Question

In 2001, a Gallup Poll surveyed 1016 households in the U.S. about their pets. Of those surveyed, 599 said they had at least one dog or cat as a pet. Find and interpret the 90% confidence interval (z*=1.645) for the population proportion. Round your answer to 3 decimal places.

Answer 1

Given that,

n = 1016

x = 599

Point estimate = sample proportion = = x / n = 599/1016=0.590

1 -   = 1- 0.590 =0.41

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E Z/2 *(( * (1 - )) / n)

= 1.645 *((0.590*0.41) /1016 )

E = 0.025

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.590- 0.025 < p < 0.590+0.025

0.565< p < 0.615