Answer: Â [tex](0.458176,\ 0.581824)[/tex]
We are 99% sure that the true population mean falls in interval [tex](0.458176,\ 0.581824)[/tex].
Step-by-step explanation:
Let [tex]\hat{p}[/tex] be the sample proportion.
As per given , we have
[tex]\hat{p}=0.52[/tex]
Standard error = 0.024
Critical value for 99% confidence interval :[tex]z_{\alpha/2}=2.576[/tex]
Confidence interval is given by :-
[tex]\hat{p}\pm z_{\alpha/2}\times(S.E.)[/tex]
Then, the 99% confidence interval will be :-
[tex]0.52\pm (2.576)\times(0.024)\\\\=0.52\pm0.061824\\\\=(0.52-0.061824,\ 0.52+0.061824)\\\= (0.458176,\ 0.581824)[/tex]
Hence, a 99% confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter : [tex](0.458176,\ 0.581824)[/tex]
Interpretation : We are 99% sure that the true population mean falls in interval [tex](0.458176,\ 0.581824)[/tex].
