Answer: We have enough evidence to support the consumer's claim that the actual mean amount is less.
Step-by-step explanation:
Let [tex]\mu[/tex] represents the population mean for the dispensed liquid into each paper cup.
According to the claim , we have the following set of hypothesis :-
[tex]H_0 : \mu=8\\\\ H_1: \mu<8[/tex]
Since the alternative hypothesis is left-tailed , so the hypothesis test is left tailed test.
For sample , we have
Sample size : n=49 , which is large (n>30) , so we use z-test.
Sample mean : [tex]\overline{x}=7.75[/tex]
Standard deviation : [tex]\sigma= \sqrt{0.81}=0.9[/tex]
The test statistic for population mean is given by :-
[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\\Rightarrow\ z=\dfrac{7.75-8}{\dfrac{0.9}{\sqrt{49}}}\\\\\Rightarrow\ z\approx-1.94[/tex]
The p-value = [tex]P(z<-1.94)=0.0261898[/tex]
Since , the p-value is less than the significance level (0.05), so we reject the null hypothesis .
Thus , we conclude that we have enough evidence to support the alternative hypothesis i.e. the actual mean amount is less.
Answer: reject the 8 ounce claim
Step-by-step explanation:
