Answer: (0.257633, 0.302367)
Step-by-step explanation:
We know that , the confidence interval for population proportion is given by :-
[tex]\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}} [/tex] , where n= sample size , z= critical value , [tex]\hat{p}[/tex]= sample proportion.
Let p be the proportion of the U.S. adults who feel that unemployment compensation should be extended an additional six months while the country is in it current economic downturn.
Here , n= 1548 , [tex]\hat{p}=\dfrac{433}{1548}\approx0.28[/tex]
For 95% confidence interval , z= 1.96
Now , a 95% confidence interval to estimate the proportion of the U.S. adults who feel this way would be :
[tex]0.28\pm (1.96)\sqrt{\dfrac{0.28(1-0.28)}{1548}} \\\\=0.28\pm (1.96)\sqrt{\dfrac{0.28\times0.72}{1548}}\\\\=0.28\pm(1.96)(0.011412)\\\\=0.28\pm0.022367\\\\=(0.28-0.022367,\ 0.28+0.022367)\\\\=(0.257633,\ 0.302367)[/tex]
Hence, the 95% confidence interval to estimate the proportion of the U.S. adults who feel this way. would be : (0.257633, 0.302367)
