Question

What is the minimum sample size needed to estimate a population proportion to within 5% with 98% confidence? Assume that there is no prior knowledge of the true value of the proportion, and enter your answer as a whole number.

Answer 1

Answer: 543

Step-by-step explanation:

When we have no prior knowledge of the true value of the proportion, then the formula to find the minimum sample size is given by :-

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2$

Given : Margin of error : E = 0.05

Significance level : $\alpha=1-0.98=0.02$

By standard normal distribution table , the critical value will be :-

$z_{\alpha/2}=z_{0.01}=2.33$

Then, $n=0.25(\dfrac{2.33}{0.05})^2=542.89\approx543$

Hence, the  minimum sample size needed to estimate a population proportion = 543