Question

70% of voters in a certain state support an increase in the minimum wage. A researcher believe that the percentage of fast food workers for support and increase is higher than 70%. In a random sample of 300 fast food workers for 240 supporters increase an minimum-wage. Test is significant level a = .05 find

Answer 1

Answer with explanation:

Let p be the proportion of voters in a certain state support an increase in the minimum wage.

As per given , we have

$H_0: p =0.70\\\\ H_a: p >0.70$

Since alternative hypothesis is right-tailed so the test is a right-tailed test.

Test statistic : $z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

, where n= sample size.

p= population proportion.

$\hat{p}$ = sample proportion.

. In a random sample of 300 fast food workers for 240 supporters increase an minimum-wage.

i.e. n= 300 and $\hat{p}=\dfrac{240}{300}=0.8$

Then,

$z=\dfrac{0.8-0.7}{\sqrt{\dfrac{0.7(1-0.7)}{300}}}\approx3.78$

For significant level α = .05 , the critical z-value is

$z_{0.05}=1.645$

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%..