Respuesta :
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:
[tex]MOE=z\times\sqrt{\frac{p(1-p)}{n}}[/tex]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.
[tex]MOE=1.645\times\sqrt{\frac{0.66(1-0.66)}{400}}[/tex]Then, solve for MOE. Here are the steps based on the formula.
1. Multiply 0.66 and the difference of 1 and 0.66.
[tex]0.66\times0.34=0.2244[/tex]2. Divide the result by 400.
[tex]0.2244\div400=0.000561[/tex]3. Get the square root of the result in step 2.
[tex]\sqrt{0.000561}=0.023685[/tex]4. Multiply the result in step 3 by the critical value z.
[tex]0.023685\times1.645=0.03896\approx0.039[/tex]Answer:
At a 90% confidence level, the margin of error of this poll is approximately 0.039.
