Asurvey was conducted that asked 1003 1003 people how many books they had read in the past year. results indicated that x overbar x equals = 10.5 10.5 books and s equals = 16.6 16.6 books. construct a 99 99% confidence interval for the mean number of books people read. interpret the interval.

The confidence interval is

.  This means that we can be 99% confident that the mean number of books people read lies between 9.15 and 11.85.

To find the confidence interval, we first find the z-score associated with it:

Convert 99% to a decimal:  0.99
Subtract from 1:  1-0.99=0.01
Divide by 2:  0.01/2 = 0.005
Subtract from 1:  1-0.005 = 0.995

Using a z-table (http://www.z-table.com) we see that this is associated with a z-score between 2.57 and 2.58.  Since both are equally far from this value we will use 2.575.

We calculate the margin of error using



This means that the confidence interval is


The lower limit is given by 10.5-1.35 = 9.15.
The upper limit is given by 10.5+1.35 = 11.85

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