Question

Use the given data to find the minimum sample size required to estimate the population proportion. Margin of error: 0.04; confidence level: 85% ; ?̂ and ?̂ unknown.

Answer 1

Solution:
Given in the question
Margin of error = 0.04 or 4%
Confidence level = 0.85
alpha or level of significance() = 1 -Confidence level = 1- 0.85 = 0.15
/2 = 0.15/2 = 0.075
From Z table we found Z/2 = 1.4395
As we know that p^ and q^ is unknown so we will use p^ = 0.5 and q^ = 0.5
Sample size can be calculated as
Sample size (n) = (Z/2 / E)^2 * (p^ * q^) = (1.4395/0.04)^2 *(0.5*0.5) = (2.07216/0.0016) * 0.25 = 323.775 or 324
So minimum sample size required to estimate the population proportion is 324.