# Confidence interval to test proportion of US households with a dog

A humane society claims that less than 35% of U.S. households own a dog. In a random sample of 400 U.S. households, 156 say they own a dog.

(5) Describe the population of interest and calculate the numerical value of the statistic p Ì? that that we will use to estimate the population proportion p.

(5) Construct a 95% confidence interval for the proportion of U.S. households with a dog.

(4) Construct a 99% confidence interval for the proportion of U.S. households with a dog.

(6) Describe the relationship between the confidence level and the size of the confidence interval. Explain why this relationship holds.

© BrainMass Inc. brainmass.com April 1, 2020, 8:06 pm ad1c9bdddfhttps://brainmass.com/statistics/confidence-interval/confidence-interval-test-proportion-usa-households-dog-448006

#### Solution Preview

Problem: A humane society claims that less than 35% of U.S. households own a dog. In a random sample of 400 U.S. households, 156 say they own a dog.

a) Describe the population of interest and calculate the numerical value of the statistic p ̂ that that we will use to estimate the population proportion p.

b) Construct a 95% confidence interval for the proportion of U.S. households with a dog.

c) Construct a 99% confidence ...

#### Solution Summary

The expert examines confidence interval to test proportions of US households with a dog.