Answer with explanation:
Given : A bottle filling process has a setting of 48 ounces which is exactly what consumers want when they buy the vegetable oil.
Let [tex]\mu[/tex] represents the population mean .
Then, the set of hypothesis will be:-
[tex]H_0: \mu=48[/tex]
[tex]H_a:\mu\neq48[/tex] , since the alternative hypothesis is two-tailed , so the hypothesis test is a two-tailed test.
We assume that this is normal distribution.
Sample size : n =36, which is a large sample (z<30) , so we use t-test.
Sample mean : [tex]\overliene{x}=48.15\text{ ounces}[/tex]
Standard deviation : [tex]\sigma=0.3\text{ ounces}[/tex]
The test statistic for population mean for large sample is given by :-
[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z=\dfrac{48.15-48}{\dfrac{0.3}{\sqrt{36}}}=3[/tex]
The p-value = [tex]2P(z>3)=0.0026998[/tex]
Since the p-value is less than the significance level of 0.02 , therefore we reject the null hypothesis and support the alternative hypothesis.
Thus we conclude that we do not have enough evidence to support the claim that a bottle filling process has a setting of 48 ounces which is exactly what consumers want when they buy the vegetable oil.
