Since we do not know the population standard deviation, we will use the t-distribution to construct the 90% confidence interval of the mean number of books people read. The value of [tex]t_{\frac{\alpha }{2}}[/tex] with 1010 degrees of freedom and with alpha equals to 0.10 is 1.64
First, we need to solve for the margin of error, E.
[tex]E=t_{\frac{\alpha }{2}}\cdot \frac{s}{\sqrt{n}}=1.64\cdot \frac{16.6}{\sqrt{1011}}=0.86[/tex]
The lower bound of the confidence interval is
[tex]LB=\overline{x}-E=14.8-0.86=13.94[/tex]
The upper bound of the confidence interval is
[tex]LB=\overline{x}+E=14.8+0.86=15.66[/tex]
Therefore, the 90% confidence interval is (13.94, 15.66).
We are 90% confident that the interval from 13.94 books to 15.66 books does contain the true value of the population mean number of books people read.
