Question

A survey was conducted that asked 1002 people how many books they had read in the past year. results indicated that x overbar equals 11.3 books and sequals16.6 books. construct a 90​% confidence interval for the mean number of books people read. interpret the interval.

Answer 1

The confidence interval would be (10.44, 12.16).  This means that if we take repeated samples, the true mean lies in 90% of these intervals.

To find the confidence interval, we use:
$\overline{x} \pm z*(\frac{\sigma}{\sqrt{n}})$

We first find the z-value associated with this.  To do this:
Convert 90% to a decimal:  90% = 90/100 = 0.9
Subtract from 1:  1-0.9 = 0.1
Divide by 2:  0.1/2 = 0.05
Subtract from 1:  1-0.05 = 0.95

Using a z-table (http://www.z-table.com) we see that this is directly between two z-scores, 1.64 and 1.65; we will use 1.645:

$11.3 \pm 1.645*(\frac{16.6}{\sqrt{1002}}) \\ \\11.3 \pm 0.86 \\(11.3-0.86, 11.3+0.86) \\(10.44, 12.16)$