Question

How much juice? One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of $180$milliliters (ml) of liquid. A quality-control inspector must check that the machine is working properly. The inspector takes a random sample of $40$bottles and measures the volume of liquid in each bottle.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

Short answer

$H_0:\mu =180$

$H_a:\mu \ne 180$

Step-by-step solution

Step 1:Given information

How much juice? One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of $180$ milliliters (ml) of liquid. A quality-control inspector must check that the machine is working properly. The inspector takes a random sample of $40$ bottles and measures the volume of liquid in each bottle.

Step 2:Explaination

$\text{Claim: mean is}180\text{millilitres}$

The null hypothesis statement is that the population value is equal to the value given in the claim:

$H_0:\mu =180$

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis statement is that the population proportion is equal to the value given in the claim. If the null hypothesis is the claim, then the alternative hypothesis statement is the opposite of the null hypothesis.

$H_a:\mu \ne 180$

$\mu$ is the mean volume of liquid in all bottles.