Question

A soft drink filling machine, when in perfect adjustment, fills thebottles with 12 ounces of soft drink.any overfilling or underfilling results in the shutdown and readjustment of the machine.Todetermine whether or not the machine is properly adjusted, thecorrect set of hypotheses is

a. H0:μ<12 Ha:μ<=12
b. H0:μ<=12 Ha:μ>12
c. H0:μ not equal to 12 Ha:μ=12
d. H0:μ=12 Ha:μ not equal to 12

Answer 1

Answer: d. H0:μ=12 ; Ha:μ not equal to 12

Explanation:

Let
`\mu` denotes the average ounces of soft drink in a bottle.

Given : a soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink

i.e.
`\mu=12` ...(i)

Any overfilling or under-filling results in the shutdown and readjustment of the machine or we can say
`\mu \\eq12` ...(ii)

As we know , Null hypothesis
`(H_0)` believes that there is no statistical difference in between the groups being tested.

Whereas Alternative hypothesis
`(H_a)` believes that there is statistical difference .

So , from (i) and (ii) , we have

`H_0:\mu=12\\H_a:\mu\\eq12`

Hence, the correct option is d. H0:μ=12 ;Ha:μ not equal to 12.