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

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.

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