Let p be the proportion of voters in a certain state support an increase in the minimum wage.
As per given , we have
[tex]H_0: p =0.70\\\\ H_a: p >0.70[/tex]
Since alternative hypothesis is right-tailed so the test is a right-tailed test.
Test statistic : [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
, where n= sample size.
p= population proportion.
[tex]\hat{p}[/tex] = sample proportion.
. In a random sample of 300 fast food workers for 240 supporters increase an minimum-wage.
i.e. n= 300 and [tex]\hat{p}=\dfrac{240}{300}=0.8[/tex]
Then,
[tex]z=\dfrac{0.8-0.7}{\sqrt{\dfrac{0.7(1-0.7)}{300}}}\approx3.78[/tex]
For significant level α = .05 , the critical z-value is
[tex]z_{0.05}=1.645[/tex]
Decision : Since calculated z-value (3.78) is greater than the critical value (1.645) , so we reject the null hypothesis.
Conclusion : We have sufficient evidence o support researcher's claim that that the percentage of fast food workers for support and increase is higher than 70%..
