bags are under - filled, it is that the mean weight $\mu$ of the bags is less than 438 grams.
$H_a:\mu<438$

Answer:

$H_0:\mu = 438$
$H_a:\mu<438$