Let [tex]\mu[/tex] be the population mean .
By considering the given information , we have the following hypothesis :-
[tex]H_0:\mu=12\\\\H_a:\mu\neq12[/tex]
Since the alternative hypotheses is two tailed so the test is a two tailed test.
We assume that the quantity of juices is normally distributed.
Given : Sample size : n=20 , which is less than 30 .
It means the sample is small so we use t-test.
Sample mean : [tex]\overline{x}=11.7\text{ ounces}[/tex]
Standard deviation : [tex]\sigma=0.7\text{ ounces}[/tex]
Test statistic for population mean :-
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]\Rightarrow\ t=\dfrac{11.7-12}{\dfrac{0.7}{\sqrt{20}}}\approx-1.917[/tex]
Critical value : [tex]t_{n-1,\alpha/2}=2.861[/tex]
Since the critical value is greater than the observed value , so we reject the null hypothesis.
Hence, we have enough evidence to support the agency's claim.
