180k views
2 votes
In a recent poll, 400 people were asked if they liked dogs, and 66% said they did. Find the margin of error of this poll, at the 90% confidence level. Give your answer to three decimals

User Jeisson
by
6.8k points

1 Answer

2 votes

Given:

sample size = 400

proportion for success p = 66% or 0.66

confidence level = 90%

Find: margin of error

Formula:

To find the margin of error of a single proportion, the formula is:


MOE=z*\sqrt{(p(1-p))/(n)}

where:

z = critical value based on the given confidence level

p = proportion of success in a decimal number

n = sample size

Assuming a two-tailed test, the critical value for a 90% confidence level is 1.645. Hence, our z = 1.645.

Let's replace the variables in the formula with their corresponding numerical values based on the given information listed above.


MOE=1.645*\sqrt{(0.66(1-0.66))/(400)}

Then, solve for MOE. Here are the steps based on the formula.

1. Multiply 0.66 and the difference of 1 and 0.66.


0.66*0.34=0.2244

2. Divide the result by 400.


0.2244/400=0.000561

3. Get the square root of the result in step 2.


√(0.000561)=0.023685

4. Multiply the result in step 3 by the critical value z.


0.023685*1.645=0.03896\approx0.039

Answer:

At a 90% confidence level, the margin of error of this poll is approximately 0.039.

User Automorphic
by
6.6k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.