Question

A Cereal filling machine, fills the bottles with 500 grams on an average. Any overfilling or under-filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

Answer 1

The correct set of hypothesis is:

`H_0: \mu = 500`

`H_1: \mu \\eq 500`

Explanation:

At the null hypothesis, we test that the mean is at the desired value of 500 grams, that is:

`H_0: \mu = 500`

At the alternate hypothesis, we test that the machine is either overfilling or under-filling, that is, the mean is different from 500. So

`H_1: \mu \\eq 500`

The correct set of hypothesis is:

`H_0: \mu = 500`

`H_1: \mu \\eq 500`