Asurvey 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.

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:


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: