In 2001, a gallup poll surveyed 1016 households in the u. s. about their pets. of those surveyed, 590 said the had at least one dog or cat as a pet. construct and interpret a 99% interval for the proportion of households who had at least one dog and one cat.

The confidence interval is 
.  

This means that if we take repeated samples, 99% of the intervals would contain the population proportion.

To construct this interval, we use
, 
where 


Since 590/1016 said they had a cat and a dog, p=0.581 and N=1016:


We need the z-score associated with this confidence level:
Convert 99% to a decimal:  99/100 = 0.99
Subtract from 1:  1-0.95 = 0.01
Divide by 2:  0.01/2 = 0.005
Subtract from 1:  1-0.005 = 0.995

Using a z-table, we see that this value is equally distant from z=2.57 and z=2.58, so we will use z=2.575: