Given
n = 1019
[tex]\bar{x}=13.1,s=16.6[/tex]
Find
Construct a 95% confidence interval for the mean number of books people read .
Explanation
first , we need to solve for the margin of error
[tex]\begin{gathered} E=t_{\frac{\alpha}{2}}.\frac{s}{\sqrt{n}} \\ \\ E=1.96\times\frac{16.6}{\sqrt{1019}} \\ \\ E=\frac{32.536}{32.921779399} \\ \\ E=1.02 \end{gathered}[/tex]
Lower bound =
[tex]\bar{x}-E=13.1-1.02=12.08[/tex]
upper bound =
[tex]\bar{x}+E=13.1+1.02=14.12[/tex]
Final Answer
Therefore , the 95% confidence interval is (12.08,14.12)
