Question

Public Policy and Political Science Early in 2013, a political report indicated that 86% of Americans disapprove of the job Congress is doing. In a poll of 1000 Americans during Summer 2013 by NBC News, 830 said they disapprove of the job Congress is doing.59 Is there any evidence to suggest that the proportion of Americans who disapprove of the job Congress is doing has decreased? Use a 5 0.01.

Answer 1

Answer with explanation:

Let p be the population proportion of Americans disapprove of the job Congress is doing .

As per given , we have

$H_0:p=0.86\\\\ H_a:p$

Since $H_a$ is left-tailed , so the test is a left-tailed test.

Also, it is given that : In a poll of 1000 Americans during Summer 2013 by NBC News, 830 said they disapprove of the job Congress is doing.

i.e. n= 1000

$\hat{p}=\dfrac{830}{1000}=0.83$

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

$z=\dfrac{0.83-0.86}{\sqrt{\dfrac{0.86(1-0.86)}{1000}}}=-2.734$

P-value for left tailed test : P(z<-2.734)=1-P(z<2.734)

[∵ P(Z<-z)=1-P(Z<z)]

=1-0.99687=0.00313

Decision : Since p-value (0.00313) < significance level (0.01), so we reject the null hypothesis.

[Rejection criteria : if p-value is less than $\alpha$ (significance level ), then null hypothesis gets rejected.]

Thus , we conclude that we have enough evidence to support the claim at 0.01 significance level that  the proportion of Americans who disapprove of the job Congress is doing has decreased.